How to make the best possible rare farm deck

[Selenbrant]

Ok that means the spinning wheel draws 5 cards and it will not draw the first 10 pillar and only 4 of the 5 drawn cards will spin?

Just a question to be able to calculate it:
Is it sampling with or without replacement?
 

....
3 different cards = 23.2% winning chance
2 different cards = 52% winning chance
...

I assume its not correct without calculating it. Just 3 different cards can be 3/1/1 and 2/2/1 and 2 different cards can be 4/1 and 3/2.
And I dont know whether its so easy to calculate.

The combined with the original post in this thread seemed like a good starting point.  So I started with a 24/6 deck cuz the math should be the simplest.

With 10 chances per variable of finding the rare, there should be a (24/30)^10 = 10.7% chance of a pillar and a 89.3% chance of finding a rare.

The fact that there are four variables rather than three or five is irrelevant, I think.  There's a 89.3%^3 = 71.1% chance of winning a rare per spin.  Chriskang says 33.8% so obviously my math is wrong.  Little help, anyone?

@Kevkev
Its not so easy to calculate or rather its complex.

1.
At least I would calculate first, how high your chance for each possible "shortlist"(5cards) is(18pillar/6rare1/6rare2):
1. 5pillar/0rare1/0rare2 = ohh small 0.000526%(without replacement)
2. 4pillar/1rare1/0rare2 = ....
3. 4pillar/0rare1/1rare2 = ....
4.  ...

2.
After that I would calculate the chance for each "small shortlist"(4cards):
For example 3/1/1 can be 2/1/1, 3/0/1 and 3/1/0 after taking 1 card away.

3.
Then I would calculate the chance for every "small shortlist to win one of each card"
For example 4/0/0 = 100% to win pillar

4.
That means 5/0/0 has an 0.000526% to appear and a 100% to win a pillar, thus you have a 0.000526% to win a pillar. If you sum all the cases up you get the total chance, but there are much cases....


I need to know whether its sampling with or without replacement to answer this question.
And the spinning wheel only has "10 fails" in total?

In this calculating I assume its without replacement, thus if the spinning wheel draws a pillar first there are only 23/6 left when drawing the next card:

1.

rares	pillars(pillars really in spin)	case	chance
0	15(5)	5/0	0,8429%
1	14(4)	4/1	7,5862%
2	13(3)	3/2	24,1379%
3	12(2)	2/3	34,8659
4	11(1)	1/4	24,1379
5	10(0)	0/5	7,5862
			=99,157%

Its hypergeometric: 15 cards(10 fails + 5) drawn and chance to draw 15/0; 14/1, .....
Its only 99,157% total, because 9/6 isnt possible.

Now you just need to look what happens if you take one card away:

shortlist	2. small shortlist1	3. chance to win rare	3. chance to win pillar	2. small shortlist 2	3. chance to win rare	3. chance to win pillar	4. chance to win pillar in total	4. chance to win rare in total
5/0(0,8429%)	4/0	0%	100%				0,8249%
4/1(7,5862%)	4/0(20% of 7,5682%= 1,51%)	0%	100%	3/1(80% of 7,5862%)	....	...	+1,51%+....	...
....	...	..	...	..	..	...	...	...
...	...	...	..	..	..	..	=total chance pillar	=total chance rare

I think its just too much work.

[venumuse]

This is great, hopefully all farm decks will follow this procedure.

[Zuphix]

I saw a farm deck once using 6x morning star and 24x pendulums of different elements. I won the morning star on all 3 spins, this makes me think that you cannot win pendulums on a spin (they could be relics or I was just lucky), so could someone test this, or confirm if this is true of false? If true, you would get a 300% chance to win with 1 rare.

Edit: recently I won some pendulums from a spin, unfortunatley this idea is false.

Edit 2: It turns out the cards I thought were pendulums were actually marks, and even though there is a small chance to win them, I ended up getting 3 morning stars.

[Immolation]

Thanks for the headache.  ???

[Toimu13]

Wow, I don't even know how you all got these numbers, but great job!

[Blues]

What exactly is meant with "card type", the element?

[Dark Weaver]

Hi,
I've already posted the decks drop rates for the False Gods, so if you want more explanations check the thread in the False God section.
I'll make 5 farm decks and compute their drop rates. DxPyRsRt... stands for Deck N°x with y Pillars, s Rare1, t Rare2, ...
Here are the 5 decks:
D1P24R6

Code: [Select]

4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vd 4vd 4vd 4vd 4vd 4vdD2P18R6R6

Code: [Select]

4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vd 4vd 4vd 4vd 4vd 4vd 4ve 4ve 4ve 4ve 4ve 4veD3P12R6R6R6

Code: [Select]

4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vc 4vd 4vd 4vd 4vd 4vd 4vd 4ve 4ve 4ve 4ve 4ve 4ve 4vf 4vf 4vf 4vf 4vf 4vfD4P6R6R6R6R6

Code: [Select]

4vc 4vc 4vc 4vc 4vc 4vc 4vd 4vd 4vd 4vd 4vd 4vd 4ve 4ve 4ve 4ve 4ve 4ve 4vf 4vf 4vf 4vf 4vf 4vf 4vg 4vg 4vg 4vg 4vg 4vgD5R6R6R6R6R6

Code: [Select]

4vd 4vd 4vd 4vd 4vd 4vd 4ve 4ve 4ve 4ve 4ve 4ve 4vf 4vf 4vf 4vf 4vf 4vf 4vg 4vg 4vg 4vg 4vg 4vg 4vh 4vh 4vh 4vh 4vh 4vhObviously you can change the 'rare' cards with whatever 'rare' you want, same goes for pillars.
Be aware that Nymphs and Marks will turn to Relics, and upgraded cards will be downgraded.

