# Open Poker riddle

On the game of Poker, two people play as follows:

Player 1 takes any 5 cards of his choice from the deck of 52 cards. Then player 2 does the same out of the remaining 47. Then player 1 may choose to discard any of his cards and replace them from the remaining 42. Then player 2 may discard any of his cards and replace them, but he may not take player 1’s discards. ALL of the transactions with the deck are public knowledge, unlike the real game of Poker.

After this process, the winner is the one who has the better poker hand. For the benefit of those who have not played poker, these are the highest ranking hands, in decreasing order of value:

Royal Flush: the A K Q J 10 of the same suit.

Straight Flush: any five consecutive of one suit. Highest card of the five is the tiebreaker. No one suit is more powerful than another.

Four of a kind: all four of one rank (i.e. four aces). A hand with 4 aces outranks 4 kings, etc.

Full house: a pair of one rank and 3-of-a-kind in another rank, i.e. Q Q 8 8 8.

Flush: Any 5 cards of the same suit that don’t satisfy #2.

Because of the clear advantage of player 1, the win is given to player 2 if the hands are equal in strength.

Which player would you rather be? What strategy do you use?

**Take 4 tens**

Obviously if you choose a royal flush, your opponent could match you with one of her own. Picking 4 Aces and a King, say, could be answered by 4 Queens and another card. You could then discard all 5 cards and draw a Jack-high straight flush. But your opponent could beat you with a Queen-high straight flush. If you draw so as to prevent a Queen-high straight flush your opponent stands pat and beats you with 4 Queens.

If you select 4 10’s and another card, the best your opponent can do is a 9-high straight flush. Any selection your opponent makes allows you either a royal flush or a 10-high straight flush.

Other winning combinations are 3 10’s and A-9, K-9, Q-9, J-9, K-8, Q-8, J-8, J-7, or J-6 in the fourth suit.

### Your Answer

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