8 Reds in a Row at Roulette: How Likely Is It Really?

Eight reds in a row and the table gets restless: black must be due now. Psychology calls this feeling the gambler's fallacy. Here are the numbers.

Probability of one red. European roulette has 37 pockets, 18 of them red. The chance of red is 18/37 = 48.65 %. The zero is why it is not 50 %.

Probability of 8 reds. Each spin is independent, so you multiply: (18/37)^8 ≈ 0.31 %. That is about once in 319 attempts. Rare, but on a wheel with hundreds of spins a day it happens regularly.

Streaks at a glance. 3 reds: 11.5 %. 5 reds: 2.7 %. 8 reds: 0.31 %. 10 reds: 0.07 %. These figures only apply before the streak starts.

The key point. After eight reds, the chance of red on the next spin is still 48.65 %. The ball has no memory. The past eight spins do not affect the ninth.

Why our brain sees it differently. We expect randomness to look balanced even in small samples. The law of large numbers only works over thousands of spins, and it does not balance results, it just dilutes deviations.

The most famous case. In 1913 black came up 26 times in a row at the Monte Carlo casino. Players bet ever more on red and lost millions of francs. The fallacy is also called the Monte Carlo fallacy.

Bottom line. 8 reds is rare but not unusual. The next spin is always 48.65 %. Boards showing the last numbers are decoration, not information.