Does martingale player strategy work?

For sure you have heard of the martingale strategy in roulette game? You bet on even money bets and if you loose you double the bet for next round until winning. The loosing streak must end sometime for sure. And when it does you have advantage over the casino - in the height of the starting bet. Right?

All that sounds interesting. But let me ask you what is the expected house edge of roulette game if you play martingale strategy? Is it lower than normal 2.7% (single zero roulette) or does the player even have an advantage? The martingale strategy assumes the player has unlimited bankroll. If this would be true and there would be no bet limits, the strategy would work.

But the assumption of no limits is wrong! The casino limits players highest bet. Even if they did not, the player would eventually run out of money. It is surprisingly easy to come up with a long loosing streak - long enough to hit the limits. And when this happens the player looses. And he looses a lot!

The RTP stays the same!

The remaining question is what is the house edge in case of such player strategy. It turns out the house edge does not change at all - it is still 2.7% per game on average! The difference is that the distribution of winning and loosing changes. There are a lot of cases where players win a small amount but there are also some cases when players loose a lot. These loosing cases make up for all the winning cases and give the casino the house edge.

The distribution of winning and loosing cases is the definition of volatility. The only thing that changes with this strategy is the volatility of the bets. In general casinos do not like high volatility. It increases the probability that the casino could be loosing money in the short term. Nevertheless in the long term the casino is always winning the money.

Should martingale players be banned?

You might argue that the casinos should limit the use of martingale strategy exactly because of this increase of volatility. Yes, the volatility of the martingale strategy is higher than volatility of a normal play. But on the other hand it is quite lower than volatility of a player playing the maximum bet all the time (on the same even money bet). It also quite lower than a player playing the straight number bet with the same bet amount. For the exact data see the table below. 

So do not fear the martingale strategy as it does not work. If a player is playing this strategy he is bringing your casino profit in the long run.

Table of volatility of bets:

For more information how to get to those numbers you can also look at my article on mathematical analysis of martingale strategy.