Secular Café: Probability and the gambler's fallacy

Secular Café Discuss philosophical concepts and moral issues.

Probability and the gambler's fallacy May 13th 2012, 05:48 We have a state-run lottery here in ZA, with 6 numbered balls out of a set of 49 being randomly dished out by a machine. The lottery even has a little mini-show with a presenter and whatnot. Whenever a ball pops out, the presenter usually says something like 'it's number 12, visiting us for the 315th time.'. Now, we all know that the balls fall randomly, but some balls have fallen 300 times and others only 270 times, for example. If we assume that, probabalistically, after say a million rolls, this percentile disparity between balls falling would be dramatically reduced so as to be close to even, doesn't it imply that to satisfy this probabalistic outcome, the ball with 270 falls has a greater chance to fall in future since it needs to 'catch up'? It sort of niggles me, even though my intuition tells me that the 30-fall difference is probably unit-based, and not a percentile to be caught up later. In other words, after a million rolls, the difference is likely (in fact, more likely) to also be 30 (or even more), although the percentile difference is pretty much wiped out. It only /appears/ to be significant currently since the current sample size is relatively small.

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