The short answer
Variance is the mathematical measure of how much your short-term results will “swing” away from the statistical average. In roulette, high variance means you win or lose big quickly (Straight-Up bets), while low variance means your bankroll drains slowly and steadily (Even-Money bets).
The full calculation
Variance ($\sigma^2$) measures the spread of possible outcomes. For a single bet, it is calculated as: $$\sigma^2 = \sum [P_i imes (x_i - EV)^2]$$
For a $1 bet on a single number (American Wheel):
- $P_{win} = 1/38$, $x_{win} = 35$
- $P_{loss} = 37/38$, $x_{loss} = -1$
- $EV = -0.0526$
$$\sigma^2 = [ rac{1}{38} imes (35 - (-0.0526))^2] + [ rac{37}{38} imes (-1 - (-0.0526))^2]$$ $$\sigma^2 = [ rac{1}{38} imes 1228.69] + [ rac{37}{38} imes 0.897]$$ $$\sigma^2 pprox 32.33 + 0.87 = 33.20$$
The Standard Deviation ($\sigma$) is $\sqrt{33.20} pprox 5.76$.
What this means at the table
If you play $25 chips on Red/Black (Low Variance), your bankroll will likely stay within a predictable range for hours. However, if you play $25 on a single number (High Variance), you are in a “boom or bust” scenario. Over 60 spins ($1,500 wagered), variance is why one player walks away with $3,000 in profit while nine others walk away with $0, despite all of them facing the same 5.26% house edge.
Common mistakes around this number
- Confusing Variance with Edge: Players think a winning streak means they have “beaten the math.” It hasn’t; they are just on the positive side of the variance curve. The 5.26% edge is still there, grinding in the background.
- Overestimating Bankroll: Playing high-variance bets (Single Numbers) with a small bankroll. You will almost certainly “tap out” (hit zero) before the math has a chance to swing back in your favor.
- The “Luck” Fallacy: Attributing variance to “hot” or “cold” dealers. The dealer’s release is physical, but the variance is purely a result of the payout structure and probability.
See also
- /roulette/odds-chart/
- /roulette/single-number-bet-odds/
- /roulette/red-or-black-odds/