The exact probability of every roulette bet, what it pays, what it ought to pay and how much you lose on average per spin.
Chance of winning
—
Chance of winning—
Which is—
You would collect—
Expected value per spin—
House edge—
Expected loss over those spins—
It should pay—
How this was worked out
Indicative result. The expected value of every roulette bet is negative: over time the house always wins. No betting system corrects that. Only play what you can afford to lose.
The formula
probability = pockets covered ÷ total pockets · house edge = 1 ÷ 37
Where it comes from
European roulette has 37 pockets: the numbers 1 to 36 and the zero. A straight-up bet covers one of those 37 and pays 35 to 1, when the fair price would be 36 to 1. That single pocket of difference is the entire house edge, and it is identical on every bet on the table.
How to work it out by hand
Count the pockets your bet covers
Divide by 37 on a European wheel or by 38 on an American one
Multiply the probability by what it pays and subtract what you lose the rest of the time
What is worth knowing
Every bet on a European wheel carries exactly the same house edge, 2.70 %. What changes is the variance, not the long-run result: a straight-up bet wins rarely and large, an even-money bet wins almost half the time, and both lose the same on average. American roulette adds a double zero and with it doubles the house edge to 5.26 %, so between the two tables there is never a question. And no progressive system, martingale included, changes the arithmetic: it only redistributes when the losses arrive.
Frequently asked questions
What are the odds on a straight-up number?
One in 37 on a European wheel, 2.70 %. It pays 35 to 1 when the fair price would be 36 to 1.
Which roulette bet is best?
They all carry the same house edge on a European wheel: 2.70 %. Only the variance differs.
Why is American roulette worse?
Because the double zero adds a pocket without changing the payouts, and that doubles the house edge to 5.26 %.
Does the martingale work?
No. Doubling after every loss runs into the table limit and into your own bankroll, and the expected value stays exactly the same.
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