Variance (volatility) of games of chance

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To put it simply, the variance (also known as volatility) of a game determines how rapidly your bankroll is changing when you play the game:
  • You often win small winnings when playing a game with low variance. In this case, your bankroll changes quite evenly, although, unfortunately, usually downwards.
  • In the case of a high-variance game, you lose in a vast majority of rounds, but when you win, you win high. Gradual drop-downs are, from time to time, replaced by a big gain.
Variance of the game can also be described by the statistical distribution of winnings. As they are usually proportional to the bet size, we are talking about the distribution of winnings expressed as a multiple of the bet. When betting on a color in roulette, all winnings are paid out as double of the bet. When betting on a single number, all winnings are paid out as 36-times the bet.

The variance of slots is a bit more complicated. You can hit many various winning combinations and win many different multiples of your bet. Due to this, it's not that simple to describe slot variance by one number, and game providers only use loose descriptions like "small", "medium", and "high" for their slot machines.

The variance of games with bitcoin significantly impacts your chance to walk away from a casino as a winner. The rule of thumb is "The higher the variance is, the better":
  • The first reason is that in a game with high variance it's easier to win the amount that satisfies you in one game round.
  • The second reason is that more rounds end up with a loss, so you don't bet that much from your previous winnings (which negatively impacts the RTP of your betting system). In other words, you lose more quickly.
  • The third reason is that if you can win a higher multiple of the bet, you can bet less to have a chance to win the same amount. This, again, reduces the total sum of your bets and therefore also reduces your long-term losses.
Just to illustrate, let's assume a game with no variance and 99% RTP. In this game, a 1€ bet would pay out 0.99€. The outcome of each round would be determined and winning in this game would be impossible. Of course, no one would like this game, but it illustrates the fact that a high RTP is not all that matters.