Elements the Game Forum - Free Online Fantasy Card Game

Opponents, Strategy and Decks => False Gods => Topic started by: kev on January 27, 2011, 09:10:54 pm

Title: Drop rates and deck selection
Post by: kev on January 27, 2011, 09:10:54 pm
I got to thinking about what a shame it is that my often used FG grinder, PuppyChow's Unoriginal (http://elementscommunity.org/forum/index.php/topic,1748.0.html), never wins against Divine Glory.  It's a shame because Divine Glory probably has a higher than average drop rate among FGs.  This got me thinking about whether it's possible to calculate drop rates for all the FGs and whether or not it'd have an impact on FG grinder deck selection.

Here's (http://elementscommunity.org/forum/index.php/topic,495.msg6904#msg6904) a post by chriskang detailing drop rates for 11 FGs.  It's so old there's no way of knowing what the FGs looked like at the time or even whether the spin methodology was changed after chris wrote it.  But check it:

Rainbow46.9%19.0%661
Fire Queen43.3%17.2%599
Gemini41.6%16.4%571
Incarnate40.2%15.8%548
Graviton39.3%15.3%533
Seism36.8%14.2%493
Hermes35.1%13.4%467
Chaos Lord34.8%13.3%462
Miracle33.0%12.5%435
Morte32.6%12.3%428
Scorpio31.8%12.0%416
The first percentage is chance of getting 1+ cards (from the chriskang thread), second percentage is chance per spin (I derived), third is how much you'd net from selling the cards you won (assumes rares sell for 1159).

Theoretically one could take the decks of each FG found here (http://elementscommunity.org/forum/index.php/topic,7919.0.html), the spin likelihood calculation found here (http://elementscommunity.org/forum/index.php/topic,1091.msg107605#msg107605), and calculate current numbers for each FG.  I don't have the mad math skillz required and it doesn't look like anyone around anymore does either, but I strongly suspect FGs like Decay (6 pests, 6 fractals, and 6 siphons in 30 cards) might have a higher droprate than any of the old FGs.  Maybe some are worse.  And if beating FG(A) is on average worth 400 electrum more than beating FG(B), I'd want my deck to have a high winrate against FG(A).

This obviously isn't worth building a deck around.  All of the math in this thread is potentially outdated, time to play and normalized winrate are both far greater considerations, and one doesn't really know his winrate against each FG until a large number of games has been played against the current AI for each FG.  Just food for thought.  ;D
Title: Re: Drop rates and deck selection
Post by: Falcon4415 on January 27, 2011, 09:13:08 pm
I think that these stats took the chance of winning a tower in consideration, like those in the wiki.

PS: dibs on calculating current drop rate.
Title: Re: Drop rates and deck selection
Post by: Newbiecake on January 27, 2011, 09:53:25 pm
I happen to be pretty good at math, so here's the formula I derived for the chance of getting 1+ cards: Take the total amount of each TYPE, then -1, followed by dividing that number by the number of cards the FG has. Follow that by calculating the average percentage (to calculate average you add the percentage of every type of cards Divide Glory then divide by x different cards there are).

Example) Divide Glory has 10 Explosions, out of a total of 80 cards. I would take that number, -1, then divide it by 80 to find out the chance of drawing 1+ Explosion. The result is 11.3% of drawing 1+ cards. If I want to calculate the chance of 2+ Explosions, I would -2 then divide by 80. The result is 10%. You get the idea.
Now to calculate the TOTAL percentage of drawing more than +1 of ANY type, I would have to calculate all the chances of drawing more than 1+ card for every type of cards Divide Glory has, with the formula given in the above example. Then I insert those numbers into the formula for calculating average, given in the first paragraph. If I want to calculate the chance of drawing 2+ of ANY type, I would have to calculate all the chances of drawing 2+ cards for every type of cards Divine Glory has, etc.
Title: Re: Drop rates and deck selection
Post by: jmizzle7 on January 27, 2011, 10:20:20 pm
The stats provided by chriskang are far out of date. The algorithm has changed since those were released, iirc.
Title: Re: Drop rates and deck selection
Post by: Falcon4415 on January 27, 2011, 10:29:45 pm
Quote from: kevkev60614 on January 27, 2011, 09:10:54 pm
Decks of each FG found here (http://elementscommunity.org/forum/index.php/topic,7919.0.html)
After a quick investigation, those calculations are all good except for Rainbow's (there was a bug with the recognition of QTs as towers by the algorithm). Only 15 FGs to go :D.

EDIT on jmizzle7's comment: if the algorithm has been changed and nobody has yet made it public, the only chance of this project is empirical testing, and I lack the skills to do that.
Title: Re: Drop rates and deck selection
Post by: teffy on January 27, 2011, 11:34:28 pm
Quote from: jmizzle7 on January 27, 2011, 10:20:20 pm
The stats provided by chriskang are far out of date. The algorithm has changed since those were released, iirc.
How do you know ?.
Title: Re: Drop rates and deck selection
Post by: BluePriest on January 27, 2011, 11:50:02 pm
Quote from: teffy on January 27, 2011, 11:34:28 pm
Quote from: jmizzle7 on January 27, 2011, 10:20:20 pm
The stats provided by chriskang are far out of date. The algorithm has changed since those were released, iirc.
How do you know ?.
better question, what is it?
Title: Re: Drop rates and deck selection
Post by: kev on January 28, 2011, 12:10:52 am
Quote from: jmizzle7 on January 27, 2011, 10:20:20 pm
The stats provided by chriskang are far out of date. The algorithm has changed since those were released, iirc.
In my opening post I linked quotes from zanz, chriskang, and Evil Hamster.  Together they describe an algorithm, and I think it's the "new" algorithm you're referring to.  Am I wrong, mizz?

As I said in the opening post I'm not sure whether chriskang's table above or the change in the algorithm came first because they're all timestamped with the new forum.  Doesn't matter, though.  I just showed the numbers to illustrate the point.  As long as we have the current algorithm we can recreate the numbers.

Quote from: Falcon4415 on January 27, 2011, 10:29:45 pm
After a quick investigation, those calculations are all good except for Rainbow's (there was a bug with the recognition of QTs as towers by the algorithm). Only 15 FGs to go :D.
Errr... out of curiosity did you recreate the algorithm and test the original 11 FGs using the current decklists?
Title: Re: Drop rates and deck selection
Post by: QuantumT on January 28, 2011, 12:39:00 am
Falcon, I will join you on the math side of this little project. I'm going to start by finding the chance of winning depending on each combination of the 5 cards chosen.

EDIT: Well that wasn't too hard. Here are the chances for all the possible combinations of the 5 cards chosen

11111=4%
2111=8.8%
221=13.2%
311=23.2%
32=28%
41=52%
5=100%

So before I do much more, is the formula still the same as to old one? It tries for non pillar cards 5 times before it takes pillars, and that's for the whole set of 5 cards.

Note: Chaos Lord will also be wrong.
Title: Re: Drop rates and deck selection
Post by: Falcon4415 on January 28, 2011, 02:41:23 pm
According to the last algorithm posted by chriskang:
- Cards are chosen ate random.
- If the card chosen is a tower, then you choose again, up to 10 times. Then the tower is kept.
- Only 4 variables are used in the spinning wheel.

However, if that is not the current algorithm, I'll say it again: this has no future unless somebody is able to hack the game and unveil its darkest secrets.

Assuming we are using the correct one:
-Chaos Lord is also wrong, my bad (thanks QuantumT).
-I there is somebody who can actually recreate the algorithm, probably using some matrix knowledge and a little programming language, he can save me the time using raw, hardcore math is going to take me (I'll end up using some Excel-like program, but still). I can't recreate that algorithm because I know 0 about programming language. The best I can do is following it in my head.
Title: Re: Drop rates and deck selection
Post by: BluePriest on January 28, 2011, 04:42:42 pm
heads up, please forgive me for being very newbish on this. I looked at the links, and I got a question. After it determines the 5 cards, is it 5 different cards for each spin, or 5 different cards used for all 3 spins (spins, not slots)? I didnt think it was quite clear on that?

edit

if it checks for towers 10 times before actually deciding to use the tower, is it even worth calculating them into it? If I did my math right then you have a approcimate 99.808138195768508416% chance of not getting a tower in the spin. Seems wrong since i remember getting several towers though Such a neglegible amount, is it even worth calculating? If I did my math right...

edit, I think I completely misunderstood, no time to post why now though...
Title: Re: Drop rates and deck selection
Post by: jmizzle7 on January 28, 2011, 04:43:34 pm
The latest patch possible from chriskang's statistics is v1.14. The drop rate during this patch held more bias regarding the recognition of pillars/towers in spins. Since then, Zanzarino has altered the algorithm so that towers don't drop as much. This makes farming Rainbow less profitable than it once was, but it evens out due to the non-pillar redundancy in other false god decks.

I don't know what the current algorithm is, so I can't give any hard stats. I do know that the drop rates are different than what is shown in the original post.
Title: Re: Drop rates and deck selection
Post by: Chemist on January 28, 2011, 06:47:23 pm
Three things, if I may:

-Do we know whether the slots currently work with four cards or five? They used to select five, then only work with four. I still don't know whether that bug has ever been fixed or not.

-Do we know whether the slots draw cards from one half or the whole of an FG's deck? (I'd assume the former, but I can't really know...)

-The SoD need to be taken into account. 10% chance to replace first card on shortlist of five cards with a shard. Though depending on how the bug with only four cards being used works (if it's still present) this might not actually be 10%...
Title: Re: Drop rates and deck selection
Post by: smuglapse on January 28, 2011, 07:31:24 pm
Maybe this old post will help you some. It doesn't include the recent changes, though (Osiris with Trebuchet).

Re: Cards you'll most likely win from the spin vs FGs (http://elementscommunity.org/forum/index.php/topic,13051.msg177295#msg177295)
Title: Re: Drop rates and deck selection
Post by: QuantumT on January 28, 2011, 07:43:15 pm
From what I recall, towers weren't actually a common thing to win with the exception of quantum towers. This isn't because rainbow has more towers than any other god (Fire queen has more and Hermes has almost the same ratio of fire towers), but because of a weird issue where it didn't try and repick quantum towers.
Title: Re: Drop rates and deck selection
Post by: Falcon4415 on January 28, 2011, 09:21:32 pm
Just realized how blind we are: the algorithm has obviously been changed since that post: who has seen a SoD appear in spins lately? :o
Title: Re: Drop rates and deck selection
Post by: QuantumT on January 28, 2011, 09:26:33 pm
Quote from: Falcon4415 on January 28, 2011, 09:21:32 pm
Just realized how blind we are: the algorithm has obviously been changed since that post: who has seen a SoD appear in spins lately? :o
I had realized that, but it won't make a huge difference really. It only slightly lowers the chances of having multiples in the spins.
Title: Re: Drop rates and deck selection
Post by: Falcon4415 on January 28, 2011, 11:00:25 pm
Quote from: QuantumT on January 28, 2011, 09:26:33 pm
Quote from: Falcon4415 on January 28, 2011, 09:21:32 pm
Just realized how blind we are: the algorithm has obviously been changed since that post: who has seen a SoD appear in spins lately? :o
I had realized that, but it won't make a huge difference really. It only slightly lowers the chances of having multiples in the spins.
My point was that, as we know that the algorithm has been modified since it was ripped open and shared with the community, we can't really be sure of whether there have been more modifications other than that obvious one, especially after what jmizzle7 told us.
Title: Re: Drop rates and deck selection
Post by: Izzythemachine on January 29, 2011, 07:54:02 am
Quote from: Falcon4415 on January 28, 2011, 11:00:25 pm
Quote from: QuantumT on January 28, 2011, 09:26:33 pm
Quote from: Falcon4415 on January 28, 2011, 09:21:32 pm
Just realized how blind we are: the algorithm has obviously been changed since that post: who has seen a SoD appear in spins lately? :o
I had realized that, but it won't make a huge difference really. It only slightly lowers the chances of having multiples in the spins.
My point was that, as we know that the algorithm has been modified since it was ripped open and shared with the community, we can't really be sure of whether there have been more modifications other than that obvious one, especially after what jmizzle7 told us.
I'm currently working on finding the algorithm from the .swf, but it's pretty complicated. Does anyone have the exact formula? I can do the probabilities, but I would like to know for sure the precise formula before I get started.
Title: Re: Drop rates and deck selection
Post by: Dark Weaver on March 02, 2011, 11:54:23 am
hi,
i've done the maths with the latest algorithm, however i wont post the algorithm (unless i'm explicitly authorised to do so).
what you should know:

First table shows the probability to win at least 1 card from the specific FG, either with 1 try|spin (2nd column) or with 3 tries|spins (3rd column).
The other tables shows the probability to win  at least 1 of a specific card from a FG deck with 1 try and 3 tries ; the first data is the probability the card will be choosen for the reel.
Results should be accurate, i did some simulations giving nearly the same results.

