What this shows. On a European wheel a bet on red wins 18 times out of 37 and pays even money, so the expected return per unit is 18/37 minus 19/37, which is minus 1/37, or minus 2.70%. Run 100 spins and the result jumps around. Run 100,000 and it converges on that number. No sequence of past spins, hot numbers or cold numbers changes it.
Run the simulation
Test the raw computational velocity of JavaScript against the mathematical Law of Large Numbers ($\lim_{n \to \infty} \bar{X}_n = \mu$). Watch simulated returns converge strictly to the theoretical -2.70% house edge as sample sizes grow.
Or spin a real wheel, one number at a time
Same 37-number European wheel, same real order (0 through 36, in the actual physical wheel sequence, not the betting-table order). Every spin below is fully independent of the last — exactly the property the full article proves mathematically.
No spins yet.
How to read the results
- Red win frequency should drift towards 48.65% (18/37). At 100 spins, anything between roughly 39% and 58% is normal.
- Simulated return is your profit or loss divided by the total staked. It can be positive after a short run. It cannot stay positive as the spin count grows, because the expectation of every spin is −1/37.
- The wheel uses the real European pocket order (0, 32, 15, 19, 4, 21, …), not the betting-table order. Each spin is independent of the last.
The numbers behind the simulator
- 2.70% house edge on every bet on a single-zero wheel; 5.26% on a double-zero wheel; 7.69% on a triple-zero wheel; 7.89% on the American five-number bet (Wizard of Odds).
- 1 in 68 million: the chance of 26 same-colour results in a row on an unbiased single-zero wheel, which is what happened at Monte Carlo on 18 August 1913. The 27th spin still had an 18/37 chance of black.
- 85%: share of even-money bets placed against a streak of six or more identical outcomes, in 18 hours of casino security video from Reno (139 players, 24,131 bets). The wheel in that study showed no bias (Croson & Sundali, 2005).
Frequently asked questions
Is this roulette simulator truly random?
It uses the browser's pseudo-random generator to pick one of 37 pockets with equal probability on every spin, and every spin is independent of the previous one. That is the same property a certified casino random number generator must have under the UK Gambling Commission's Remote Technical Standards (RTS 7A).
Why does a short run sometimes show a positive return?
Variance. Over 100 spins the result swings widely in both directions. Over 10,000 or 100,000 spins the simulated return settles close to minus 2.70%, which is the law of large numbers at work. Short winning runs are noise, not a pattern.
Can I use the simulator to find hot or cold numbers?
You can count them, but they carry no information about the next spin. Each number has probability 1/37 every time, whatever came before. In a real casino study of 24,131 bets, players who bet against streaks of six or more did so 85% of the time and still faced exactly the same house edge.
What changes on an American double-zero wheel?
The wheel has 38 pockets, so the single-number probability is 1/38 while the payout stays 35 to 1. The house edge rises from 2.70% to 5.26%, and to 7.69% on a triple-zero wheel. The simulator here models the European single-zero wheel.
Sources
- Wizard of Odds. "Roulette for Beginners: Rules, Odds and House Edge." wizardofodds.com/games/roulette/basics/
- Croson, R. and Sundali, J. (2005). "The Gambler's Fallacy and the Hot Hand: Empirical Data from Casinos." The Journal of Risk and Uncertainty, 30(3), 195–209. doi:10.1007/s11166-005-1153-2
- UK Gambling Commission. Remote Gambling and Software Technical Standards, RTS 7A. gamblingcommission.gov.uk
- Wikipedia. "Gambler's fallacy", Monte Carlo Casino, 18 August 1913. en.wikipedia.org/wiki/Gambler%27s_fallacy