Full Idea
The Gambler's Fallacy says if black has come up ten times in a row, red must be highly probable next time. It overlooks how the impact of an initial run of one color can become more and more insignificant as the sequence gets longer.
Gist of Idea
The Gambler's Fallacy (ten blacks, so red is due) overemphasises the early part of a sequence
Source
Gilbert Harman (Change in View: Principles of Reasoning [1986], 1)
Book Reference
Harman,Gilbert: 'Change in View: Principles of Reasoning' [MIP 1986], p.8
A Reaction
At what point do you decide that the roulette wheel is fixed, rather than that you have fallen for the Gambler's Fallacy? Interestingly, standard induction points to the opposite conclusion. But then you have prior knowledge of the wheel.