DeckName
P(win a card) in 1 spin[%]
P(win a card) in 3 spin[%]
Akebono         20.7480370550.22284357
Chaos Lord      13.0957043834.36677695
Dark Matter     14.0111225136.41907543
Decay           20.5093069749.77165716
Destiny         15.3623720039.36959757
Divine Glory    23.8680492855.87335859
Dream Catcher   12.5282279633.07262768
Elidnis         12.5091986233.02893835
Eternal Phoenix 19.0865937547.02616033
Ferox           14.9428472238.46353803
Fire Queen      18.7044003346.27194528
Gemini          17.1513509543.13352697
Graviton        15.9688443440.66362524
Hecate          18.3636667045.59353983
Hermes          13.2047356134.61349998
Incarnate       16.3101086041.38361745
Jezebel         21.6453292051.89450688
Lionheart       16.7607345242.32538319
Miracle         13.0122701934.17755799
Morte           12.6561178733.36575632
Neptune         15.8239991440.35626022
Obliterator     16.5138913441.81076384
Octane          20.3174592349.40710619
Osiris          20.3445794149.45874692
Paradox         16.0749894140.88819591
Rainbow         12.1929649732.30011393
Scorpio         12.3565474432.67777942
Seism           14.1404337636.70548589
Serket          16.4048649141.58249401

Akebono         
Akebono         
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Tower Shield 
5.87364320
0.56876238
1.69660082
Gravity Tower
0.14806567
0.00937755
0.02813000
Elite Armagio
11.74728639
1.57123995
4.64004391
Massive Dragon
35.24185917
10.83017686
29.09877876
Unstoppable   
5.87364320
0.56876238
1.69660082
Titan         
5.87364320
0.56876238
1.69660082
Chimera       
11.74728639
1.57123995
4.64004391
Overdrive     
23.49457278
5.05971560
14.42407838

Chaos Lord     
Chaos Lord     
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Quantum Tower   
0.00775813
0.00048522
0.00145566
Amethyst Tower   
0.00775813
0.00048522
0.00145566
Maxwell's Demon 
3.02983284
0.24204442
0.72437713
Amethyst Dragon 
3.02983284
0.24204442
0.72437713
Dissipation Field
6.05966568
0.59362062
1.77031122
Werewolf         
6.05966568
0.59362062
1.77031122
Chaos Power     
9.08949852
1.06098663
3.14930855
Supernova       
18.17899704
3.22040398
9.35342177
Improved Mutation
9.08949852
1.06098663
3.14930855
Discord         
3.02983284
0.24204442
0.72437713
Fallen Druid     
12.11933136
1.65040050
4.86993638
Unstoppable     
3.02983284
0.24204442
0.72437713
Explosion       
3.02983284
0.24204442
0.72437713
Congeal         
3.02983284
0.24204442
0.72437713
Ray of Light     
18.17899704
3.22040398
9.35342177
Improved Steal   
3.02983284
0.24204442
0.72437713

Dark Matter     
Dark Matter     
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Relic           
7.14079759
0.74677853
2.22364690
Gravity Tower   
0.02883379
0.00180679
0.00542027
Elite Charger   
14.28159517
2.14913188
6.30982524
Elite Armagio   
3.57039879
0.29656280
0.88705252
Massive Dragon   
3.57039879
0.29656280
0.88705252
Unstoppable     
3.57039879
0.29656280
0.88705252
Elite Otyugh     
7.14079759
0.74677853
2.22364690
Titan           
3.57039879
0.29656280
0.88705252
Gravity Force   
14.28159517
2.14913188
6.30982524
Black Hole       
21.42239276
4.28898622
12.32298634
Gravity Nymph   
0.00000000
0.00000000
0.00000000
Archangel       
14.28159517
2.14913188
6.30982524
Improved Blessing
3.57039879
0.29656280
0.88705252
Morning Glory   
3.57039879
0.29656280
0.88705252

Decay           
Decay           
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Pest         
26.08690304
6.12412415
17.27019402
Improved Dusk
4.34781717
0.38115293
1.13910600
Improved Steal
8.69563435
0.99346292
2.95087776
Eclipse       
4.34781717
0.38115293
1.13910600
Siphon Life   
26.08690304
6.12412415
17.27019402
Aether Tower 
0.00020502
0.00001281
0.00003844
Electrocutor 
4.34781717
0.38115293
1.13910600
Fractal       
26.08690304
6.12412415
17.27019402

Destiny         
Destiny         
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Amethyst Tower   
0.02517490
0.00157700
0.00473091
Maxwell's Demon   
6.89374709
0.71046591
2.11629073
Chaos Power       
17.23436773
2.93986770
8.56285931
Supernova         
17.23436773
2.93986770
8.56285931
Fallen Druid     
6.89374709
0.71046591
2.11629073
Time Tower       
0.01549224
0.00096962
0.00290882
Fate Egg         
20.68124128
4.03017929
11.60981347
Rewind           
13.78749419
2.02928775
5.96515865
Electrum Hourglass
10.34062064
1.28922523
3.81802691
Eternity         
6.89374709
0.71046591
2.11629073

Divine Glory   
Divine Glory   
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Burning Tower   
0.01268699
0.00079384
0.00238151
Explosion       
29.97970082
7.93982874
21.97831319
Light Tower     
0.05497696
0.00345307
0.01035884
Morning Glory   
29.97970082
7.93982874
21.97831319
Improved Miracle
14.98985041
2.32708425
6.82005330
Animate Weapon 
24.98308401
5.65706064
16.02921578

Dream Catcher   
Dream Catcher   
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Relic           
3.12499981
0.25138853
0.75227130
Amethyst Tower   
0.00000610
0.00000038
0.00000114
Micro Abomination
18.74999886
3.39660609
9.84762892
Supernova       
18.74999886
3.39660609
9.84762892
Discord         
6.24999962
0.61950678
1.84703047
Butterfly Effect
9.37499943
1.11122121
3.29675647
Purple Nymph     
0.00000000
0.00000000
0.00000000
Black Hole       
3.12499981
0.25138853
0.75227130
Protect Artifact
3.12499981
0.25138853
0.75227130
Quicksand       
3.12499981
0.25138853
0.75227130
Rage Elixir     
3.12499981
0.25138853
0.75227130
Physalia         
3.12499981
0.25138853
0.75227130
Congeal         
3.12499981
0.25138853
0.75227130
Shockwave       
6.24999962
0.61950678
1.84703047
Elite Deja Vu   
3.12499981
0.25138853
0.75227130
Fate Egg         
3.12499981
0.25138853
0.75227130
Pest             
6.24999962
0.61950678
1.84703047
Thunderbolt     
3.12499981
0.25138853
0.75227130
Quintessence     
3.12499981
0.25138853
0.75227130

Elidnis         
Elidnis         
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Forest Spectre   
15.38427854
2.42936093
7.11246270
Improved Heal     
5.12809285
0.47348539
1.41374113
Jade shield       
2.56404642
0.19786566
0.59242324
Jade Staff       
2.56404642
0.19786566
0.59242324
Ferald Bond       
12.82023211
1.80479694
5.31725994
Water Tower       
0.00128795
0.00008051
0.00024152
Abyss Crawler     
7.69213927
0.83065197
2.47131376
Congeal           
12.82023211
1.80479694
5.31725994
Puffer Fish       
7.69213927
0.83065197
2.47131376
Ulitharid         
7.69213927
0.83065197
2.47131376
Aether Tower     
0.00090157
0.00005635
0.00016906
Twin Universe     
12.82023211
1.80479694
5.31725994
Elite Phase Dragon
7.69213927
0.83065197
2.47131376
Quintessence     
5.12809285
0.47348539
1.41374113


Eternal Phoenix
Eternal Phoenix
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Burning Tower
0.01197962
0.00074953
0.00224858
Ruby Dragon 
10.52505478
1.32465774
3.92156411
Fire Lance   
10.52505478
1.32465774
3.92156411
Explosion   
21.05010955
4.15788885
11.96221354
Fire Storm   
5.26252739
0.49015311
1.46326361
Minor Phoenix
31.57516433
8.76202796
24.05015870
Thunderbolt 
5.26252739
0.49015311
1.46326361
Fractal     
15.78758217
2.53630571
7.41756329

Ferox           
Ferox           
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Emerald Tower   
0.00508053
0.00031768
0.00095303
Jade Dragon     
11.76410817
1.57477755
4.65032545
Giant Frog     
11.76410817
1.57477755
4.65032545
Leaf Dragon     
17.64616226
3.06049174
8.90334357
Elite Cockatrice
11.76410817
1.57477755
4.65032545
Jade shield     
2.94102704
0.23342237
0.69863381
Jade Staff     
2.94102704
0.23342237
0.69863381
Ferald Bond     
17.64616226
3.06049174
8.90334357
Epinephrine     
5.88205409
0.56987693
1.69990650
Ray of Light   
17.64616226
3.06049174
8.90334357

Fire Queen     
Fire Queen     
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Emerald Tower
0.23136628
0.01476196
0.04427936
Ferald Bond   
25.98510506
6.08018143
17.15396370
Fire Lance   
12.99255253
1.84381664
5.43008696
Fahrenheit   
8.66170169
0.98774159
2.93405213
Wind Tower   
0.15906431
0.01008399
0.03024892
Animate Weapon
12.99255253
1.84381664
5.43008696
Elite Queen   
25.98510506
6.08018143
17.15396370
Eagle's Eye   
12.99255253
1.84381664
5.43008696

Gemini         
Gemini         
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Gravity Tower     
0.01346689
0.00084270
0.00252808
Massive Dragon   
11.53354094
1.52663154
4.51033231
Unstoppable       
15.37805459
2.42772930
7.10780268
Aether Tower     
0.02917827
0.00182843
0.00548519
Twin Universe     
23.06708189
4.89496673
13.97780790
Elite Immortal   
3.84451365
0.32555207
0.97348014
Phase Shield     
15.37805459
2.42772930
7.10780268
Electrocutor     
3.84451365
0.32555207
0.97348014
Elite Phase Dragon
3.84451365
0.32555207
0.97348014
Phase Recluse     
23.06708189
4.89496673
13.97780790

Graviton       
Graviton       
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Gravity Tower     
0.02621440
0.00164227
0.00492672
Elite Charger     
9.52131291
1.13738712
3.37349902
Elite Armagio     
4.76065646
0.42907124
1.28169855
Gravity Shield     
4.76065646
0.42907124
1.28169855
Unstoppable       
14.28196937
2.14922398
6.31008978
Elite Otyugh       
14.28196937
2.14922398
6.31008978
Titan             
4.76065646
0.42907124
1.28169855
Gravity Force     
4.76065646
0.42907124
1.28169855
Graviton Firemaster
28.56393874
7.24862368
20.20768081
Explosion         
9.52131291
1.13738712
3.37349902
Fire Storm         
4.76065646
0.42907124
1.28169855

Hecate         
Hecate         
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Rage Elixir   
26.08639444
6.12390417
17.26961242
Obsidian Tower
0.00215464
0.00013469
0.00040407
Improved Dusk
4.34773241
0.38114330
1.13907734
Improved Steal
8.69546481
0.99343430
2.95079359
Eclipse       
8.69546481
0.99343430
2.95079359
Vampire Dagger
4.34773241
0.38114330
1.13907734
Liquid Shadow
17.39092963
2.98542516
8.69155341
Voodoo Doll   
26.08639444
6.12390417
17.26961242
Nightmare     
4.34773241
0.38114330
1.13907734

Hermes         
Hermes         
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Heavy Armor     
7.89419265
0.86237557
2.56488009
Protect Artifact
5.26279510
0.49018653
1.46336287
Burning Tower   
0.00689315
0.00043109
0.00129326
Brimstone Eater
10.52559019
1.32476127
3.92186654
Ruby Dragon     
2.63139755
0.20409454
0.61103483
Fire Spectre   
10.52559019
1.32476127
3.92186654
Fire Lance     
15.78838529
2.53652107
7.41817702
Fire Buckler   
2.63139755
0.20409454
0.61103483
Explosion       
15.78838529
2.53652107
7.41817702
Fahrenheit     
2.63139755
0.20409454
0.61103483
Fire Storm     
5.26279510
0.49018653
1.46336287
Lava Destroyer 
15.78838529
2.53652107
7.41817702
Rage Elixir     
5.26279510
0.49018653
1.46336287

Incarnate       
Incarnate       
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Retrovirus   
14.28462157
2.14987678
6.31196491
Graveyard     
17.85577696
3.12288298
9.07912254
Bone Wall     
14.28462157
2.14987678
6.31196491
Obsidian Tower
0.00764901
0.00047839
0.00143517
Bloodsucker   
14.28462157
2.14987678
6.31196491
Eclipse       
14.28462157
2.14987678
6.31196491
Vampire Dagger
3.57115539
0.29664157
0.88728742
Vampire       
21.42693235
4.29059853
12.32741719

Jezebel         
Jezebel         
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Quantum Tower   
0.11488971
0.00725491
0.02176316
Water Tower     
0.08042279
0.00506283
0.01518771
Permafrost Shield
5.87086397
0.56839429
1.69550908
Nymph's Tears   
35.22518382
10.82019609
29.07496818
Improved Steal   
23.48345588
5.05539311
14.41238942
Vampire Dagger   
5.87086397
0.56839429
1.69550908
Siphon Life     
11.74172794
1.57007188
4.63664891
Cloak           
17.61259191
3.05056180
8.87534642

Lionheart (Eternal Crusader)
Lionheart
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Quantum Tower     
0.01943615
0.00121688
0.00365061
Light Tower       
0.03239358
0.00203050
0.00609138
Crusader         
23.78021534
5.17148130
14.72594805
Animate Weapon   
4.75604307
0.42852419
1.28007145
Time Tower       
0.05182972
0.00325447
0.00976310
Turtle Shield     
9.51208613
1.13572859
3.36863589
Electrum Hourglass
23.78021534
5.17148130
14.72594805
Elite Anubis     
14.26812920
2.14581903
6.30030895
Eternity         
9.51208613
1.13572859
3.36863589
Pharaoh           
4.75604307
0.42852419
1.28007145
Quintessence     
9.51208613
1.13572859
3.36863589
Aether Pendulum   
0.01943615
0.00121688
0.00365061

Miracle         
Miracle         
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Emerald Tower   
0.01688881
0.00105716
0.00317143
Jade Dragon     
4.75848679
0.42881393
1.28093323
Leaf Dragon     
9.51697358
1.13660698
3.37121150
Jade shield     
4.75848679
0.42881393
1.28093323
Jade Staff       
4.75848679
0.42881393
1.28093323
Light Tower     
0.03799982
0.00238311
0.00714917
Light Dragon     
14.27546037
2.14762229
6.30548897
Elite Pegasus   
9.51697358
1.13660698
3.37121150
Solar Buckler   
4.75848679
0.42881393
1.28093323
Improved Blessing
14.27546037
2.14762229
6.30548897
Morning Glory   
4.75848679
0.42881393
1.28093323
Improved Miracle
14.27546037
2.14762229
6.30548897
Wind Tower       
0.01688881
0.00105716
0.00317143
Elite Queen     
14.27546037
2.14762229
6.30548897

