Roulette
Roulette probability and streaks
A previous spin does not change the next one on a fair wheel. Calculate a specified sequence separately from the chance of a streak appearing somewhere in a session.
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.