What are the odds and the formula of the same number would come up 100 times in a row in roulette?

The odds of the same number coming up 100 times in a row in roulette, assuming a fair and unbiased wheel, are extremely low. The probability of any specific number coming up on a single spin of the roulette wheel in European roulette is 1 in 37, or approximately 2.70%.

To calculate the probability of the same number coming up 100 times in a row, we need to multiply this probability by itself 100 times. This gives us:

(1/37)^100 = 1 in 1.071509e+171

In other words, the odds of the same number coming up 100 times in a row are essentially zero. It's important to remember, however, that each spin of the roulette wheel is an independent event, and the outcomes of previous spins do not affect the probability of future spins. So while the odds of the same number coming up 100 times in a row are astronomically low, each spin has the same 1 in 37 chance of any particular number coming up.