Morte           
Morte           
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Bone Tower     
0.00116503
0.00007282
0.00021847
Ivory Dragon   
5.26309658
0.49022416
1.46347466
Retrovirus     
15.78928973
2.53676361
7.41886820
Flesh Recluse   
2.63154829
0.20410854
0.61107666
Condor         
7.89464487
0.86244717
2.56509120
Graveyard       
7.89464487
0.86244717
2.56509120
Deadly Poison   
13.15774144
1.88161659
5.53930151
Improved Plague
7.89464487
0.86244717
2.56509120
Arsenic         
5.26309658
0.49022416
1.46347466
Bone Wall       
7.89464487
0.86244717
2.56509120
Ray of Light   
15.78928973
2.53676361
7.41886820
Archangel       
7.89464487
0.86244717
2.56509120
Improved Miracle
2.63154829
0.20410854
0.61107666

Neptune         
Neptune         
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Water Tower     
0.00397023
0.00024823
0.00074468
Abyss Crawler   
15.99936476
2.59342766
7.58025128
Congeal         
3.99984119
0.34238264
1.02363516
Permafrost Shield
7.99968238
0.87914928
2.61432868
Arctic Octopus   
15.99936476
2.59342766
7.58025128
Poseidon         
3.99984119
0.34238264
1.02363516
Arctic Dragon   
7.99968238
0.87914928
2.61432868
Inundation       
15.99936476
2.59342766
7.58025128
Eagle's Eye     
3.99984119
0.34238264
1.02363516
Shockwave       
23.99904714
5.25802144
14.95919737

Obliterator     
Obliterator     
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Unstoppable     
14.80803707
2.28070621
6.68725634
Gravity Force   
18.51004633
3.32194857
9.63845132
Stone Tower     
0.04574980
0.00287114
0.00861317
Basalt Dragon   
18.51004633
3.32194857
9.63845132
Diamond Shield 
7.40401853
0.78633146
2.34049349
Pulverizer     
7.40401853
0.78633146
2.34049349
Elite Shrieker 
22.21205560
4.57444826
13.10514977
Protect Artifact
11.10602780
1.43930567
4.25606716

Octane         
Octane         
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Fire Lance   
9.99853350
1.22472688
3.62936566
Fire Buckler 
4.99926675
0.45772337
1.36689437
Explosion     
9.99853350
1.22472688
3.62936566
Wind Tower   
0.01466498
0.00091777
0.00275329
Animate Weapon
19.99706700
3.79902485
10.96957982
Eagle's Eye   
24.99633376
5.66254456
16.04385797
Unstable Gas 
29.99560051
7.94779493
21.99856565

Osiris         
Osiris         
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Unstoppable 
12.47558594
1.72801437
5.09497809
Trebuchet   
12.47558594
1.72801437
5.09497809
Time Tower   
0.19531250
0.01242189
0.03726103
Turtle Shield
6.23779297
0.61783289
1.84207072
Rewind       
12.47558594
1.72801437
5.09497809
Eternity     
6.23779297
0.61783289
1.84207072
Precognition
12.47558594
1.72801437
5.09497809
Pharaoh     
37.42675781
12.18443428
32.28038032

Paradox         
Paradox         
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Ray of Light     
19.99998976
3.79999660
10.97227775
Improved Blessing
19.99998976
3.79999660
10.97227775
Mirror Shield     
4.99999744
0.45781219
1.36715840
Morning Glory     
4.99999744
0.45781219
1.36715840
Improved Miracle 
7.49999616
0.80097597
2.38373243
Elite Deja Vu     
19.99998976
3.79999660
10.97227775
Electrum Hourglass
9.99999488
1.22499905
3.63016229
Aether Tower     
0.00005120
0.00000320
0.00000960
Twin Universe     
12.49999360
1.73339703
5.11057195

Rainbow         
Rainbow         
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Quantum Tower     
0.02621440
0.00164227
0.00492672
Werewolf         
11.10819840
1.43974269
4.25734073
Gravity Force     
8.33114880
0.93280135
2.77238167
Elite Graboid     
11.10819840
1.43974269
4.25734073
Forest Spectre   
11.10819840
1.43974269
4.25734073
Explosion         
11.10819840
1.43974269
4.25734073
Congeal           
8.33114880
0.93280135
2.77238167
Improved Miracle 
5.55409920
0.52707629
1.57290922
Eagle's Eye       
5.55409920
0.52707629
1.57290922
Electrum Hourglass
13.88524800
2.05271903
6.03261238
Improved Steal   
8.33114880
0.93280135
2.77238167
Thunderbolt       
5.55409920
0.52707629
1.57290922

Scorpio         
Scorpio         
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Deadly Poison   
15.14843277
2.36793102
6.93690785
Arsenic         
3.02968655
0.24203014
0.72433449
Water Tower     
0.01743745
0.00109155
0.00327462
Physalia         
9.08905966
1.06091025
3.14908424
Abyss Crawler   
9.08905966
1.06091025
3.14908424
Congeal         
9.08905966
1.06091025
3.14908424
Ice Lance       
3.02968655
0.24203014
0.72433449
Permafrost Shield
6.05937311
0.59358118
1.77019430
Purify           
3.02968655
0.24203014
0.72433449
Arctic Octopus   
6.05937311
0.59358118
1.77019430
Poseidon         
3.02968655
0.24203014
0.72433449
Arctic Dragon   
3.02968655
0.24203014
0.72433449
Puffer Fish     
18.17811933
3.22013699
9.35267156
Ulitharid       
6.05937311
0.59358118
1.77019430
Aether Tower     
0.00290624
0.00018169
0.00054506
Twin Universe   
6.05937311
0.59358118
1.77019430

Seism           
Seism           
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Stone Tower     
0.00745177
0.00046605
0.00139814
Elite Antlion   
3.33308494
0.27219707
0.81437050
Steel Golem     
6.66616988
0.67770699
2.01937349
Basalt Dragon   
6.66616988
0.67770699
2.01937349
Diamond Shield 
3.33308494
0.27219707
0.81437050
Gnome Gemfinder
9.99925482
1.22486121
3.62975886
Pulverizer     
3.33308494
0.27219707
0.81437050
Elite Graboid   
19.99850965
3.79950447
10.97091145
Protect Artifact
6.66616988
0.67770699
2.01937349
Quicksand       
19.99850965
3.79950447
10.97091145
Granite skin   
3.33308494
0.27219707
0.81437050
Rewind         
13.33233976
1.92199122
5.65586216
Silurian Dragon
3.33308494
0.27219707
0.81437050

Serket         
Serket         
P(choose card)[%]
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Relic       
7.99882680
0.87901265
2.61392597
Bone Tower   
0.00684366
0.00042799
0.00128397
Flesh Recluse
19.99706700
3.79902485
10.96957982
Arsenic     
7.99882680
0.87901265
2.61392597
Deathstalker
19.99706700
3.79902485
10.96957982
Emerald Tower
0.00782132
0.00048918
0.00146752
Scorpion     
19.99706700
3.79902485
10.96957982
Life Nymph   
0.00000000
0.00000000
0.00000000
Eclipse     
11.99824020
1.62442395
4.79453791
Cloak       
11.99824020
1.62442395
4.79453791

Title: Re: Drop rates and deck selection
Post by: kev on March 02, 2011, 03:03:14 pm
Wow.  Thanks, Dark Weaver.  That's an amazing body of work.

I'd love to hear a little more about the methodology.  jmizzle says above that only zanz knows the current algorithm, and afaik you aren't zanz.  :) You mention using four cards in the spins but some previous sources point to five.  And you didn't mention the number of repicks to find a non-pillar card.

I have to ask, essentially because it's your first forum post and the complex math might as well be witchcraft to me.  Thanks again.  Even as an approximation this is tremendously useful information.  +karma  :D
Title: Re: Drop rates and deck selection
Post by: Falcon4415 on March 02, 2011, 03:46:14 pm
That is certainly one of the most epic first posts I have ever seen. I'm guessing he used the same method Chriskang used eons ago (i.e. dwelving into the depths of the game's code, getting the algorithm, calculating and then testing the results). If this is right, the algorithm has been changed a little, because these results aren't the same Chriskang got.
If I were to say how many repicks towers get, I' say it's still or around 10, as my calculations placed 0.01% as the chance of winning a tower from a half-tower deck, which are close to those of FGs (some more than others).

Oh, I went ahead and calculated the mean chanced of winning a card, yielding an impressive 41.25% (the last time we heard about this from Zanz, he talked about a mean chance around 33%).
Title: Re: Drop rates and deck selection
Post by: teffy on March 02, 2011, 04:22:21 pm
I´m always careful with this kind of "epic post". There are many people in this forum, who talk about probabilities and make beginner mistakes like not using the right distributions , independence mistakes, adding probabilities, although you are not allowed to do this.

Did you use the algorithm of the Slot Wheel Mystery (http://elementscommunity.org/forum/index.php/topic,590.0.html), but with 4, not 5 cards ?
Title: Re: Drop rates and deck selection
Post by: BluePriest on March 02, 2011, 05:17:34 pm
Quote from: teffy on March 02, 2011, 04:22:21 pm
I´m always careful with this kind of "epic post". There are many people in this forum, who talk about probabilities and make beginner mistakes like not using the right distributions , independence mistakes, adding probabilities, although you are not allowed to do this.

Did you use the algorithm of the Slot Wheel Mystery (http://elementscommunity.org/forum/index.php/topic,590.0.html), but with 4, not 5 cards ?
I have a feeling he grabbed the swf, decompiled, and looked through the code.
Title: Re: Drop rates and deck selection
Post by: Izzythemachine on March 02, 2011, 05:26:21 pm
This is so EPIC!! Thanks for the good work. I tried to figure this out a few months back, but was only able to decompile and view the code. I couldn't decipher what the algorithm was (I couldn't even find it lol). Thanks again.

+Karma :)
Title: Re: Drop rates and deck selection
Post by: kev on March 02, 2011, 06:50:58 pm
Using the elements card tracking spreadsheet found here  (http://elementscommunity.org/forum/index.php/topic,13271.0.html) and the drop rates fore each card Dark Weaver came up with here (http://elementscommunity.org/forum/index.php/topic,20376.msg300757#msg300757), the following table shows expected sale value of cards received from a win.

Divine Glory873
Osiris763
Jezebel756
Octane731
Akebono727
Decay715
Eternal Phoenix664
Fire Queen663
Hecate640
Gemini599
Lionheart590
Obliterator579
Serket570
Incarnate569
Neptune564
Paradox564
Graviton557
Destiny537
Ferox521
Seism493
Dark Matter487
Miracle467
Hermes460
Chaos Lord456
Morte443
Dream Catcher437
Elidnis436
Scorpio434
Rainbow428
Title: Re: Drop rates and deck selection
Post by: BluePriest on March 02, 2011, 07:14:11 pm
Let me see if Im understanding how you did this.


You took the chance to win each card and multiplied that by the cards sell value. Then you averaged those together, and got the avg sell value of the card?

Edit:I gotta add this to my spreadsheet...

Double Edit
1 thing NOT being calculated is the value of the double spin (5:electrum) although, that would be too much work probably
Title: Re: Drop rates and deck selection
Post by: Dark Weaver on March 02, 2011, 08:01:41 pm
Quote from: Falcon4415 on March 02, 2011, 03:46:14 pm
I'm guessing he used the same method Chriskang used eons ago (i.e. dwelving into the depths of the game's code, getting the algorithm, calculating and then testing the results).
that's what i did, but i could have misunderstood the algorithm. I've never programmed in flash and i dont even know how to start, i also dont know how a flash program works :p
Still i think what i've done is accurate.

Quote from: kevkev60614 on March 02, 2011, 03:03:14 pm
I'd love to hear a little more about the methodology.  jmizzle says above that only zanz knows the current algorithm, and afaik you aren't zanz.  :) You mention using four cards in the spins but some previous sources point to five.  And you didn't mention the number of repicks to find a non-pillar card.
I'm not zanz indeed :), and that's why didn't post the algorithm, maybe he will keep that secret. But i think its interesting to see what the real chances are to win when fighting FG, especially when you're a newb to the game and have a hard try to win vs FG for no rewards :p

The general methodology is not so complex (due to the fact that afaik there is no 10% chance to turn the first card into a shard). Here is what i did:
The probability to win a card from a FG in 1 spin is equal to the sum of the probabilities to win a specific card in 1 spin. P[win a card in 1 spin] = SUM(P[win card n° i in 1 spin]) i going from 1 to inf (whe check all cards)
the slot machine has 3 reels, each reel has the same 4 cards on it (and no, its not 5) . To calculate the probability to win a specific card C, you must know how many times that card is on the reel (otherwise said, how many card C are among the 4 cards).
if n° C is 0 : probability to win the card is = 0 (you cant win the card if it is not present on the reel)
if n° C is 1 : probability to win the card is = (1/4)*(1/4)*(1/4) = 1.5625 %
if n° C is 2 : probability to win the card is = (2/4)*(2/4)*(2/4) = 12.5   %
if n° C is 3 : probability to win the card is = (3/4)*(3/4)*(3/4) = 42.18  %
if n° C is 4 : probability to win the card is = 1
Ill call those probabilities P(w0),P(w1),P(w2),P(w3),P(w4)
On the tables i've listed the probability a specific card C will be choosen for the reel, lets call it P(c). This mean that each of the 4 cards has a probability of P(c) to be the card c, and (1-p(c)) to be another card. P(c) depends on the algorithm.P(c) is very low for towers,unless you deck is solely made of towers :p
To have 4 cards C in the reel, the algorithm has to choose 4 times the card C and the probability is given by P(c)*P(c)*P(c)*P(c).
To have 3 cards C in the reel, the algorithm has to choose 3 times the card C and 1 time another card and the probability is given by 4*P(c)*P(c)*P(c)*(1-P(c)). In this case there are 4 possibilities, one where the non C card is choosen first, one where it is choosen 2nd, 3rd, ...
To have 2 cards C in the reel, the probability is given by 6*P(c)*P(c)*(1-P(c))*(1-P(c)). There are 6 possibilities (6 is the number of ways to choose 2 objects among 4).
To have 1 cards C in the reel, the probability is given by 4*P(c)*(1-P(c))*(1-P(c))*(1-P(c)).
I'll call those probabilities P(c1) P(c2) P(c3) P(c4)
So the  probability to win card C is given by:
P(w0)*P(c0) + P(w1)*P(c1) +P(w2)*P(c2) +P(w3)*P(c3) +P(w4)*P(c4)
= 0 + (1/4)^3 * 4 * P(c) * (1-P(c))^3 + (2/4)^3 * 6 * P(c)^2 * (1-P(c))^2 + (3/4)^3 * 4 * P(c)^3 * (1-P(c)) + P(c)^4

Quote from: teffy on March 02, 2011, 04:22:21 pm
I´m always careful with this kind of "epic post". There are many people in this forum, who talk about probabilities and make beginner mistakes like not using the right distributions , independence mistakes, adding probabilities, although you are not allowed to do this.

