You are playing a simplified version of poker with a friend. The game only has 3

Question

You are playing a simplified version of poker with a friend. The game only has 3 cards in play at any time: a 1, 2, and 3. Larger numbers win. First, two cards are randomly chosen from the deck of 3, one is given to you and one is given to your friend. You go first. Your friend is forced to put 1 dollar in the pot. Now, you can either fold or raise. If you fold, your friend wins. If you raise, you must put 2 dollars in the pot. Now your friend can either call or fold. If your friend folds now, you win. Otherwise, the person with the larger number wins. If both players play optimally, what is your expected winnings from the game?

Explanation / Answer

The game only has 3 cards in play at any time: a 1, 2, and 3.

two cards are randomly chosen from the deck of 3

Probability: 3 C 2

friend is forced to put 1 dollar in the pot

Prob:3C1

you can either fold or raise

Fold: Friend has larger (3C1)

Raise: put 2 dollars in the pot.

friend can either call or fold.

Prob:3C1

Fold:You are larger

Prob of win optimal: ((3C2)*(3C1)*(3C1)/(52C3) = 9/22100

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