Jackie A.

asked • 10/15/20

Probabilty of matching hand to dealer's hand

Hey, so I have to make this gambling style game for a math project and I need some help finding the probability distribution.

The way the game goes is the dealer takes 3 cards from a 52 card deck for himself and deals 5 cards to each player. For this scenario let us say there's only one player for simplicity's sake.

The dealer flips over his 3 cards and the player wants to match three different cards to the dealer's cards. they can be matched by same suit or same number, but two player cards can't be matched to one dealer's card.

Right now I'm trying to find the probability of:

0 of the cards matching the dealer's

1 card matching the dealer's

2 cards maching the dealer's

3 cards matching the dealer's

I have absolutely no idea how to do this, and I probably bit off more than I can chew. I'm looking for the formula I can use to find these probabilites.

I also need to find the expected value of the game to the dealer and the player if you could help out with that too. Thanks!

Tom K.

I would break the 3 cards into cases, find the probability of each case, and figure out the probability of the different number of matches with each case. The cases are: 3 cards of the same rank 2 cards of the same rank and the third card of the same suit as one of the first two 2 cards of the same rank and the third card of a different suit 3 cards of the same suit 2 cards of the same suit and the other of a different suit (all different rank) 3 cards of different suit and rank If, after figuring out the probability of each of these cases, you are having trouble finding the probability of 0, 1, 2, and 3 match, you could select a particular set of cards meeting the case requirement, then loop through the C(49,5) possible selections of the other hand. I think doing this problem with either ranks or suits would have been enough.
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10/16/20

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