Did you use the algorithm of the Slot Wheel Mystery (http://elementscommunity.org/forum/index.php/topic,590.0.html), but with 4, not 5 cards ?
I dont say i did any mistakes, but i've verified the calculus methodology with a simulation(the two being base on my understanding of the algorithm). And the hard part was to find the slot machine mechanism, this is basic probabilities, but i'm aware its very easy to do mistakes.
And the algorithm mentionned in the first page is outdated.



Title: Re: Drop rates and deck selection
Post by: primarycolors on March 04, 2011, 07:11:59 pm
Quote from: Dark Weaver on March 02, 2011, 11:54:23 am
hi,
i've done the maths with the latest algorithm, however i wont post the algorithm (unless i'm explicitly authorised to do so).
what you should know:
    The slot machine works with 3 reels, each reel is composed of 4 cards (not necessarily different), reels are the same.Each try uses a different set of 4 cards.You wont get upgraded cards unless you play against the FG or the Half Blood.There are cards you cannot win, you'll get a relic instead.Quantum tower is fixed (its considered a tower/pillar).I've seen nowhere a 10% thing related to shards.(would have done the calculus more interesting :) )

First table shows the probability to win at least 1 card from the specific FG, either with 1 try|spin (2nd column) or with 3 tries|spins (3rd column).
The other tables shows the probability to win  at least 1 of a specific card from a FG deck with 1 try and 3 tries ; the first data is the probability the card will be choosen for the reel.
Results should be accurate, i did some simulations giving nearly the same results.

DeckNameP(win a card) in 1 spin[%]P(win a card) in 3 spin[%]
Akebono         20.7480370550.22284357
Chaos Lord      13.0957043834.36677695
Dark Matter     14.0111225136.41907543
Decay           20.5093069749.77165716
Destiny         15.3623720039.36959757
Divine Glory    23.8680492855.87335859
Dream Catcher   12.5282279633.07262768
Elidnis         12.5091986233.02893835
Eternal Crusader16.7607345242.32538319
Eternal Phoenix 19.0865937547.02616033
Ferox           14.9428472238.46353803
Fire Queen      18.7044003346.27194528
Gemini          17.1513509543.13352697
Graviton        15.9688443440.66362524
Hecate          18.3636667045.59353983
Hermes          13.2047356134.61349998
Incarnate       16.3101086041.38361745
Jezebel         21.6453292051.89450688
Miracle         13.0122701934.17755799
Morte           12.6561178733.36575632
Neptune         15.8239991440.35626022
Obliterator     16.5138913441.81076384
Octane          20.3174592349.40710619
Osiris          20.3445794149.45874692
Paradox         16.0749894140.88819591
Rainbow         12.1929649732.30011393
Scorpio         12.3565474432.67777942
Seism           14.1404337636.70548589
Serket          16.4048649141.58249401

Akebono         
Akebono         P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Tower Shield  5.873643200.568762381.69660082
Gravity Tower 0.148065670.009377550.02813000
Elite Armagio 11.747286391.571239954.64004391
Massive Dragon35.2418591710.8301768629.09877876
Unstoppable   5.873643200.568762381.69660082
Titan         5.873643200.568762381.69660082
Chimera       11.747286391.571239954.64004391
Overdrive     23.494572785.0597156014.42407838

Chaos Lord     
Chaos Lord      P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Quantum Tower    0.007758130.000485220.00145566
Amethyst Tower   0.007758130.000485220.00145566
Maxwell's Demon  3.029832840.242044420.72437713
Amethyst Dragon  3.029832840.242044420.72437713
Dissipation Field6.059665680.593620621.77031122
Werewolf         6.059665680.593620621.77031122
Chaos Power      9.089498521.060986633.14930855
Supernova        18.178997043.220403989.35342177
Improved Mutation9.089498521.060986633.14930855
Discord          3.029832840.242044420.72437713
Fallen Druid     12.119331361.650400504.86993638
Unstoppable      3.029832840.242044420.72437713
Explosion        3.029832840.242044420.72437713
Congeal          3.029832840.242044420.72437713
Ray of Light     18.178997043.220403989.35342177
Improved Steal   3.029832840.242044420.72437713

Dark Matter     
Dark Matter     P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Relic            7.140797590.746778532.22364690
Gravity Tower    0.028833790.001806790.00542027
Elite Charger    14.281595172.149131886.30982524
Elite Armagio    3.570398790.296562800.88705252
Massive Dragon   3.570398790.296562800.88705252
Unstoppable      3.570398790.296562800.88705252
Elite Otyugh     7.140797590.746778532.22364690
Titan            3.570398790.296562800.88705252
Gravity Force    14.281595172.149131886.30982524
Black Hole       21.422392764.2889862212.32298634
Gravity Nymph    0.000000000.000000000.00000000
Archangel        14.281595172.149131886.30982524
Improved Blessing3.570398790.296562800.88705252
Morning Glory    3.570398790.296562800.88705252

Decay           
Decay           P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Pest          26.086903046.1241241517.27019402
Improved Dusk 4.347817170.381152931.13910600
Improved Steal8.695634350.993462922.95087776
Eclipse       4.347817170.381152931.13910600
Siphon Life   26.086903046.1241241517.27019402
Aether Tower  0.000205020.000012810.00003844
Electrocutor  4.347817170.381152931.13910600
Fractal       26.086903046.1241241517.27019402

Destiny         
Destiny         P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Amethyst Tower    0.025174900.001577000.00473091
Maxwell's Demon   6.893747090.710465912.11629073
Chaos Power       17.234367732.939867708.56285931
Supernova         17.234367732.939867708.56285931
Fallen Druid      6.893747090.710465912.11629073
Time Tower        0.015492240.000969620.00290882
Fate Egg          20.681241284.0301792911.60981347
Rewind            13.787494192.029287755.96515865
Electrum Hourglass10.340620641.289225233.81802691
Eternity          6.893747090.710465912.11629073

Divine Glory   
Divine Glory    P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Burning Tower   0.012686990.000793840.00238151
Explosion       29.979700827.9398287421.97831319
Light Tower     0.054976960.003453070.01035884
Morning Glory   29.979700827.9398287421.97831319
Improved Miracle14.989850412.327084256.82005330
Animate Weapon  24.983084015.6570606416.02921578

Dream Catcher   
Dream Catcher   P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Relic            3.124999810.251388530.75227130
Amethyst Tower   0.000006100.000000380.00000114
Micro Abomination18.749998863.396606099.84762892
Supernova        18.749998863.396606099.84762892
Discord          6.249999620.619506781.84703047
Butterfly Effect 9.374999431.111221213.29675647
Purple Nymph     0.000000000.000000000.00000000
Black Hole       3.124999810.251388530.75227130
Protect Artifact 3.124999810.251388530.75227130
Quicksand        3.124999810.251388530.75227130
Rage Elixir      3.124999810.251388530.75227130
Physalia         3.124999810.251388530.75227130
Congeal          3.124999810.251388530.75227130
Shockwave        6.249999620.619506781.84703047
Elite Deja Vu    3.124999810.251388530.75227130
Fate Egg         3.124999810.251388530.75227130
Pest             6.249999620.619506781.84703047
Thunderbolt      3.124999810.251388530.75227130
Quintessence     3.124999810.251388530.75227130

Elidnis         
Elidnis         P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Forest Spectre    15.384278542.429360937.11246270
Improved Heal     5.128092850.473485391.41374113
Jade shield       2.564046420.197865660.59242324
Jade Staff        2.564046420.197865660.59242324
Ferald Bond       12.820232111.804796945.31725994
Water Tower       0.001287950.000080510.00024152
Abyss Crawler     7.692139270.830651972.47131376
Congeal           12.820232111.804796945.31725994
Puffer Fish       7.692139270.830651972.47131376
Ulitharid         7.692139270.830651972.47131376
Aether Tower      0.000901570.000056350.00016906
Twin Universe     12.820232111.804796945.31725994
Elite Phase Dragon7.692139270.830651972.47131376
Quintessence      5.128092850.473485391.41374113

Eternal Crusader
Eternal CrusaderP(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Quantum Tower     0.019436150.001216880.00365061
Light Tower       0.032393580.002030500.00609138
Crusader          23.780215345.1714813014.72594805
Animate Weapon    4.756043070.428524191.28007145
Time Tower        0.051829720.003254470.00976310
Turtle Shield     9.512086131.135728593.36863589
Electrum Hourglass23.780215345.1714813014.72594805
Elite Anubis      14.268129202.145819036.30030895
Eternity          9.512086131.135728593.36863589
Pharaoh           4.756043070.428524191.28007145
Quintessence      9.512086131.135728593.36863589
Aether Pendulum   0.019436150.001216880.00365061

Eternal Phoenix
Eternal Phoenix P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Burning Tower0.011979620.000749530.00224858
Ruby Dragon  10.525054781.324657743.92156411
Fire Lance   10.525054781.324657743.92156411
Explosion    21.050109554.1578888511.96221354
Fire Storm   5.262527390.490153111.46326361
Minor Phoenix31.575164338.7620279624.05015870
Thunderbolt  5.262527390.490153111.46326361
Fractal      15.787582172.536305717.41756329

Ferox           
Ferox           P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Emerald Tower   0.005080530.000317680.00095303
Jade Dragon     11.764108171.574777554.65032545
Giant Frog      11.764108171.574777554.65032545
Leaf Dragon     17.646162263.060491748.90334357
Elite Cockatrice11.764108171.574777554.65032545
Jade shield     2.941027040.233422370.69863381
Jade Staff      2.941027040.233422370.69863381
Ferald Bond     17.646162263.060491748.90334357
Epinephrine     5.882054090.569876931.69990650
Ray of Light    17.646162263.060491748.90334357

Fire Queen     
Fire Queen      P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Emerald Tower 0.231366280.014761960.04427936
Ferald Bond   25.985105066.0801814317.15396370
Fire Lance    12.992552531.843816645.43008696
Fahrenheit    8.661701690.987741592.93405213
Wind Tower    0.159064310.010083990.03024892
Animate Weapon12.992552531.843816645.43008696
Elite Queen   25.985105066.0801814317.15396370
Eagle's Eye   12.992552531.843816645.43008696

Gemini         
Gemini          P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Gravity Tower     0.013466890.000842700.00252808
Massive Dragon    11.533540941.526631544.51033231
Unstoppable       15.378054592.427729307.10780268
Aether Tower      0.029178270.001828430.00548519
Twin Universe     23.067081894.8949667313.97780790
Elite Immortal    3.844513650.325552070.97348014
Phase Shield      15.378054592.427729307.10780268
Electrocutor      3.844513650.325552070.97348014
Elite Phase Dragon3.844513650.325552070.97348014
Phase Recluse     23.067081894.8949667313.97780790

Graviton       
Graviton        P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Gravity Tower      0.026214400.001642270.00492672
Elite Charger      9.521312911.137387123.37349902
Elite Armagio      4.760656460.429071241.28169855
Gravity Shield     4.760656460.429071241.28169855
Unstoppable        14.281969372.149223986.31008978
Elite Otyugh       14.281969372.149223986.31008978
Titan              4.760656460.429071241.28169855
Gravity Force      4.760656460.429071241.28169855
Graviton Firemaster28.563938747.2486236820.20768081
Explosion          9.521312911.137387123.37349902
Fire Storm         4.760656460.429071241.28169855

Hecate         
Hecate          P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Rage Elixir   26.086394446.1239041717.26961242
Obsidian Tower0.002154640.000134690.00040407
Improved Dusk 4.347732410.381143301.13907734
Improved Steal8.695464810.993434302.95079359
Eclipse       8.695464810.993434302.95079359
Vampire Dagger4.347732410.381143301.13907734
Liquid Shadow 17.390929632.985425168.69155341
Voodoo Doll   26.086394446.1239041717.26961242
Nightmare     4.347732410.381143301.13907734

Hermes         
Hermes          P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Heavy Armor     7.894192650.862375572.56488009
Protect Artifact5.262795100.490186531.46336287
Burning Tower   0.006893150.000431090.00129326
Brimstone Eater 10.525590191.324761273.92186654
Ruby Dragon     2.631397550.204094540.61103483
Fire Spectre    10.525590191.324761273.92186654
Fire Lance      15.788385292.536521077.41817702
Fire Buckler    2.631397550.204094540.61103483
Explosion       15.788385292.536521077.41817702
Fahrenheit      2.631397550.204094540.61103483
Fire Storm      5.262795100.490186531.46336287
Lava Destroyer  15.788385292.536521077.41817702
Rage Elixir     5.262795100.490186531.46336287

Incarnate       
Incarnate       P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Retrovirus    14.284621572.149876786.31196491
Graveyard     17.855776963.122882989.07912254
Bone Wall     14.284621572.149876786.31196491
Obsidian Tower0.007649010.000478390.00143517
Bloodsucker   14.284621572.149876786.31196491
Eclipse       14.284621572.149876786.31196491
Vampire Dagger3.571155390.296641570.88728742
Vampire       21.426932354.2905985312.32741719

