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Re: Drop rates and deck selection https://elementscommunity.org/forum/index.php?topic=20376.msg281786#msg281786
« Reply #24 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.

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Offline kevTopic starter

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Re: Drop rates and deck selection https://elementscommunity.org/forum/index.php?topic=20376.msg281821#msg281821
« Reply #25 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

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Re: Drop rates and deck selection https://elementscommunity.org/forum/index.php?topic=20376.msg281827#msg281827
« Reply #26 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
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Re: Drop rates and deck selection https://elementscommunity.org/forum/index.php?topic=20376.msg281847#msg281847
« Reply #27 on: March 02, 2011, 08:01:41 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.

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

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.




Re: Drop rates and deck selection https://elementscommunity.org/forum/index.php?topic=20376.msg283241#msg283241
« Reply #28 on: March 04, 2011, 07:11:59 pm »
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.

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Re: Drop rates and deck selection https://elementscommunity.org/forum/index.php?topic=20376.msg283459#msg283459
« Reply #29 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.

Offline Essence

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Re: Drop rates and deck selection https://elementscommunity.org/forum/index.php?topic=20376.msg295350#msg295350
« Reply #30 on: March 21, 2011, 08:14:05 am »
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?
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Offline kevTopic starter

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Re: Drop rates and deck selection https://elementscommunity.org/forum/index.php?topic=20376.msg295425#msg295425
« Reply #31 on: March 21, 2011, 02:19:05 pm »
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

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Re: Drop rates and deck selection https://elementscommunity.org/forum/index.php?topic=20376.msg295882#msg295882
« Reply #32 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. :)
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Re: Drop rates and deck selection https://elementscommunity.org/forum/index.php?topic=20376.msg390968#msg390968
« Reply #33 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?



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Re: Drop rates and deck selection https://elementscommunity.org/forum/index.php?topic=20376.msg391208#msg391208
« Reply #34 on: September 09, 2011, 02:03:38 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?

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.
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Re: Drop rates and deck selection https://elementscommunity.org/forum/index.php?topic=20376.msg391608#msg391608
« Reply #35 on: September 10, 2011, 09:18:59 am »

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?

 

blarg: