My friend has gotten into an argument with me about betting in roulette. He believes betting 1 unit on zeroes (1/19 chance in the long run) and then DOUBLING (lol martingale) every 19 spins would yield a profit. He argues the a computer is never 'truly' random and is bound to hit 0 eventually (ala Gambler's Fallacy). The flaw in this is that at our particular casino, roulette pays 0's out 18 to 1 and I told him that. His rebuke was to instead double your bet every 18 spins instead then. Is anyone able to run this through a simulator and produce some numbers? Thanks in advance.

The problem with a system like this is it will work the vast majority of the time, so it is hard to disprove. If you bet one unit for the first 18 spins, and two units for the next 17, then three for the next 16, the chances of you hitting a zero once in that sequence are extremely high. The problem is that eventually you will hit a sequence that zero does not come up and you'll lose your shirt. Can a wheel go three hundred spins without hitting a zero? Of course. Will it? Eventually.