Monte Carlo

See Gambler's Fallacy.

Gambler's

This fallacy occurs when the gambler falsely assumes that the history of outcomes will affect future outcomes.

Example:

I know this is a fair coin, but it has come up heads five times in a row now, so tails is due on the next toss.

The fallacious move was to conclude that the probability of the next toss coming up tails must be more than a half. The assumption that it's a fair coin is important because, if the coin comes up heads five times in a row, one would otherwise become suspicious that it's not a fair coin and therefore properly conclude that the probably is high that heads is more likely on the next toss.