Re: Single Bet = -EV, Multiple Bets = +EV
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I am 99% sure there is a flaw in the logic here, but my brain is completely fried. The first case looks correct, but I don't see the EV shifting here. In the second case, you have the EV of winning twice and the EV of losing twice, but if you win one & lose one, you lose as well.
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The "flaw", if you want to call it that, is that the scenario posed suggests that the house doesn't take their taxes out every time you win, rather only the cumulative winnings. If the tax is taken out step-by-step for each game played, then it's a negative game all along.
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