The Gambler's Fallacy

Something in yesterday’s piece about scientific method made me think of what is known as the ‘Gambler’s Fallacy’. Recently I read Dostoevsky’s novel ‘The Gambler’ in English translation. It wasn’t clear who made the translation or when, but it seemed to me bad. But how would I know? I don’t know any Russian: perhaps it was a good and faithful translation of a badly written original. We know the book — much shorter than usual for Dostoevsky — was written under pressure and in a hurry, to comply with a publisher’s draconian contractual demands. (That sort of thing is why we need the Society of Authors, but I digress.)

Anyway, the story concerns a gambler. (Duh.) His favoured game is roulette, and it soon becomes clear that he believes the gambler’s fallacy. Over and over again he says to himself things like ’37 has come up three times this evening already, so I won’t bet on it: it’s had more than its share, so the chances of its coming up again before tomorrow are reduced.’

But it’s only in an infinitely long run of wheel-spins that the numbers would be evenly shared. And infinity is not ‘a very big number’, it’s something quite different from any imaginable number. There is no reason at all why 37 should not come up every time until kingdom come, though no doubt if it did people might wonder if the wheel were like the one in ‘Casablanca’. (You know, the bit where Humphrey Bogart saves an innocent young girl from a fate worse than death by arranging for her boyfriend to win enough for exit visas.)

I just digressed again I fear. Let’s be clear about this: in matters of chance, such as the spin of a properly balanced roulette wheel, previous outcomes have nothing to tell us about the next outcome. I don’t know how many numbers there are on a roulette wheel and it doesn’t matter: let’s say 54 just for the sake of argument. Then the chances of any one number coming up on the next spin are one in 54, and it makes not the slightest difference whether that one number has come up time and again all evening, or not come up for weeks: the chance remains one in 54.

Dostoevsky was a gambler: ‘The Gambler’ is surely autobiographical. Like his protagonist, Dostoevsky probably believed the gambler’s fallacy. Surprising? He was of course an educated well-read man. But gambling, like erotic love, is a passion, and when one is in the throes of passion (what exactly is a ‘Throe’?) one is not reasonable. A reasonable gambler would be, and have, as much fun as a reasonable lover.