Jezebel         
Jezebel         P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Quantum Tower    0.114889710.007254910.02176316
Water Tower      0.080422790.005062830.01518771
Permafrost Shield5.870863970.568394291.69550908
Nymph's Tears    35.2251838210.8201960929.07496818
Improved Steal   23.483455885.0553931114.41238942
Vampire Dagger   5.870863970.568394291.69550908
Siphon Life      11.741727941.570071884.63664891
Cloak            17.612591913.050561808.87534642

Miracle         
Miracle         P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Emerald Tower    0.016888810.001057160.00317143
Jade Dragon      4.758486790.428813931.28093323
Leaf Dragon      9.516973581.136606983.37121150
Jade shield      4.758486790.428813931.28093323
Jade Staff       4.758486790.428813931.28093323
Light Tower      0.037999820.002383110.00714917
Light Dragon     14.275460372.147622296.30548897
Elite Pegasus    9.516973581.136606983.37121150
Solar Buckler    4.758486790.428813931.28093323
Improved Blessing14.275460372.147622296.30548897
Morning Glory    4.758486790.428813931.28093323
Improved Miracle 14.275460372.147622296.30548897
Wind Tower       0.016888810.001057160.00317143
Elite Queen      14.275460372.147622296.30548897

Morte           
Morte           P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Bone Tower      0.001165030.000072820.00021847
Ivory Dragon    5.263096580.490224161.46347466
Retrovirus      15.789289732.536763617.41886820
Flesh Recluse   2.631548290.204108540.61107666
Condor          7.894644870.862447172.56509120
Graveyard       7.894644870.862447172.56509120
Deadly Poison   13.157741441.881616595.53930151
Improved Plague 7.894644870.862447172.56509120
Arsenic         5.263096580.490224161.46347466
Bone Wall       7.894644870.862447172.56509120
Ray of Light    15.789289732.536763617.41886820
Archangel       7.894644870.862447172.56509120
Improved Miracle2.631548290.204108540.61107666

Neptune         
Neptune         P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Water Tower      0.003970230.000248230.00074468
Abyss Crawler    15.999364762.593427667.58025128
Congeal          3.999841190.342382641.02363516
Permafrost Shield7.999682380.879149282.61432868
Arctic Octopus   15.999364762.593427667.58025128
Poseidon         3.999841190.342382641.02363516
Arctic Dragon    7.999682380.879149282.61432868
Inundation       15.999364762.593427667.58025128
Eagle's Eye      3.999841190.342382641.02363516
Shockwave        23.999047145.2580214414.95919737

Obliterator     
Obliterator     P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Unstoppable     14.808037072.280706216.68725634
Gravity Force   18.510046333.321948579.63845132
Stone Tower     0.045749800.002871140.00861317
Basalt Dragon   18.510046333.321948579.63845132
Diamond Shield  7.404018530.786331462.34049349
Pulverizer      7.404018530.786331462.34049349
Elite Shrieker  22.212055604.5744482613.10514977
Protect Artifact11.106027801.439305674.25606716

Octane         
Octane          P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Fire Lance    9.998533501.224726883.62936566
Fire Buckler  4.999266750.457723371.36689437
Explosion     9.998533501.224726883.62936566
Wind Tower    0.014664980.000917770.00275329
Animate Weapon19.997067003.7990248510.96957982
Eagle's Eye   24.996333765.6625445616.04385797
Unstable Gas  29.995600517.9477949321.99856565

Osiris         
Osiris          P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Unstoppable  12.475585941.728014375.09497809
Trebuchet    12.475585941.728014375.09497809
Time Tower   0.195312500.012421890.03726103
Turtle Shield6.237792970.617832891.84207072
Rewind       12.475585941.728014375.09497809
Eternity     6.237792970.617832891.84207072
Precognition 12.475585941.728014375.09497809
Pharaoh      37.4267578112.1844342832.28038032

Paradox         
Paradox         P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Ray of Light      19.999989763.7999966010.97227775
Improved Blessing 19.999989763.7999966010.97227775
Mirror Shield     4.999997440.457812191.36715840
Morning Glory     4.999997440.457812191.36715840
Improved Miracle  7.499996160.800975972.38373243
Elite Deja Vu     19.999989763.7999966010.97227775
Electrum Hourglass9.999994881.224999053.63016229
Aether Tower      0.000051200.000003200.00000960
Twin Universe     12.499993601.733397035.11057195

Rainbow         
Rainbow         P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Quantum Tower     0.026214400.001642270.00492672
Werewolf          11.108198401.439742694.25734073
Gravity Force     8.331148800.932801352.77238167
Elite Graboid     11.108198401.439742694.25734073
Forest Spectre    11.108198401.439742694.25734073
Explosion         11.108198401.439742694.25734073
Congeal           8.331148800.932801352.77238167
Improved Miracle  5.554099200.527076291.57290922
Eagle's Eye       5.554099200.527076291.57290922
Electrum Hourglass13.885248002.052719036.03261238
Improved Steal    8.331148800.932801352.77238167
Thunderbolt       5.554099200.527076291.57290922

Scorpio         
Scorpio         P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Deadly Poison    15.148432772.367931026.93690785
Arsenic          3.029686550.242030140.72433449
Water Tower      0.017437450.001091550.00327462
Physalia         9.089059661.060910253.14908424
Abyss Crawler    9.089059661.060910253.14908424
Congeal          9.089059661.060910253.14908424
Ice Lance        3.029686550.242030140.72433449
Permafrost Shield6.059373110.593581181.77019430
Purify           3.029686550.242030140.72433449
Arctic Octopus   6.059373110.593581181.77019430
Poseidon         3.029686550.242030140.72433449
Arctic Dragon    3.029686550.242030140.72433449
Puffer Fish      18.178119333.220136999.35267156
Ulitharid        6.059373110.593581181.77019430
Aether Tower     0.002906240.000181690.00054506
Twin Universe    6.059373110.593581181.77019430

Seism           
Seism           P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Stone Tower     0.007451770.000466050.00139814
Elite Antlion   3.333084940.272197070.81437050
Steel Golem     6.666169880.677706992.01937349
Basalt Dragon   6.666169880.677706992.01937349
Diamond Shield  3.333084940.272197070.81437050
Gnome Gemfinder 9.999254821.224861213.62975886
Pulverizer      3.333084940.272197070.81437050
Elite Graboid   19.998509653.7995044710.97091145
Protect Artifact6.666169880.677706992.01937349
Quicksand       19.998509653.7995044710.97091145
Granite skin    3.333084940.272197070.81437050
Rewind          13.332339761.921991225.65586216
Silurian Dragon 3.333084940.272197070.81437050

Serket         
Serket          P(choose card)[%]P(win card) in 1 spin[%]P(win card) in 3 spin[%]
Relic        7.998826800.879012652.61392597
Bone Tower   0.006843660.000427990.00128397
Flesh Recluse19.997067003.7990248510.96957982
Arsenic      7.998826800.879012652.61392597
Deathstalker 19.997067003.7990248510.96957982
Emerald Tower0.007821320.000489180.00146752
Scorpion     19.997067003.7990248510.96957982
Life Nymph   0.000000000.000000000.00000000
Eclipse      11.998240201.624423954.79453791
Cloak        11.998240201.624423954.79453791
   Very impressive, Dark Weaver. I have no issues with the methodology, but came up with two minor decklist discrepancies.

1) With Akebono, your data states that it has 4 Overdrive and 0 Gravity Force. The counts on the False Gods decklists page are 3 and 1.

2) With Hecate, your data states that it has 2 Eclipse and 1 Nightmare. The counts on the False Gods decklists page are 1 and 3. The difference in non-tower card number will impact the other card probabilities.

   Afaik, teffy's list is accurate. Do you have different information regarding the two FGs' decklists?

   +Karma for all your hard work.
Title: Re: Drop rates and deck selection
Post by: Dark Weaver on March 05, 2011, 12:22:57 am
Hi,
thx
I didn't verify all the decks with the post from teffy, just a couple, so thanks again for having spot the differences.

Quote
Afaik, teffy's list is accurate. Do you have different information regarding the two FGs' decklists
Yes, i use what the program use to create the FG decks.

In doubt i'll post the 2 decks stats based on teffy's list here, if anyone can confirm that teffy's list is correct or mine? The easiest way would be asking players if they have encoutered a Gravity Force against Akebono.
My previous post was correct so i remove the info of this one.
Title: Re: Drop rates and deck selection
Post by: Essence on March 21, 2011, 08:14:05 am
Quote from: kevkev60614 on March 02, 2011, 06:50:58 pm
Using the elements card tracking spreadsheet found here  (http://elementscommunity.org/forum/index.php/topic,13271.0.html) and the drop rates fore each card Dark Weaver came up with here (http://elementscommunity.org/forum/index.php/topic,20376.msg300757#msg300757), the following table shows expected sale value of cards received from a win.
Divine Glory873
Osiris763
Jezebel756
Octane731
Akebono727
Decay715
Eternal Phoenix664
Fire Queen663
Hecate640
Gemini599
Lionheart590
Obliterator579
Serket570
Incarnate569
Neptune564
Paradox564
Graviton557
Destiny537
Ferox521
Seism493
Dark Matter487
Miracle467
Hermes460
Chaos Lord456
Morte443
Dream Catcher437
Elidnis436
Scorpio434
Rainbow428

Maybe I don't get it -- but doesn't every upgraded card sell for at least 1100+ep?  Or is this the expected ep value not per card sold, but per victory (i.e. with %-to-win already factored in?
Title: Re: Drop rates and deck selection
Post by: kev on March 21, 2011, 02:19:05 pm
Quote from: Essence on March 21, 2011, 08:14:05 am
Maybe I don't get it -- but doesn't every upgraded card sell for at least 1100+ep?  Or is this the expected ep value not per card sold, but per victory (i.e. with %-to-win already factored in?
I wanted to show the average value of cards won from each FG.  I started to use 1159 as an estimated average value per card sold but then figured I might as well use actual card values since they're readily available.  The table I have above doesn't include win percentage, five electrum for double spins, or the electrum from the win itself (e.g. 120 for EMs).

Divine Glory   
Card Value
P(win card) in 1 spin[%]
E(V) 3 spins
Burning Tower   
1156
0.00079384
0.03
Explosion       
1157
7.93982874
275.59
Light Tower     
1156
0.00345307
0.12
Morning Glory   
1301
7.93982874
309.89
Improved Miracle
1308
2.32708425
91.31
Animate Weapon 
1157
5.65706064
196.36
Total
873.30
Title: Re: Drop rates and deck selection
Post by: Essence on March 22, 2011, 10:40:03 am
Aha!  So, essentially if you've collected enough stats to have a good idea of your winrate vs. each specific god with a specific deck, you can go down this chart and multiply the collected values by your god-specific winrate to give you a pretty solid estimate of how much any given game of FG farming with this deck is worth to you -- and multiply by your average game length to get ep/hour averages for each of your statted decks.


That seems...useful. :)
Title: Re: Drop rates and deck selection
Post by: Jangoo on September 08, 2011, 11:23:00 pm


So ...  what's the verdict here?

Dark Weaver, are you 100% sure that your math is solid?

I am asking because I am about to merge all the data gathered in the FG-efficiency study (http://elementscommunity.org/forum/index.php/topic,25609.0.html) into one big file, which will yield the empirical spin/drop-rates as played out in over 5000 games.

I then wanted to compare them to those percentages posted here
but there is one problem I see right away:

Dark Weavers second column of percentages shows "chance to win at least 1 card" whereas the studies results are
all cards won / all games won x 100% which should translate as "chance to win exactly 1 card".

But I can't quite wrap my head around it right now, not to mention recalculate Weavers table to make it compatible with the studys results.

Any help?


Title: Re: Drop rates and deck selection
Post by: 10 men on September 09, 2011, 02:03:38 pm
Quote from: Jangoo on September 08, 2011, 11:23:00 pm

So ...  what's the verdict here?

Dark Weaver, are you 100% sure that your math is solid?

From the results of the False God card drop rate study (http://elementscommunity.org/forum/index.php/topic,30140.0.html) I come to the following conclusion: Dark Weaver's math is correct and the spin mechanic as well except for one detail: The pillar repick mechanism. In theory we should have won pretty exactly 0 towers, but we did win, well, a couple more. That is also the reason why the numbers here (http://elementscommunity.org/forum/index.php/topic,1091.msg317219#msg317219) are quite far off from reality, as pillar repick plays a much bigger role in farm decks (the drop rates from a real 24-6 farm deck is much lower than the calculated one). For normal decks (like those of the FGs) it's less significant which is why the experimental data fits the theory pretty well.
@ Dark Weaver: Could you double check the mechanism for the pillar repick and if need be correct your results?

Quote from: Jangoo on September 08, 2011, 11:23:00 pm
but there is one problem I see right away:

Dark Weavers second column of percentages shows "chance to win at least 1 card" whereas the studies results are
all cards won / all games won x 100% which should translate as "chance to win exactly 1 card".

Completely ignore the second column. It's more or less irrelevant. It is the probability to win 1, 2 or 3 cards from 3 spins, but it doesn't differentiate between the three possibilities.
What you need to look at is simply the first column multiplied by 3. This will give you the average number of won cards after a win.
Title: Re: Drop rates and deck selection
Post by: Jangoo on September 10, 2011, 09:18:59 am

Quote from: 10 men on September 09, 2011, 02:03:38 pm
Completely ignore the second column. It's more or less irrelevant. It is the probability to win 1, 2 or 3 cards from 3 spins, but it doesn't differentiate between the three possibilities.
What you need to look at is simply the first column multiplied by 3. This will give you the average number of won cards after a win.
*facepalm* ... right, simple as that. Thanks for the jumpstart.

