Roulette probability and streaks

Consecutive reds or blacks

If p is the one-spin chance of red, the chance of red on all n specified future spins is p^n. On European roulette, ten reds have probability (18/37)^10, about 0.07425%. Ten losses on a red wager instead use (19/37)^10.

At least one hit

The chance of at least one hit in n independent spins is 1 − (1 − p)^n. For one chosen number over ten European spins, use p = 1/37. This does not guarantee a hit after 37 spins.

A repeat versus a chosen repeat

A chosen number twice from before both spins is 1/37^2. Any same number on two spins is 37 × 1/37^2 = 1/37. Once the first number is known, a matching next spin is also 1/37.

Either color is a different event

All red or all black over n European spins has probability 2 × (18/37)^n, since these two sequences do not overlap. Any nonzero color on every spin instead has probability (36/37)^n and permits mixed colors.

Runs anywhere need a different model

A run of ten within 100 spins is not the same event as the next ten spins all being red. Overlapping runs cannot simply be added. Our sequence calculator deliberately handles a fixed block, not a run-anywhere calculation.

Odds of the same color in a row

For either color, double the single-color figure: 2 × (18/37)^n on a European wheel.

Odds of losing several times in a row

A red bet loses on 19 of 37 European pockets, so losing n times in a row has probability (19/37)^n.

The Martingale roulette page shows why these streaks matter when stakes double after each loss.

Odds of the same number twice or three times