Changes

*Bet #4: bet $80 on red. If red comes up, you've won $80 - $70 = $10 and the sequence is complete. If black comes up, you've lost a total of $150 so far; make a fifth bet...

*Bet #4: bet $80 on red. If red comes up, you've won $80 - $70 = $10 and the sequence is complete. If black comes up, you've lost a total of $150 so far; make a fifth bet...

and so on. Since red must eventually come up, it appears as if the gambler is '''guaranteed''' to win $10 on each sequence of bets. This would seem to be true even when playing against a "house percentage" (e.g. a roulette wheel with 0 and a 00 slots on which nobody wins), which should make one suspicious.

and so on. Since red must eventually come up, it appears as if the gambler is '''guaranteed''' to win $10 on each sequence of bets.  

 

This would seem to be true even when playing against a "house percentage" (e.g. a roulette wheel with 0 and a 00 slots on which nobody wins), which should instantly raise suspicions.

The flaw in the martingale is the assumption that the series of bets can continue for as long as is needed to reach that eventual win. In fact, the run of bets is limited either by the amount of money the gambler has or by casino betting limits.  

The flaw in the martingale is the assumption that the series of bets can continue for as long as is needed to reach that eventual win. In fact, the run of bets is limited either by the amount of money the gambler has or by casino betting limits.