2. Draw Poker

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TWO MEN PLAY a game of draw poker in the following curious manner. They
spread a deck of 52 cards face up on the table so that they can see all the cards.
The first player draws a hand by picking any five cards he chooses. The second
player does the same. The first player now may keep his original hand or draw
up to five cards. His discards are put aside out of the game. The second player
may now draw likewise. The person with the higher hand then wins. Suits have
equal value, so that two flushes tie unless one is made of higher cards. After a
while the players discover that the first player can always win if he draws his
first hand correctly. What hand must this be?

The ANSWER

There are 88 winning first hands. They fall into two categories: (1) four tens
and any other card (48 hands); (2) three tens and any of the following pairs from
the suit not represented by a ten: A-9, K-9, Q-9, J-9, K-8, Q-8, J-8, Q-7, J-7, J-6
(40 hands).

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