Q: If you double your bet every time you lose, won’t you eventually win and come out ahead?

Q: If you double your bet every time you lose, won’t you eventually win and come out ahead?

This system sounds like a clever way to beat any game: just place larger and larger bets, to cover all of your previous loses and a little more, because eventually you’ll win. That way if you win, you’ll recoup your 1 chip loss and come out 1 chip ahead. If you lose again, you’re down 3, so by doubling your bet again (4 chips), you might recoup your net loses and come out 1 chip ahead. After n rounds you’ve bet chips (you can add this up easily because it’s a geometric series). On the first round you bet one chip, on the nth round you bet chips, and if you win on the nth round, you’ll earn f times your last bet, .

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