Smash Vegas

Imagine you’re playing a game where you bet on the flip of a coin against a casino, and the casino gives you even money on the bet. They don’t have a house edge. Even without a house edge, if you play for long enough you will lose all your money.

That might not seem to make any sense, but I’ll explain. Let’s say you’re playing the game for £1 per flip, and you have £100 as a bankroll. For the most part you and the casino will be pretty much even - after all the game has a house edge of zero, so in the long run you don’t expect to win or lose anything. The problem with that is that the longer you play, the more likely you are to get a long enough string of losses (it will take about 100) to make you lose all your money. And once your money’s gone you have nothing to win it back with - the casino has won.

It’s known in probability theory as the gambler’s ruin problem, and it highlights the problem with playing a game against an opponent with much more money than you. You don’t stand a chance of making the casino run out of money, but unless you’re careful to always bet small amounts compared to your bankroll the casino can wipe you out with a run of bad luck. The exact chance of this happening is known as the risk of ruin and in general is pretty tough to calculate. Essentially though it depends on two things - what proportion of your bankroll you bet each game, and what the variance of the game is (in other words how risky it is).

Our game above isn’t very volatile, and £100 is quite a large bankroll for a £1 game. The odds of getting 100 losses in a row is 1/1267650600228229401496703205376, which is very small indeed. Imagine we were playing a £10 version of the same game. The odds of getting the 10 losses in a row we’d need to wipe us out is 1/1024. That might seem small but considering we could easily play over 100 games an hour you can see we’d have a very high risk of ruin if we played for long.

Without going into specific figures, it’s crucial to have a large bankroll in proportion to the bet size, and the more volatile the game is (the bigger the up and down swings) the larger bankroll you should have. What sets apart the pros from the amateurs is having a bankroll that can take the downswings which are natural to any gambling activity.