Now I am excited to see how the data matches the results from the Efficiency-study ...
if there are little differences, they should be that the study yields very slight higher results
to account for the pillar-repick, right?
Title: Re: Drop rates and deck selection
Post by: Dark Weaver on September 15, 2011, 11:18:06 am
Hi,
You are right, my results are all false… and I’ll now return hide myself in the darkness of the internet :P 

I’ll redo the maths but it is now a lot more complex.
here is how the spin works
My mistake was to believe that the loop variable was reset after finding a card, it is not the case.
The maths are more complex because without the mistake, the probabilities to choose the cards for the reel are not independent.
In other words, the probability to choose a card for the reel depend on the previous cards chosen or discarded.

What does it change in term of the probabilities to win specific cards ?
The tower/pillar probabilities are now much higher and not virtually impossible to get like before.
Because the probabilities are interdependent, the probabilities for non tower/pillar cards are reduced (the common cards are reduced more than the rare cards).
This reduction is not compensate by the augmentation of the tower/pillar probabilities, so the overall probability to win a card is reduced.

for example i did a simulation (correct) of 10M spins for akebono and chaos lord :
probability to win the card in 1 spin

Code: [Select]
card            simulation%   theory%(false)
-------------------------------------------
Tower Shield     0.52748000   ( 0.56876238)
Gravity Tower    0.83779000   ( 0.00937755)
Elite Armagio    1.43309000   ( 1.57123995)
Massive Dragon   9.68794000   (10.83017686)
Unstoppable      0.52224000   ( 0.56876238)
Titan            0.52363000   ( 0.56876238)
Chimera          1.43396000   ( 1.57123995)
Overdrive        4.57686000   ( 5.05971560)

card               simulation%   theory%(false)
----------------------------------------------
Quantum Tower       0.06988000    (0.00048522)
Amethyst Tower      0.07134000    (0.00048522)
Maxwell's Demon     0.23792000    (0.24204442)
Amethyst Dragon     0.23723000    (0.24204442)
Dissipation Field   0.58310000    (0.59362062)
Werewolf            0.58117000    (0.59362062)
Chaos Power         1.03907000    (1.06098663)
Supernova           3.13892000    (3.22040398)
Improved Mutation   1.03290000    (1.06098663)
Discord             0.23871000    (0.24204442)
Fallen Druid        1.60062000    (1.65040050)
Unstoppable         0.23609000    (0.24204442)
Explosion           0.23886000    (0.24204442)
Congeal             0.23512000    (0.24204442)
Ray of Light        3.13489000    (3.22040398)
Improved Steal      0.23496000    (0.24204442)simulation of 10M spins for the farm decks (30 cards ; 6 of each card + towers) :

Code: [Select]
card                simulation%   theory%(false)
----------------------------------------------

Amethyst Tower      21.68583000   ( 1.94284015)
Maxwell's Demon     25.12644000   (71.91141071)

Amethyst Tower       3.24584000   ( 0.06873673)
Maxwell's Demon     15.78760000   (21.42120598)
Micro Abomination   15.76401000   (21.42120598)

Amethyst Tower       0.25612000    (0.00164227)
Maxwell's Demon      9.31205000    (9.71730774)
Micro Abomination    9.31531000    (9.71730774)
Amethyst Dragon      9.28382000    (9.71730774)
                     
Amethyst Tower       0.00398000    (0.00000320)
Maxwell's Demon      5.66418000    (5.66405720)
Micro Abomination    5.65200000    (5.66405720)
Amethyst Dragon      5.66213000    (5.66405720)
Dissipation Field    5.65709000    (5.66405720)
                                   
Maxwell's Demon      3.79560000    (3.80000000)
Micro Abomination    3.80821000    (3.80000000)
Amethyst Dragon      3.80205000    (3.80000000)
Dissipation Field    3.80081000    (3.80000000)
Werewolf             3.79149000    (3.80000000)
Title: Re: Drop rates and deck selection
Post by: 10 men on September 15, 2011, 01:18:42 pm
Quote from: Dark Weaver on September 15, 2011, 11:18:06 am
here is how the spin works
    1. (init) loop:=0, ncard:=02. C:=random card from deck, loop:=loop+13. if loop > 8 goto step 5.4. if C is a tower/pillar goto step 2.5. ncard:=ncard+1(error)5bis. loop:=0 (error)6. if C is upped and lvl is not 5 or 6 then C:= downgrade version of C7. if C is a banned card then C:= relic (upped one if C is still upped)8. if ncard <= 4 goto step 2.9. the 4 first cards = the reel
My mistake was to believe that the loop variable was reset after finding a card, it is not the case.
Ah interesting, thanks for checking. :) So for example if the first pick is a pillar (after picking and repicking 8 times), the second pick has a pretty good chance to be a pillar as well because they don't get get repicked anymore. Also for the last pick the loop value will automatically start with 4, even when there never was a pillar picked before? I would have guessed that maybe it starts at 1 and gets raised in step 4 (if a pillar was picked).
Well of course that makes the math... a little more complicated. :))
Title: Re: Drop rates and deck selection
Post by: Dark Weaver on September 15, 2011, 07:43:49 pm
hi,
I’ve redone the maths  8), I hope this time it is correct.
First table shows the probability to win at least 1 card from the specific FG, either with 1 try|spin (2nd column) or with 3 tries|spins (3rd column).
The other tables shows the probability to win  at least 1 of a specific card from a FG deck with 1 try and 3 tries
Results should be accurate, I did some simulations giving nearly the same results.(unless of course I misinterpreted the code ;))

DeckName
P(win a card) in 1 spin[%]
P(win a card) in 3 spin[%]
Akebono        19.5449744447.92137235
Chaos Lord     12.8935673533.90772760
Dark Matter    13.7537213635.84639060
Decay          20.4698334049.69679266
Destiny        14.9130091038.39875418
Divine Glory   22.6656813653.74946184
Dream Catcher  12.5262794333.06815495
Elidnis        12.4448115732.88097162
Eternal Phoenix18.7500440746.36239196
Ferox          14.8086465538.17180698
Fire Queen     16.9716860342.76276355
Gemini         16.5870339741.96356960
Graviton       15.6258395739.93404406
Hecate         18.2367408645.33937626
Hermes         13.0874485834.34806996
Incarnate      16.1125218940.96746743
Jezebel        19.9080206548.62319653
Lionheart      15.7853095140.27398067
Miracle        12.5832955133.19894980
Morte          12.6134086033.26796040
Neptune        15.6905671740.07217676
Obliterator    16.0506145340.83667629
Octane         19.9026295948.61282117
Osiris         19.0718799846.99725586
Paradox        16.0635194740.86395636
Rainbow        12.0322034531.92758769
Scorpio        12.1792456132.26837578
Seism          13.9960164736.38556092
Serket         16.0950445540.93056276

Akebono       
Akebono       
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Tower Shield 
0.52539722
1.56792490
Gravity Tower
0.83543843
2.48543488
Elite Armagio
1.43558188
4.24521463
Massive Dragon
9.69725507
26.36185236
Unstoppable   
0.52539722
1.56792490
Titan         
0.52539722
1.56792490
Chimera       
1.43558188
4.24521463
Overdrive     
4.56492553
13.07913287

Chaos Lord     
Chaos Lord     
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Quantum Tower   
0.07142495
0.21412185
Amethyst Tower   
0.07142495
0.21412185
Maxwell's Demon 
0.23701873
0.70937218
Amethyst Dragon 
0.23701873
0.70937218
Dissipation Field
0.57983513
1.72943863
Werewolf         
0.57983513
1.72943863
Chaos Power     
1.03440577
3.07122814
Supernova       
3.12820866
9.09411648
Improved Mutation
1.03440577
3.07122814
Discord         
0.23701873
0.70937218
Fallen Druid     
1.60668720
4.74303305
Unstoppable     
0.23701873
0.70937218
Explosion       
0.23701873
0.70937218
Congeal         
0.23701873
0.70937218
Ray of Light     
3.12820866
9.09411648
Improved Steal   
0.23701873
0.70937218

Dark Matter   
Dark Matter   
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Relic           
0.72170310
2.14952124
Gravity Tower   
0.27190651
0.81350356
Elite Charger   
2.06681000
6.07316178
Elite Armagio   
0.28770342
0.86062943
Massive Dragon   
0.28770342
0.86062943
Unstoppable     
0.28770342
0.86062943
Elite Otyugh     
0.72170310
2.14952124
Titan           
0.28770342
0.86062943
Gravity Force   
2.06681000
6.07316178
Black Hole       
4.11175813
11.83502931
Gravity Nymph   
0.00000000
0.00000000
Archangel       
2.06681000
6.07316178
Improved Blessing
0.28770342
0.86062943
Morning Glory   
0.28770342
0.86062943

Decay         
Decay         
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Pest         
6.10886259
17.22983887
Improved Dusk
0.38048097
1.13710544
Improved Steal
0.99146931
2.94501504
Eclipse       
0.38048097
1.13710544
Siphon Life   
6.10886259
17.22983887
Aether Tower 
0.01033343
0.03099709
Electrocutor 
0.38048097
1.13710544
Fractal       
6.10886259
17.22983887

Destiny       
Destiny       
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Amethyst Tower   
0.17381640
0.52054335
Maxwell's Demon   
0.68195577
2.03194710
Chaos Power       
2.79968218
8.16609440
Supernova         
2.79968218
8.16609440
Fallen Druid     
0.68195577
2.03194710
Time Tower       
0.09260558
0.27755954
Fate Egg         
3.83143937
11.05954480
Rewind           
1.93649980
5.69772464
Electrum Hourglass
1.23341629
3.65479705
Eternity         
0.68195577
2.03194710

Divine Glory   
Divine Glory   
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Burning Tower   
0.05378755
0.16127588
Explosion       
7.39461722
20.58387478
Light Tower     
0.35616511
1.06469423
Morning Glory   
7.39461722
20.58387478
Improved Miracle
2.18590501
6.41541408
Animate Weapon 
5.28058925
15.01995380

Dream Catcher 
Dream Catcher 
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Relic           
0.25134054
0.75212804
Amethyst Tower   
0.00105875
0.00317622
Micro Abomination
3.39569588
9.84508062
Supernova       
3.39569588
9.84508062
Discord         
0.61937356
1.84663572
Butterfly Effect
1.11096232
3.29599697
Purple Nymph     
0.00000000
0.00000000
Black Hole       
0.25134054
0.75212804
Protect Artifact
0.25134054
0.75212804
Quicksand       
0.25134054
0.75212804
Rage Elixir     
0.25134054
0.75212804
Physalia         
0.25134054
0.75212804
Congeal         
0.25134054
0.75212804
Shockwave       
0.61937356
1.84663572
Elite Deja Vu   
0.25134054
0.75212804
Fate Egg         
0.25134054
0.75212804
Pest             
0.61937356
1.84663572
Thunderbolt     
0.25134054
0.75212804
Quintessence     
0.25134054
0.75212804

Elidnis       
Elidnis       
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Forest Spectre   
2.40710819
7.04889420
Improved Heal     
0.46997644
1.40331337
Jade shield       
0.19654867
0.58848783
Jade Staff       
0.19654867
0.58848783
Ferald Bond       
1.78884918
5.27112054
Water Tower       
0.02530640
0.07589998
Abyss Crawler     
0.82401479
2.45173032
Congeal           
1.78884918
5.27112054
Puffer Fish       
0.82401479
2.45173032
Ulitharid         
0.82401479
2.45173032
Aether Tower     
0.01674003
0.05021168
Twin Universe     
1.78884918
5.27112054
Elite Phase Dragon
0.82401479
2.45173032
Quintessence     
0.46997644
1.40331337

Eternal Phoenix
Eternal Phoenix
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Burning Tower
0.15043160
0.45061626
Ruby Dragon 
1.29507136
3.83511500
Fire Lance   
1.29507136
3.83511500
Explosion   
4.05180952
11.66956568
Fire Storm   
0.48053668
1.43469368
Minor Phoenix
8.52156411
23.44806177
Thunderbolt 
0.48053668
1.43469368
Fractal     
2.47502274
7.24281223

Ferox         
Ferox         
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Emerald Tower   
0.08488713
0.25444527
Jade Dragon     
1.55258743
4.58582071
Giant Frog     
1.55258743
4.58582071
Leaf Dragon     
3.01381711
8.77169601
Elite Cockatrice
1.55258743
4.58582071
Jade shield     
0.23084928
0.69095033
Jade Staff     
0.23084928
0.69095033
Ferald Bond     
3.01381711
8.77169601
Epinephrine     
0.56284723
1.67905562
Ray of Light   
3.01381711
8.77169601

Fire Queen     
Fire Queen     
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Emerald Tower
0.70901539
2.11200073
Ferald Bond   
5.11978620
14.58641237
Fire Lance   
1.58512106
4.68038320
Fahrenheit   
0.85872957
2.55412953
Wind Tower   
0.40900548
1.22200473
Animate Weapon
1.58512106
4.68038320
Elite Queen   
5.11978620
14.58641237
Eagle's Eye   
1.58512106
4.68038320

Gemini         
Gemini         
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Gravity Tower     
0.07571311
0.22696740
Massive Dragon   
1.45743467
4.30889012
Unstoppable       
2.31152211
6.77550736
Aether Tower     
0.20556924
0.61544084
Twin Universe     
4.64252291
13.29098420
Elite Immortal   
0.31340897
0.93728324
Phase Shield     
2.31152211
6.77550736
Electrocutor     
0.31340897
0.93728324
Elite Phase Dragon
0.31340897
0.93728324
Phase Recluse     
4.64252291
13.29098420

Graviton       
Graviton       
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Gravity Tower     
0.25491866
0.76280812
Elite Charger     
1.09909579
3.26117979
Elite Armagio     
0.41633314
1.24380665
Gravity Shield     
0.41633314
1.24380665
Unstoppable       
2.07101731
6.08526683
Elite Otyugh       
2.07101731
6.08526683
Titan             
0.41633314
1.24380665
Gravity Force     
0.41633314
1.24380665
Graviton Firemaster
6.94902899
19.43197303
Explosion         
1.09909579
3.26117979
Fire Storm         
0.41633314
1.24380665

