The Poker Game

by Kevin J. Lin

A card shark offers to play you in a round of poker. Knowing of his reputation, you decline (he has been known to use marked cards in the past). Persisting, he offers a variation which would eliminate the possibility of cheating. The game will be played with standard five-card draw rules, but instead of drawing from a shuffled deck, all the fifty-two cards will be laid face up. Whenever it is time to draw, you simply pick the cards you want from the remainder of the stack.

"This doesn't sound like a very interesting game," you observe.

"Well, I'll wager twenty dollars I can beat you, even with you picking your cards. And I'll let you go first."

The rules are standard five card draw; no jokers, wildcards, or bugs. Draws result in a re-ante and deal-off (all cards returned to the deck) with change of first player. The first player draws five, then the second. (We'll skip the betting) The first player may then discard up to three cards, or four if the last card they are holding is an ace, and fill their hand from the remaining deck. The second player then does the same. At this point, the best hand collects the pot. Apart from these distinctions, hand values are standard (See The rec.gambling.poker FAQ for a refresher).

Now back to the game: Should you accept this bet?

See the Solution