The Poker Problem

Two players play draw poker as follows: all the cards are turned face up. The first player selects any five cards she wishes. the second player then selects any five of the remaining cards. the first player then discards as many as she chooses (all five, if she wants) and replaces her discards with any of the remaining cards she chooses. the second player does likewise. Which cards should the first player choose to insure a win? (normal poker hands apply.)

Questions from Sean B.:

[Do you] HAVE to discard at least one card? No.
Once a card is discarded, it is no longer in play? (as in poker?) That's right.
What is the order of suits in poker? There is no rank of suits in poker. You must win, i.e. do better than a tie.
Do you know where my mommy is? No.

Solution