Hecate         
Hecate         
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Rage Elixir   
6.06245037
17.10703348
Obsidian Tower
0.04813314
0.14432992
Improved Dusk
0.37842330
1.13097920
Improved Steal
0.98538032
2.92710739
Eclipse       
0.98538032
2.92710739
Vampire Dagger
0.37842330
1.13097920
Liquid Shadow
2.95767645
8.61318119
Voodoo Doll   
6.06245037
17.10703348
Nightmare     
0.37842330
1.13097920

Hermes         
Hermes         
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Heavy Armor     
0.84900982
2.52546614
Protect Artifact
0.48313669
1.44241871
Burning Tower   
0.10398449
0.31162920
Brimstone Eater
1.30305007
3.85843327
Ruby Dragon     
0.20145773
0.60315644
Fire Spectre   
1.30305007
3.85843327
Fire Lance     
2.49152363
7.28988684
Fire Buckler   
0.20145773
0.60315644
Explosion       
2.49152363
7.28988684
Fahrenheit     
0.20145773
0.60315644
Fire Storm     
0.48313669
1.44241871
Lava Destroyer 
2.49152363
7.28988684
Rage Elixir     
0.48313669
1.44241871

Incarnate     
Incarnate     
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Retrovirus   
2.11021574
6.19799658
Graveyard     
3.06273860
8.90967772
Bone Wall     
2.11021574
6.19799658
Obsidian Tower
0.11145126
0.33398129
Bloodsucker   
2.11021574
6.19799658
Eclipse       
2.11021574
6.19799658
Vampire Dagger
0.29239632
0.87462659
Vampire       
4.20507276
12.09217486

Jezebel       
Jezebel       
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Quantum Tower   
0.44624116
1.33275843
Water Tower     
0.26979204
0.80719444
Permafrost Shield
0.51865099
1.54789696
Nymph's Tears   
9.52503244
25.93972707
Improved Steal   
4.48931526
12.87237497
Vampire Dagger   
0.51865099
1.54789696
Siphon Life     
1.41466398
4.18423683
Cloak           
2.72567379
7.95616744

Lionheart     
Lionheart     
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Quantum Tower     
0.06225938
0.18666189
Light Tower       
0.11428845
0.34247364
Crusader         
4.70911790
13.47252279
Animate Weapon   
0.39978223
1.19455829
Time Tower       
0.20870126
0.62479801
Turtle Shield     
1.04975247
3.11631367
Electrum Hourglass
4.70911790
13.47252279
Elite Anubis     
1.97074339
5.79648067
Eternity         
1.04975247
3.11631367
Pharaoh           
0.39978223
1.19455829
Quintessence     
1.04975247
3.11631367
Aether Pendulum   
0.06225938
0.18666189

Miracle       
Miracle       
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Emerald Tower   
0.07259084
0.21761447
Jade Dragon     
0.40703121
1.21613014
Leaf Dragon     
1.07131688
3.17964201
Jade shield     
0.40703121
1.21613014
Jade Staff       
0.40703121
1.21613014
Light Tower     
0.20229307
0.60565237
Light Dragon     
2.01450773
5.92259350
Elite Pegasus   
1.07131688
3.17964201
Solar Buckler   
0.40703121
1.21613014
Improved Blessing
2.01450773
5.92259350
Morning Glory   
0.40703121
1.21613014
Improved Miracle
2.01450773
5.92259350
Wind Tower       
0.07259084
0.21761447
Elite Queen     
2.01450773
5.92259350

Morte         
Morte         
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Bone Tower     
0.03212777
0.09635235
Ivory Dragon   
0.48770120
1.45597964
Retrovirus     
2.52060159
7.37280324
Flesh Recluse   
0.20316675
0.60826278
Condor         
0.85765764
2.55096870
Graveyard       
0.85765764
2.55096870
Deadly Poison   
1.87005355
5.50590163
Improved Plague
0.85765764
2.55096870
Arsenic         
0.48770120
1.45597964
Bone Wall       
0.85765764
2.55096870
Ray of Light   
2.52060159
7.37280324
Archangel       
0.85765764
2.55096870
Improved Miracle
0.20316675
0.60826278

Neptune       
Neptune       
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Water Tower     
0.07207977
0.21608348
Abyss Crawler   
2.55970551
7.48423090
Congeal         
0.33895056
1.01340896
Permafrost Shield
0.86917057
2.58491364
Arctic Octopus   
2.55970551
7.48423090
Poseidon         
0.33895056
1.01340896
Arctic Dragon   
0.86917057
2.58491364
Inundation       
2.55970551
7.48423090
Eagle's Eye     
0.33895056
1.01340896
Shockwave       
5.18417804
14.76019592

Obliterator   
Obliterator   
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Unstoppable     
2.16820878
6.36461177
Gravity Force   
3.15113179
9.15863537
Stone Tower     
0.37218366
1.11240050
Basalt Dragon   
3.15113179
9.15863537
Diamond Shield 
0.75229512
2.23994949
Pulverizer     
0.75229512
2.23994949
Elite Shrieker 
4.33129049
12.43919469
Protect Artifact
1.37207779
4.06001375

Octane         
Octane         
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Fire Lance   
1.19443282
3.54066876
Fire Buckler 
0.44776339
1.33728440
Explosion     
1.19443282
3.54066876
Wind Tower   
0.17229970
0.51600899
Animate Weapon
3.69168540
10.67123119
Eagle's Eye   
5.49586639
15.59806277
Unstable Gas 
7.70614907
21.38266797

Osiris         
Osiris         
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Unstoppable 
1.55507326
4.59304825
Trebuchet   
1.55507326
4.59304825
Time Tower   
1.01318359
3.00885856
Turtle Shield
0.56320578
1.68011918
Rewind       
1.55507326
4.59304825
Eternity     
0.56320578
1.68011918
Precognition
1.55507326
4.59304825
Pharaoh     
10.71199179
28.81648896

Paradox       
Paradox       
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Ray of Light     
3.79613102
10.96154519
Improved Blessing
3.79613102
10.96154519
Mirror Shield     
0.45745763
1.36610443
Morning Glory     
0.45745763
1.36610443
Improved Miracle 
0.80030637
2.38175566
Elite Deja Vu     
3.79613102
10.96154519
Electrum Hourglass
1.22391446
3.62698771
Aether Tower     
0.00419891
0.01259621
Twin Universe     
1.73179142
5.10592061

Rainbow       
Rainbow       
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Quantum Tower     
0.25491866
0.76280812
Werewolf         
1.38981842
4.11177587
Gravity Force     
0.90218435
2.68220838
Elite Graboid     
1.38981842
4.11177587
Forest Spectre   
1.38981842
4.11177587
Explosion         
1.38981842
4.11177587
Congeal           
0.90218435
2.68220838
Improved Miracle 
0.51101104
1.52521249
Eagle's Eye       
0.51101104
1.52521249
Electrum Hourglass
1.97842494
5.81862426
Improved Steal   
0.90218435
2.68220838
Thunderbolt       
0.51101104
1.52521249

Scorpio       
Scorpio       
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Deadly Poison   
2.29198703
6.71956899
Arsenic         
0.23619397
0.70690959
Water Tower     
0.17275829
0.51738003
Physalia         
1.03006992
3.05848774
Abyss Crawler   
1.03006992
3.05848774
Congeal         
1.03006992
3.05848774
Ice Lance       
0.23619397
0.70690959
Permafrost Shield
0.57758108
1.72275452
Purify           
0.23619397
0.70690959
Arctic Octopus   
0.57758108
1.72275452
Poseidon         
0.23619397
0.70690959
Arctic Dragon   
0.23619397
0.70690959
Puffer Fish     
3.11323245
9.05194827
Ulitharid       
0.57758108
1.72275452
Aether Tower     
0.01976390
0.05927999
Twin Universe   
0.57758108
1.72275452

Seism         
Seism         
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Stone Tower     
0.10952671
0.32822037
Elite Antlion   
0.26839833
0.80303580
Steel Golem     
0.66707569
1.98790706
Basalt Dragon   
0.66707569
1.98790706
Diamond Shield 
0.26839833
0.80303580
Gnome Gemfinder
1.20409476
3.56896353
Pulverizer     
0.26839833
0.80303580
Elite Graboid   
3.72582902
10.76620513
Protect Artifact
0.66707569
1.98790706
Quicksand       
3.72582902
10.76620513
Granite skin   
0.26839833
0.80303580
Rewind         
1.88751822
5.55634537
Silurian Dragon
0.26839833
0.80303580

Serket         
Serket         
P(win card) in 1 spin[%]
P(win card) in 3 spin[%]
Relic       
0.85818119
2.55251253
Bone Tower   
0.06330024
0.18978053
Flesh Recluse
3.69168540
10.67123119
Arsenic     
0.85818119
2.55251253
Deathstalker
3.69168540
10.67123119
Emerald Tower
0.07473128
0.22402633
Scorpion     
3.69168540
10.67123119
Life Nymph   
0.00000000
0.00000000
Eclipse     
1.58279723
4.67363080
Cloak       
1.58279723
4.67363080

Title: Re: Drop rates and deck selection
Post by: Jangoo on September 17, 2011, 12:35:27 pm
Allright,

I took the new values from DarkWeaver and multiplied the [chance to win one card in one spin] by 3,  like 10men said.
-> These theoretical values should show how many cards a FG will yield per game played , right?
-> right column

Then I took the data from the FG-efficiency-study (http://elementscommunity.org/forum/index.php/topic,25609.0.html) and compared it to DarkWeavers values.
-> left column

The data has been gathered over 6755 games. The number of games against each FG ranges between 199 and 277.
-> very left column shows the number of games actually won against each FG


Now here is the table, and with it, the sad part:


The values don't really match.  :(

I marked those FGs where the values are off over 10% in red,
those where they are off over 5% in yellow.

Now ... what am I supposed to do with these results? Can these huge margins be explained somehow?

I was really hoping the margin of error would be somewhere around 1-3% ... explicable through odd probabilities even during over 200 games per god but this ...
As far as I can see, there isn't even really a clear trend like: "The less games played, the more off is the empirical value." ... or is there?

Would you guys say that e.g. 100 games played and won against a god are enoug to "count" on empirical results?
Are only 39 games (as for Phoenix who is way off) just not enough?

Any ideas, because I am also guessing even some pillar-repick can't explain those 15% margin for DG or those 13-14% for EtPh, Hecate, Serket etc.

games won
FG
FG-efficiency-study cardspin:
all cards won/all games won (*100%)
P(win a card) in 1 spin[%]x3
(DarkWeaver)
81Akebono         53,0958,62
73Chaos Lord      31,5138,67
69Dark Matter     40,5841,25
67Decay           65,6761,40
175Destiny         48,0044,73
53Divine Glory    83,0267,98
50Dream Catcher   30,0037.56
100Elidnis         31,0037,32
39Eternal Phoenix 41,0356,25
70Ferox           57,1444,43
106Fire Queen      51,8950,91
104Gemini          40,3849,74
43Graviton        46,5146,86
78Hecate          41,0354,69
39Hermes          38,4639,24
144Incarnate       45,1448,33
58Jezebel         50,0059,73
121Lionheart       38,0247,34
144Miracle         32,6437,74
108Morte           26,8537,83
154Neptune         38,3147,07
91Obliterator     46,1548,15
68Octane          55,8859,70
85Osiris          50,5957,21
176Paradox         43,1848,18
56Rainbow         30,3636,09
73Scorpio         30,1436,54
80Seism           38,7541,97
104Serket          35,5848,27


Title: Re: Drop rates and deck selection
Post by: Xenocidius on September 17, 2011, 01:04:43 pm
What if you took the values of all the testing and the data from the False God Card droprate spreadsheet (https://docs.google.com/spreadsheet/ccc?key=0AurJM9dMuH3bdDBwdGJINjdiQ1hqLUNULUZjWXl1a3c&hl=en_US#gid=36)?

This (http://elementscommunity.org/forum/index.php/topic,31068) may also be interesting.

The problem is that we don't really know for sure the algorithm used to select cards in the spinner. We have one, but it may be outdated. If we had the algorithm we could calculate the probabilities exactly.

I can also attest that Divine Glory does NOT have that high a droprate. Or maybe I'm just really unlucky.
Title: Re: Drop rates and deck selection
Post by: Jenkar on September 17, 2011, 02:01:57 pm
*pops in* Quotie time!
Jenkar : how many spins would make the data relevant?
Higu : over 9000.

Which is actually quite right. The probability to win a tower in three spins is 1.5 in 100 (for akebonub). That means you need a very large test number to get relevant data, which would  average out errors.

Now, i need to change my sheet's stats >.<
Can someone redo 2k's table with deduced $/win/fg?
 *pops out*
Title: Re: Drop rates and deck selection
Post by: Jangoo on September 17, 2011, 02:17:35 pm

Quote from: Xenocidius on September 17, 2011, 01:04:43 pm
What if you took the values of all the testing and the data from the False God Card droprate spreadsheet (https://docs.google.com/spreadsheet/ccc?key=0AurJM9dMuH3bdDBwdGJINjdiQ1hqLUNULUZjWXl1a3c&hl=en_US#gid=36)?

[...]

I can also attest that Divine Glory does NOT have that high a droprate. Or maybe I'm just really unlucky.
Nice ... someone is editing the spreadsheet as I read it and puts in the new numbers from DarkWeaver.  :D

Also, those are pretty large sample sizes in that spreadsheet: 93 games on average ... the FG-eff-study has 90 games.
I might just throw them both together in an extra column in that spreadsheet to double the sample ...

As for DG: Yeah, subjectively I know what you mean.
An yet, in both studies DG apparently beat the math by far:
80% in the droprate-study and 83% in the FG-eff-study.
In both studies together, 124 games have been played and won ... I find it pretty hard to neglect the empirical evidence here.  :(
Title: Re: Drop rates and deck selection
Post by: Dark Weaver on September 17, 2011, 02:33:48 pm
I posted the algorithm, and it is taken from the 1.282 version.

