One betting system for roulette is to bet ($ 1) on black. If black comes up on
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One betting system for roulette is to bet \(\$ 1\) on black. If black comes up on the first spin of the wheel, you win \(\$ 1\) and the game is over. If black does not come up, double your bet \(\$ 2\). If you win, the game is over and your net winnings for two spins is still \$1 (show this). If black does not come up, double your bet again (\$4). If you win, the game is over and your net winnings for three spins is still \(\$ 1\) (show this). Continue in this doubling procedure until you eventually win; in every case your net winnings amount to \(\$ 1\) (show this). What is the fallacy with this betting system?
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