What is the longest recorded sequence of a single number in roulette?
Notwithstanding the ‘gambler’s fallacy’, or ‘Monte Carlo fallacy’, roulette players are often reminded that each spin of a roulette wheel is an independent, random event, such that the probability of each possible outcome is not influenced by past outcomes. In other words, the probability – or odds, which are calculated as a reciprocal of probability – of any single number occurring remains the same after each spin.
Granted that the odds against a single number occurring in a single spin are 37/1 in single-zero, ‘French’ or ‘European’ roulette and 38/1 in double-zero, ‘American’ roulette, the same number occurring twice, three times or four times in a row is obviously unusual, but by no means impossible.
Indeed, according to one reliable report, not long after the opening of the iconic El San Chuan Hotel in Puerto Rico, in June, 1959, the number 10 occurred in six consecutive spins of American roulette. Multiplying the odds for single occurrence gives combined odds of an astronomical, eye-watering (38)^6 or 3,010,936,384/1. In other words, a player placing a single $1 chip on 10 black and being sufficiently gung-ho to ‘let it ride’ for six spins would have profited by over $3 billion. To put that figure in perspective, regardless of inflation, six decades later, in 2019, the gross domestic product of the United Kingdom was just $2.7 billion.