"If a number has appeared 2131 times less than chance would have dictated after 100,000 spins, then it is on target to be still 2131 short of expectation after 1,000,000 spins, or any other huge number of future spins. Fate doesn't dictate that it will regress to the norm in terms of absolute count, only in percentage terms. eg, in your example, instead of appearing 1/38th of the time, or 2.631578947368421%, it instead came out 500/100,000 = 0.5%: It's 2.131578947368421% short, which is way out.But if after 1,000,000 spins it is still 2131 appearances short, then it will have appeared (1,000,000/38 - 2131) = 24184 times: It will have appeared 2.418478947368421% of the time. At 2.418478947368421% It will be closer to the expected 2.63158% and so can be said to be regressing to the mean.Now lets say we spin 1,000,000,000,000 times starting out 2131 appearances short and ending at 2131 short. It would then have appeared (1,000,000,000,000/38 -2131) times = 26315787342 times or 2.6315787342% : It has pretty much regressed almost exactly to the expected appearance frequency, but it is still numerically just as far away.Purely and simply, regressing to the mean does not mean any short term variation gets cancelled out, only that it becomes statistically insignificant in percentage terms.Oh, and just to be controversial 400/infinity = 0 EXACTLY. Not close to, but exactly: That's the nature of infinity." -Wizardofvegas forum

In the end, regression toward the mean appears to happen because the sum of all spins yet to happen dwarf the number of spins that you have collected.

What is described early in the thread is simply part of the gambler's fallacy.

-Real