Variance
Variance is a measure of how far results are spread around their average, worked out as the average squared distance from the expected value.
Variance is the maths behind volatility. Take every possible result of a bet and measure how far each is from the expected value. Square those distances, then average them, weighted by how likely each result is. A bigger number means a wider spread. The square root of the variance is the standard deviation, which is in the same units as your bet.
Example. Stake 1 on a dice game with a 99% RTP. At 2x you get back 2 with a 49.5% chance, otherwise 0. The variance is 0.495 × 2² − 0.99² ≈ 1.0, so the standard deviation is about 1. At 100x you get back 100 with a 0.99% chance. The variance is 0.0099 × 100² − 0.99² ≈ 98, so the standard deviation is about 9.9. Same average, about ten times the swing.
What people get wrong. Players say "variance" to mean bad luck. It is not a force and it owes you nothing. It describes spread in both directions and does not change the expected result. It tells you how big a bankroll you need to last, not whether you will win.
Related terms
- Volatility
Volatility is how much a game's results swing around its average, from small frequent wins at the low end to rare large wins at the high end.
- Expected value (EV)
Expected value (EV) is the average result of a bet if you could repeat it a huge number of times, found by weighting each possible outcome by its chance.
- Bankroll
A bankroll is the fixed amount of money you set aside for gambling and can afford to lose, kept separate from the money you need to live on.
- Gambler's fallacy
The gambler's fallacy is the mistaken belief that a random result is more or less likely to happen because of what happened in earlier rounds.