It does not matter what you bet on
The wheel has 37 pockets: 1 to 36 and the green zero. But prizes are paid as if there were only 36. That zero is the casino’s business. And the curious thing is that it hits every bet equally: red, a dozen or a single number. Of every €100 you bet, in the long run you get back about €97.30, whatever you choose.
| Bet | Pays | Chance | You get back from €100 |
|---|---|---|---|
| Red or black | 1 to 1 | 48.6% | €97.30 |
| Even or odd | 1 to 1 | 48.6% | €97.30 |
| 1–18 or 19–36 | 1 to 1 | 48.6% | €97.30 |
| A dozen | 2 to 1 | 32.4% | €97.30 |
| A single number | 35 to 1 | 2.7% | €97.30 |
Technical The expectation of every bet
A bet covering k numbers pays (36/k − 1) to 1. Its expectation per unit staked is:
E = (k/37)·(36/k − 1) − (37 − k)/37 = (36 − k − 37 + k)/37 = −1/37The k cancels out, which is why every bet in European roulette carries the same house edge, 2.70%. In American roulette, with two zeros, the denominator is 38 and the edge rises to 2/38 = 5.26%. The project’s tests check this for every bet in the simulator.
The wheel has no memory
Many casinos display the last numbers on a screen. It looks like useful information, but it is not. After five reds in a row it is very tempting to think black is “due”. That is the gambler’s fallacy: the ball does not know what happened before, and the chance of red on the next spin is exactly the same. Try it in the simulator: when three or more of the same colour come up, we will remind you.
Technical Independence
Spins are independent and identically distributed: P(red | five reds before) = P(red) = 18/37 ≈ 48.6%. What is unlikely is the whole sequence seen in advance: (18/37)⁵ ≈ 2.7%. Over hundreds of spins such streaks appear many times by pure chance. The illusion comes from mixing up the probability of a streak with the probability of the next spin.
What about winning systems?
Doubling after a loss, raising the stake little by little, betting on “hot” numbers… No system changes the sum above, because every bet keeps the same disadvantage. All they change is the way you lose. You can check it with thousands of players at once in the Ruin Lab by choosing the Martingale strategy.