A game theoretical question...
I haven't seen a good math discussion in here for a while so I thought I'd try entertaining you all with this little tid bit.
My question involves a card game. There are nine cards, face up, valued 1 through 9. There are two players and they alternate picking cards from this list. Their goal is to have exactly three cards (out of the cards that they have chosen, of which there may be more than three) that sum to 15. The first one to do so, wins.
So, it is a finite, perfect knowledge game.
The question is this. Does there exist a winning strategy for this game? In other words (in case you're unfamiliar with game theoretical terms), can either player guarantee that they will win, regardless of what the other player does?
What do you think? Why?
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