Also if you want to properly compare the results then you must divide your results by 3 and not multiply mine by 3 because you artificially multiply the error by a factor 3.
So the error for Divine glory is more like a 5%, and if you look at the droprate spreadsheet you’ll see that there are 23 morning glory vs 15 explosion but in theory there should be the same number because there are 6 of each in the deck, the high error % come from there. Looking at the card occurrence for Divine Glory, it seems that there where too much morning glory wins.
Without any maths, there should be the same number of morning glory and explosion, less animated weapon, less miracle.
If you take my results then there should be 15.75 morning glory, 15.75 explosion, 11.24 animated weapon, 4.66 miracles, 0.11 burning tower, 0.76 light towers. Compare this to 23, 15, 13, 6, 0, 0 then my conclusion is that my results are pretty accurate and there is a mistake in the number of morning glory. Mistake is maybe too much for this low amount of spins, better say someone was lucky.
Title: Re: Drop rates and deck selection
Post by: Polari on September 17, 2011, 02:43:30 pm
Here's something I quickly put together in Excel. The numbers are =BINOMDIST( [cards won] ; [total spins] ; [DW's P(win a spin)] ; 1), which basically means the probability of winning at most as many cards as in the FG study, given DW's spin probabilities. So 0,5 is the expected value and 0,94 means a 6% chance of winning at least that many spins. Looks like there are consistently way less drops than DW's numbers would indicate, except for a few specific gods.

Also, note that the numbers in Jangoo's post represent the expected number of cards won in a single game on a scale of 0-300% (!?), not exactly any probabilities of winning.

(http://i54.tinypic.com/wsts9u.png)

edit - please do point out if I fucked up somewhere, the formula used is up there. Also I just noticed that Hermes and Graviton are slightly over 0.50 even thoug looking at Jangoo's table they should be slightly under it? Not sure what's up with that.
Title: Re: Drop rates and deck selection
Post by: Jenkar on September 17, 2011, 02:52:58 pm
Quote from: Dark Weaver on September 17, 2011, 02:33:48 pm
Also if you want to properly compare the results then you must divide your results by 3 and not multiply mine by 3 because you artificially multiply the error by a factor 3.
*ahum*. Unless this is only true for very big numbers, you're wrong (tested on sheet. error didn't move by a iota)
Title: Re: Drop rates and deck selection
Post by: 10 men on September 17, 2011, 03:44:36 pm
To me Dark Weaver's numbers look pretty good now, but if you want to seriously verify them, and a couple hundred matches probably aren't very significant, I'd propose the following: Go to trainer, load up a very strong deck for yourself, like:
6 Ruby Dragon, 6 Sky Dragon, 6 Silurian Dragon, 6 Sky Blitz, 6 Fractal.
(give yourself 100 starting quanta obv.)
Then load up Divine Glory's deck (to take one with a big deviation from the theoretical value) as your opponent deck. Play lots of games. Tell other people to do the same and then compare drop rates again. This way you should easily get a couple thousand games for a certain deck. If there's still that large of a difference, then something might be wrong.



Quote from: Jenkar on September 17, 2011, 02:52:58 pm
Quote from: Dark Weaver on September 17, 2011, 02:33:48 pm
Also if you want to properly compare the results then you must divide your results by 3 and not multiply mine by 3 because you artificially multiply the error by a factor 3.
*ahum*. Unless this is only true for very big numbers, you're wrong (tested on sheet. error didn't move by a iota)
If you multiply Experimental Value and Expected Value by the same number the absolute error (Experimental Value - Expected Value) will change and the relative error (absolute error/Expected Value) won't.
xD

Title: Re: Drop rates and deck selection
Post by: Dark Weaver on September 17, 2011, 03:49:31 pm
Jenkar, I’m not wrong maybe we dont speak about the same thing, I was referring to the 12.27% margin from the spreadsheet. You seemed surprised about it.
For divine glory I calculate the probability to win a card in 1 spin and it gives 22.67%, the spreadsheet gives 80.28% (57/71) which is the probability to win a card per 3 spins. My results gives x/213 so what is done on the spreadsheet to compare is to multiply this by 3 : 3*x/213 thus x/71. The value for x is 22.67%*213 = 48.28, and 57-48.28 = 8.72 so the theory has 8.72 less cards won but those cards should be compared to 213 and not 71. If you compare it to 71 it gives the 12.27% margin but if you compare it to 213 then the margin decrease to 4% (nearly what you expected by the 1-3%).
Remember, my table gives the % to win a card per spin and it is normal that the margin triples if you want compare the % to win a card per 3 spins.


Title: Re: Drop rates and deck selection
Post by: Jenkar on September 17, 2011, 04:20:33 pm
I'm not surprised, imo we need way more data for it to be relevant.

On the note about multiplication : what we're calculatin is :
1- (Min (experimental,theorical)/Max (experimental,theorical))
for which multiplyin' your value by 3 or dividin' ours by 3 doesn't change a thing.
Title: Re: Drop rates and deck selection
Post by: Dark Weaver on September 17, 2011, 05:53:41 pm
sorry it was Jangoo who was surprised about it, and he talked about absolute error like 10men pointed out.
Title: Re: Drop rates and deck selection
Post by: Jangoo on September 18, 2011, 10:46:53 am


So I went ahead, downloaded the spreadsheet and merged its data with the data from the FG-efficiency-study,
thus effectively doubling the sample-size.

What can I say? ... The two studies averaged each other out towards DWs values pretty friggin well!

Overall, there is a lot less red and yellow in that table now and those values that didn't make it to yellow-status before,
more often than not are now almost identical with DWs.  ;)

My conclusion:
DarkWeavers numbers are the shit!
I will just go ahead and use them to tune the Statmasta now ...  :))



FGDarkWeaverMerged studiesSample size
Akebono
Chaos Lord
Dark Matter
Decay
Destiny
Divine Glory
Dream Catcher
Elidnis
Eternal Phoenix
Ferox
Fire Queen
Gemini
Graviton
Hecate
Hermes
Incarnate
Jezebel
Lionheart
Miracle
Morte
Neptune
Obliterator
Octane
Osiris
Paradox
Rainbow
Scorpio
Seism
Serket
58,63%
38,68%
41,26%
61,41%
44,74%
68,00%
37,58%
37,33%
56,25%
44,43%
50,92%
49,76%
46,88%
54,71%
39,26%
48,34%
59,72%
47,36%
37,75%
37,84%
47,07%
48,15%
59,71%
57,22%
48,19%
36,10%
36,54%
41,99%
48,29%
56,86%
40,71%
38,40%
59,74%
43,54%
80,80%
34,02%
35,07%
43,42%
50,28%
51,94%
44,39%
45,88%
56,29%
30,99%
45,51%
54,13%
39,29%
37,37%
34,45%
41,14%
44,83%
54,74%
54,75%
52,16%
31,78%
37,21%
41,46%
42,92%
204
140
125
154
294
125
97
211
76
177
206
223
85
167
71
334
109
252
281
209
333
203
137
179
324
107
129
164
219

---

As for the "tripled error" thing:

Whatever the mathematical explanations behind it, tripling DWs first column is the only way to make sense of these numbers for practical purposes.
Nobody really wants to know how big the chance is to win ONE card in howevermany spins ... You'd wanna know how many cards you win from a FG
once you win the game. Since it will always be three spins ... why split around with the probabilities?


Title: Re: Drop rates and deck selection
Post by: Polari on September 18, 2011, 11:29:54 am
Quote from: Jangoo on September 18, 2011, 10:46:53 am
As for the "tripled error" thing:

Whatever the mathematical explanations behind it, tripling DWs first column is the only way to make sense of these numbers for practical purposes.
Nobody really wants to know how big the chance is to win ONE card in howevermany spins ... You'd wanna know how many cards you win from a FG
once you win the game. Since it will always be three spins ... why split around with the probabilities?
Like I said earlier, the way you've done this works for the purposes of comparing the two numbers, but I don't think you understand what these numbers actually represent. They lie on a scale from 0 to 3 and it's bound to get confusing at some point if you're going to denote them as percentages or refer to them as probabilities.
Title: Re: Drop rates and deck selection
Post by: moonlighting on September 19, 2011, 09:55:27 am
if you want to calculate the "expected number of cards you win in x games", then you should use darkweaver's first column and multiply by 3.

and if you want to test " the probability of winning one card in one spin", you should use the number of cards won / number of games won / 3
Title: Re: Drop rates and deck selection
Post by: Jangoo on September 19, 2011, 10:56:41 am


What those various numbers imply is in fact crystal clear to me guys ...


Except for one thing:

Probabilities can never be higher than 100%, which is why you couldn't call DWs first column x3 a probability, right?



Title: Re: Drop rates and deck selection
Post by: Dark Weaver on September 19, 2011, 12:48:32 pm
Quote
Probabilities can never be higher than 100%, which is why you couldn't call DWs first column x3 a probability, right?
No, it’s because the first column multiplied by 3 is not a probability that it can be > 100%
What the first column ×3 means is what moonlight said, even I called it probability but it isn’t and I was wrong.
y% chance to win a card in one spin is easy to interpret, each time you spin the reels there are y% chances you’ll win a card. It also means that in n spins you expect to win n×y% cards.  If you multiply y% by 3, it doesn’t mean anything, it is not the probability to win a card in 3 spins, it’s just a probability multiplied by 3 which is just a number.
To interpret the number, you can say that winning a game always give 3 spins, so in 3×n spins you expect to win 3×n×y% cards, which is equivalent to say : in n winning game you expect to win n×(3×y%) ; and with n=1, you have the meaning of the number, 3×y% is the number of cards you expect to win in 1 game (which obviously has nothing to do with a probability).
Suppose a FG has a 60% probability to drop a card in 1 spin :
you win on average 0.6 cards per spin
you win on average 1.8 cards per game
In the first case the probability is equivalent to the number of cards wins because 0.6 = 0×0.4 + 1×0.6 , for the second case 1.8 = 0×(0.4)³ + 1×(0.4)²(0.6)×3 + 2×(0.4)(0.6)²×3 + 3×(0.6)³
And putting 1.8 in % (180%) has no sense, you can just put 180 for the average in 100 games.
Title: Re: Drop rates and deck selection
Post by: 10 men on September 19, 2011, 12:51:42 pm
Quote from: Jangoo on September 19, 2011, 10:56:41 am
Probabilities can never be higher than 100%, which is why you couldn't call DWs first column x3 a probability, right?


Yes. First column x 3 is not a probability but the expected value. That is fine because the expected value is what you're looking for - "If I pick this deck up and click on False God, how many cards/Electrum can I expect to win?"

The expected value for one win is calculated by calculating the expected value of one spin which in turn is the probability to win one card in one spin.
Title: Re: Drop rates and deck selection
Post by: Jangoo on September 19, 2011, 02:58:11 pm


Great guys ... thanks.


This thread and study has really helped a lot.  :)
Title: Re: Drop rates and deck selection
Post by: Rainmaker on September 27, 2011, 01:07:51 am
Quote from: Dark Weaver on September 19, 2011, 12:48:32 pm
To interpret the number, you can say that winning a game always give 3 spins, so in 3×n spins you expect to win 3×n×y% cards, which is equivalent to say : in n winning game you expect to win n×(3×y%) ; and with n=1, you have the meaning of the number, 3×y% is the number of cards you expect to win in 1 game (which obviously has nothing to do with a probability).
Suppose a FG has a 60% probability to drop a card in 1 spin :
you win on average 0.6 cards per spin
you win on average 1.8 cards per game
In the first case the probability is equivalent to the number of cards wins because 0.6 = 0×0.4 + 1×0.6 , for the second case 1.8 = 0×(0.4)³ + 1×(0.4)²(0.6)×3 + 2×(0.4)(0.6)²×3 + 3×(0.6)³
And putting 1.8 in % (180%) has no sense, you can just put 180 for the average in 100 games.
This is wrong.
This probability distribution is called Binomial:

If your probability of success is p=0,6; and you have 3 oportunities then:

B(p=0,6/n=3/r=?) = (r/n) * p^r * (1-p)^(n-r)

r=1 means the chances of winning only 1 card in 3 spins; the r/n = r!/(n-r)!
Which explains the different sorting: (w=win, f=failure)
w.f.f - f.w.f - f.f.w

r=2 means the chances of winning 2 cards in 3 spins:
w.w.f - w.f.w - f.w.w

r=3 means the chances of winning 3 cards in 3 spins:
w.w.w

r= means the chances of winning 0 cards in 3 spins:
f.f.f

B(r=0) + B(r=1) + B(r=2) + B(r=n=3) = 1 (sum of all probabilities).

The chances of winning AT LEAST 1 card would be:
 B(r=1) + B(r=2) + B(r=3)
Which is the same as:
 B(r=1) + B(r=2) + B(r=3) =1-B(r=0) =
Title: Re: Drop rates and deck selection
Post by: Dark Weaver on September 27, 2011, 02:19:09 pm
I don’t know what you are trying to say nor what is wrong for you, also I know what a Binomial distribution is.
If you want me to be more explicit :
1.8 cards = 0cards × (probability to win 0 cards) + 1card × (probability to win 1 card) + 2cards × (probability to win 2 cards) + 3cards × (probability to win 3 cards)
this is not a probability, probability distribution or whatever, it is the average number of cards won per game (or 3spins)
And yes, (probability to win x cards) is a Binomial distribution so what ? we can say that the expected value is n×p (n is the number of experiments and p the probability for a success) which in this case is 3 × 0.6 or that the expected value is the sum of the expected value of the n Bernouilli trials in this case 0.6 +0.6 +0.6
I used the old fashion Expected value definition, and it is plainly correct.

Title: Re: Drop rates and deck selection
Post by: Bhlewos on September 29, 2011, 05:16:35 am
Dunno if it might help, but I used Xeno's XenoSim (http://elementscommunity.org/forum/index.php/topic,31602.0.html) to calculate droprates, and got these results (http://elementscommunity.org/forum/index.php/topic,31106.msg427170#msg427170).

So according to runs of 10k each, the 5 FGs with the highest droprates are Divine Glory, Decay, Octane, Jezebel, and Akebono. Make of that what you will.
blarg: