cute Gardner problem involving pseudo-poker

[gumpzilla]

I saw this problem last night flipping through an old Martin Gardner book. I don't think it's very hard, but it's kinda fun, and I'll present a slightly more open-ended version of the question.

Two players A and B agree to play a game. They spread a normal 52 card deck face up. Player A first draws five cards, and then player B draws five cards. Following the initial draws, player A may discard any number of his cards that he chooses and draw from the remaining unchosen cards; his discards are out of play. Player B does likewise.

Does either player have a winning strategy? If so, what is it?