Re: Probability question for all you math guys....
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In the long run (playing this game many times), I will win an infinite amount of money.
As soon as I get $1 ahead, I quit the game. I'm ahead $1. That will happen a substantial share of the time -- certainly more than 50% of the time. In the event that I am never ahead by $1, I simply play through the whole deck and break even at the end. It's clearly a +EV game, played properly or even sensibly.
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You're assuming that your opponent will always choose to continue to the end of the deck, which seems unlikely.
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