[QuikSand]

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.


There probably is an optimal strategy to maximize your EV from a single iteration of this game -- perhaps your EV is greater is you want until you are +$2, for instance. You'll get there a smaller share of the time, but you'll win more in each win, of course. At some point, the gains from added winnings per win will be offset by the reduced share of the time that you will get that far ahead. The cutoff would probably also be dependent upon the number of cards left, as well. Stopping at +$1 with 51 cards to go may not be optimal, but stopping at $1 with 1 card left clearly is.

I suspect the exact calculation of such is possible... but it's beyond me at the moment. The framework, though, isn't that tough.