I thought I should explain that I don’t actually believe that I can create a betting strategy that will allow me to beat the house. Gambling can be a real problem for some and I don’t want to encourage the idea that there exists any way to beat the odds of roulette.

Rather than go into the details of gambler’s ruin, I’ll reference the explanation on the Wikipedia page here. The odds of winning an outside bet on a 38 position roulette wheel are 18/38, since 0 and 00 are not red, black, even or odd.  I tried arguing that 0 is even with the croupier, but that didn’t change anything. This means that we are not playing a “fair” game.  Fair games in gambler’s ruin come out to who has the highest bankroll has the highest probability of winning.  In the notation of a random walk, , Let where the minimum bet is $10. Now if cannot go negative (no borrowing) the game is over so, .

This explains how the game makes money for the casino- by eventually taking all of the money.  What if an individual plays a limited number of games?  Certainly, ruin is still a possibility with a martingale strategy since the exponentially increasing bets could easily exhaust the bankroll a regular individual would stake in only a hand full of games.  A large number of individuals playing a small number of games is no different to the casino than an individual playing a large number of games (independence of the events).  Some are winners and most are losers.  How can I decide on the bets to place, the number of games to limit myself to and how much should I stake? These are the decisions that I must make.  Whatever strategy I decide upon, if a large number of people employ it, the casinos will be very happy because they will take a large number of people’s money.