First table shows the probability to win at least 1 rare card from the specific Deck, 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 Deck with 1 try or 3 tries ; the first data is the probability the card will be choosen for the reel.

DeckName	P(win a rare card) in 1 spin[%]	P(win a rare card) in 3 spin[%]
D1P24R6	71.91141071	97.78389781
D2P18R6R6	42.84241195	81.32667388
D3P12R6R6R6	29.15192321	64.43816221
D4P6R6R6R6R6	22.65622880	53.73250018
D5R6R6R6R6R6	15.20000000	39.01998080

D1P24R6     

D1P24R6	P(choose card)[%]	P(win card) in 1 spin[%]	P(win card) in 3 spin[%]
Amethyst Pillar	13.42177280	1.94284015	5.71601497
Maxwell's Demon	86.57822720	71.91141071	97.78389781

D2P18R6R6   

D2P18R6R6	P(choose card)[%]	P(win card) in 1 spin[%]	P(win card) in 3 spin[%]
Amethyst Pillar	1.00776960	0.06873673	0.20606848
Maxwell's Demon	49.49611520	21.42120598	51.48052670
Abomination	49.49611520	21.42120598	51.48052670

D3P12R6R6R6

D3P12R6R6R6	P(choose card)[%]	P(win card) in 1 spin[%]	P(win card) in 3 spin[%]
Amethyst Pillar	0.02621440	0.00164227	0.00492672
Maxwell's Demon	33.32459520	9.71730774	26.41089784
Abomination	33.32459520	9.71730774	26.41089784
Purple Dragon	33.32459520	9.71730774	26.41089784

D4P6R6R6R6R6

D4P6R6R6R6R6	P(choose card)[%]	P(win card) in 1 spin[%]	P(win card) in 3 spin[%]
Amethyst Pillar	0.00005120	0.00000320	0.00000960
Maxwell's Demon	24.99998720	5.66405720	16.04789645
Abomination	24.99998720	5.66405720	16.04789645
Purple Dragon	24.99998720	5.66405720	16.04789645
Dissipation Shield	24.99998720	5.66405720	16.04789645

D5R6R6R6R6R6

D5R6R6R6R6R6	P(choose card)[%]	P(win card) in 1 spin[%]	P(win card) in 3 spin[%]
Maxwell's Demon	20.00000000	3.80000000	10.97228720
Abomination	20.00000000	3.80000000	10.97228720
Purple Dragon	20.00000000	3.80000000	10.97228720
Dissipation Shield	20.00000000	3.80000000	10.97228720
Lycanthrope	20.00000000	3.80000000	10.97228720

As you can see, a deck with 24 pillars and 6 rare of the same type gives you 71.9% chance to win the rare with only one spin! this gives a 97.8% chance to win at least one rare from the 3 spins.
If you choose the 12 pillars and 2 X 6 rare deck then the chance to win a rare card in 1 spin drops to 42.8% , this gives a 81.3% chance to win at least one rare from the 3 spins.
Deck1 is better for gaining a specific card but Deck2 is a good compromise to make more versatile farm decks. Deck1 on the other hand gives more winning cards than deck2.

[Chromatophore]

Is there any consensus about which card distribution gives the best drop rate?  Some people seem to be saying 18/6/6 gives more rares per spin while others advocate 24/6

[Rastafla]

Is there any consensus about which card distribution gives the best drop rate?  Some people seem to be saying 18/6/6 gives more rares per spin while others advocate 24/6

The RNG behaves very strange at times. I find it very rare that anyone would wins stuff from 12/6/6/6 farms or larger decks at all consistently. I never did. Personally i win just as much from 18/6/6 as from 24/6 just that in the later I know what i will get. Also Dark Weavers excellent numbers and testing shows large amount of games and specific decks, while the normal player doesnt do many games NOR is able to pick which he wants to fight so the general consensus (I preume) is that the "best" is either 18/6/6 or 24/6. Here the normal player will have a high chance of winning a card without spending HOURS and several hundreds to thousand games just to find the farms he/she needs. Personally i racked up between 1300-1800 losses just from quitting vs the t50 to reroll farms in the first month of playing 1½ year ago.

I would put it like this. If you want to spread rares and help multiple people go 18/6/6, this allows more people to get 2 types of rares and make more of them show up in the population of players. If someone requests a specific rare go 24/6, this will benefit just him though.

Hypothetically:
The best thing is probably having 15+ people do 24/6 farms with each one focusing on one rare. This would be best for someone with lots of time to farm t50.
I personally would prefer all those people to pick 2 rares each so that at least 2 people in t50 had the chance for the same rare. So that all casual player have a good chance to hit one during an hour or two.

[Chromatophore]

The statistical complexities behind all this are pretty intriguing.  Nevertheless i would never have thought to invest the time and energy to figure out so many of the details.  If it weren't for the work of chriskang, darkweaver and everyone else who has contributed here, i imagine  i would still be naively putting up 6/6/6/6/6 farms.

So to everyone who has helped make the dissemination of the rare cards a much more streamlined and painless process, thank you!  : D