Drop rates and deck selection

[Dark Weaver]

Hi,
You are right, my results are all false… and I’ll now return hide myself in the darkness of the internet  

I’ll redo the maths but it is now a lot more complex.
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.
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)

[10 men]

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.

[Dark Weaver]

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	19.54497444	47.92137235
Chaos Lord	12.89356735	33.90772760
Dark Matter	13.75372136	35.84639060
Decay	20.46983340	49.69679266
Destiny	14.91300910	38.39875418
Divine Glory	22.66568136	53.74946184
Dream Catcher	12.52627943	33.06815495
Elidnis	12.44481157	32.88097162
Eternal Phoenix	18.75004407	46.36239196
Ferox	14.80864655	38.17180698
Fire Queen	16.97168603	42.76276355
Gemini	16.58703397	41.96356960
Graviton	15.62583957	39.93404406
Hecate	18.23674086	45.33937626
Hermes	13.08744858	34.34806996
Incarnate	16.11252189	40.96746743
Jezebel	19.90802065	48.62319653
Lionheart	15.78530951	40.27398067
Miracle	12.58329551	33.19894980
Morte	12.61340860	33.26796040
Neptune	15.69056717	40.07217676
Obliterator	16.05061453	40.83667629
Octane	19.90262959	48.61282117
Osiris	19.07187998	46.99725586
Paradox	16.06351947	40.86395636
Rainbow	12.03220345	31.92758769
Scorpio	12.17924561	32.26837578
Seism	13.99601647	36.38556092
Serket	16.09504455	40.93056276

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

[Jangoo]

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)
81	Akebono	53,09	58,62
73	Chaos Lord	31,51	38,67
69	Dark Matter	40,58	41,25
67	Decay	65,67	61,40
175	Destiny	48,00	44,73
53	Divine Glory	83,02	67,98
50	Dream Catcher	30,00	37.56
100	Elidnis	31,00	37,32
39	Eternal Phoenix	41,03	56,25
70	Ferox	57,14	44,43
106	Fire Queen	51,89	50,91
104	Gemini	40,38	49,74
43	Graviton	46,51	46,86
78	Hecate	41,03	54,69
39	Hermes	38,46	39,24
144	Incarnate	45,14	48,33
58	Jezebel	50,00	59,73
121	Lionheart	38,02	47,34
144	Miracle	32,64	37,74
108	Morte	26,85	37,83
154	Neptune	38,31	47,07
91	Obliterator	46,15	48,15
68	Octane	55,88	59,70
85	Osiris	50,59	57,21
176	Paradox	43,18	48,18
56	Rainbow	30,36	36,09
73	Scorpio	30,14	36,54
80	Seism	38,75	41,97
104	Serket	35,58	48,27

[Xenocidius]

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.

[Jenkar]

*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*

[Jangoo]

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. 

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. 

[Dark Weaver]

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.

[Polari]

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.



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.

[Jenkar]

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)

[10 men]

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.

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

[Dark Weaver]

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.