The math behind gambling systems (and why they don’t work)

We’ve all been there- you’re thinking how best to place those last few roulette chips. You’ve lost two or three in a row so it’s now vitally important you place your bets smart. You’ve bet black the last few times and it’s always been red so what do you do?

Your gut will probably say “put it on red” but here’s the thing: there is not a single reason why that ball is more likely to land in red now than it did the last three times.

This is the peril of just about every game, they are all designed to rely on luck and nearly all of them have a house edge built into them (except for games where you play against other people so if your game is poker online then, congrats! The odds are slightly better for you). This is important because just about every gambling system relies on the idea that this isn’t the case, so let’s get into the numbers and talk about the Gambler’s Fallacy a little.

The Gambler’s Fallacy, otherwise known as the fallacy of maturity of chances, is the belief that prior events will affect future outcomes. Or another way, if something happens more frequently than normal during a given period, it will happen less frequently in the future. To go back to our first example of the roulette wheel, if the ball lands on black three times in a row, then the belief that it next needs to land on red in order to ‘balance’ out. Another name for this is the Monte Carlo fallacy because a perfect example of this occurred in 1913 in Monte Carlo, a roulette wheel was spun and landed on black not two or three times but twenty-six time in a row. Gamblers lost millions of francs betting against black as they expected it to go red with every spin.

How does this relate to gambling systems you ask? Well, it’s because just about every system will rely on past events dictating future ones. These systems tend to come in two flavours, either you raise when you win or when you lose. The Martingale is the most famous example of these, born in France, the system says every time you lose you double your stake and go again. In the traditional example, the gambler has to call heads or tails for a coin toss. As the toss has approximately 50:50 odds then eventually the coin will land on what you call and you’ll win all your money back. Technically, this is correct, if you have infinite money and infinite time then the coin landing on the side you called is very nearly a certainty. The problem being you don’t have infinite time, you don’t have infinite money and the odds are unlikely to be a straight 50:50 so there’s no guarantee you’ll get the result you need before you go bust.

Which isn’t to say these systems can’t be helpful, it’s just that they aren’t going to dramatically shift the odds in your favour. They might even pay off, short term, but it’s going to be through luck rather than the system.