What Is Variance and Why It Matters in Gambling

Expected value (EV) is the number most people focus on in probability and gambling. Positive EV means you profit on average; negative EV means you lose. But EV alone is incomplete. It tells you the destination without describing the journey. Variance tells you about the journey.

What variance measures

Variance measures how spread out outcomes are around the expected value. High variance means results are scattered widely — you might win big or lose big. Low variance means results cluster tightly around the average.

Variance = E[(X - μ)²]

Where μ is the expected value.
Standard deviation = √Variance

High SD = outcomes spread widely from average
Low SD  = outcomes cluster near average

Two games with identical EV, different variance

Consider two games, both with an expected value of -$1 per round:

Game A: You lose exactly $1 every time. Zero variance.

Game B: You win $99 with probability 1% and lose $2 with probability 99%. EV = -$1, but results range from +$99 to -$2.

Mathematically equivalent in expected value. Completely different experiences. Most people would prefer Game A for consistent small stakes. Some prefer Game B for the chance of a large win. Neither preference is irrational — they reflect different risk tolerances.

Variance in casino games

Different casino games have dramatically different variance profiles. Baccarat on the banker bet has low variance — the house edge is small and outcomes are near-50/50. Slot machines with large jackpots have extreme variance — most spins return nothing and rare spins return thousands.

Bankroll requirements and variance

High variance games require larger bankrolls to survive losing streaks long enough for the edge to assert itself. This is the practical implication. A poker player with a small edge needs a bankroll of hundreds of buy-ins to reduce their probability of ruin to near zero. A card counter with a 1% edge over the casino needs a large enough stake to weather the inevitable negative swings.

Variance is not luck

Casual language often calls variance "luck." This framing is misleading. Variance is a mathematical property of a probability distribution — it is predictable, calculable, and unavoidable. What appears to be a lucky streak is a normal statistical fluctuation above the mean. What appears to be bad luck is a fluctuation below it. The probability explorer lets you visualise how variance changes with sample size — and how even extreme-seeming results often fall within expected bounds.