1 The game of poker You are given 5 cards (this is 5-card stud poker) The goal is to obtain the best hand you can The possible poker hands are (in increasing order): –No pair –One pair (two cards of the same face) –Two pair (two sets of two cards of the same face) –Three of a kind (three cards of the same face) –Straight (all five cards sequentially – ace is either high or low) –Flush (all five cards of the same suit) –Full house (a three of a kind of one face and a pair of another face) –Four of a kind (four cards of the same face) –Straight flush (both a straight and a flush) –Royal flush (a straight flush that is 10, J, K, Q, A)

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Game Night Project! -Work with a group of 3-4 -Keep in mind: you must take into account all the possibilities for each type of hand *If it helps, write out some combinations -You will have multiple combinations for every type of hand (remember to multiply them!) -Take into account the number and suit of each card 3

Recall from yesterday… Choice of card # for pair Choice of suits for pair Choice of card # for others Choice of suits for others

5 Poker probability: royal flush What is the chance of getting a royal flush? –That’s the cards 10, J, Q, K, and A of the same suit There are only 4 possible royal flushes, so 4 C 1. Possibilities for 5 cards: 52 C 5 = 2,598,960 Probability = 4/2,598,960 = –Or about 1 in 650,000

6 Poker probability: high card What is the chance of getting a high card hand? –A hand of cards ranked by the highest number Since the number showing for the cards must all be different, we have to pick 5 different numbers from a choice of 13 numbers. So, 13 C 5 Also, each card can have any of the four suits So, 4 C 1 * 4 C 1*4 C 1*4 C 1*4 C 1 Multiply everything together to get your possibilities! Then, divide by the total possible 5 hands in a deck to get your probability!

Some things to keep in mind as you work… -Does the hand involve having the same suit, same number, or both? -Once you’ve found the possibilities for what’s needed in a hand, what is left over for the remaining cards? (i.e.- in a 3 of a kind, you need to figure out how many 3 of a kinds you can get, but also have to account for the remaining 2 cards in the hand) -To find the probability, always divide your total possibilities for the hand by 52 C 5 !! 7

Poker hand odds The possible poker hands are (in increasing order): –Nothing1,302, –One pair1,098, –Two pair123, –Three of a kind54, –Straight10, –Flush5, –Full house3, –Four of a kind –Straight flush –Royal flush