Variance, explained.

Why results wander

Imagine two games with the same 4% house edge. One usually returns 80 or 120 cents on a $1 wager. The other usually returns nothing but occasionally awards a very large prize. Their average value can match while the second produces much wider short-term swings.

Variance measures squared distance from the average. Its square root, standard deviation, is easier to interpret because it uses the same units as the result. For independent identical wagers, expected loss grows in direct proportion to the number of wagers, while standard deviation grows roughly with the square root of that number.

Volatility changes the experience, not the average

High volatility generally means a greater chance of both large wins and rapid losses over a limited sample. Low volatility usually means smaller, more frequent movements. Neither label alone tells you which game has the better return.

Risk of ruin

A finite bankroll can be exhausted before long-run averages become visible. Risk of ruin rises with larger wagers, higher variance, longer play, and a more negative edge. There is no universal “safe” bankroll because the answer depends on the game’s outcome distribution and the player’s acceptable failure probability.

Common interpretation errors

• A long losing streak is not evidence that a win is due.
• A recent jackpot does not make another one less likely in an independent game.
• Observed volatility over a few sessions is not a reliable estimate of the full distribution.
• Reducing variance does not necessarily reduce house edge.

Use RTP or house edge to compare average cost, then use volatility to judge whether the likely swings fit your budget and purpose. Both dimensions matter, but they answer different questions.