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February 2nd, 2012, 07:46 AM   #1
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Combination Probability Problem

My deck of cards has 23 cards in it. The deck has 6 F cards, 5 E cards, 4 D cards, 3 C cards, 2 B cards, 1 A card and 2 WILD which are the card they are played with. The game is played by laying down multiples of the same card: if 2 F cards are played, it can be beat by 2 Es, 2 Ds, 2 Cs, 2 Bs, or 2 As (one would have to be a WILD, since there is only 1 A in the deck). The object is to get rid of your cards before the other players..

The deck is shuffled and dealt out to 3 players.


Let just take a single play as an our problem. Player1 goes first and would like to lay out 3 E cards. Looking at the card spread we can see that the other two players cannot beat that play, but he doesn't know that and would like to know the probability of that play winning the trick.
I tried starting on the problem by finding how many combinations of hands there are with an 'n' choose 'm' equation.
(n+m-1)!/((n-1)! * m!)
But I don't think this equation quite cuts it because the 'n' is variable based on the type.
Would 'n' = 23 or does 'n' = 7 (the number of distinct card types)
If 'n' is 7 how do limit the number of times a card type is repeatable in a combination?

Any help moving me in the right direction will be very much appreciated!
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February 2nd, 2012, 10:00 AM   #2
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Re: Combination Probability Problem

Is there a way to calculate Combination with conditional replacement?
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