Red eight times in a row

Question

A fair European roulette wheel has 37 pockets: 18 red, 18 black, and 1 green zero. Red has just come up eight spins in a row. What is the probability that the next spin is red?

Accepted Answer

The spins are independent, so the eight past reds change nothing about the next one. On a single spin, red covers 18 of the 37 pockets, so P(	ext{red}) = \frac{18}{37} \approx 48.6\%. Two ideas are worth stressing. First, the wheel has no memory: it cannot "owe" you a black after a run of reds, which is the gambler's fallacy. Second, notice the chance is not even 	frac12; the green zero means red is slightly under even money on every single spin, streak or no streak. That built-in gap is exactly the house edge. Betting black because red "must be due" is doubly mistaken: the streak is irrele…

Red eight times in a row

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