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Another caveat about stopping rollouts at 3 jsds

Posted By: Timothy Chow
Date: Monday, 5 April 2010, at 2:33 p.m.

In Response To: Another caveat about stopping rollouts at 3 jsds (Stick)

Stick wrote:

If the minimum number of trials is high it would seem to stymie this possible effect.

That certainly helps. Again assuming my code is bug-free, if I change the minimum to 1296 and the maximum to 46656, then the probability of a spurious 3 jsd result (in the sense I described) drops from about 7% to about 3%.

Just to clarify, though, it's not just the minimum number of trials that matters, but the size of the range over which you're allowing yourself to exit early. So if you raise the maximum number of trials (e.g., because computers get a lot faster) then the problem could resurface.

The point is that a difference of 3 jsds occurring just by chance is a rare event, but if you look for a rare event over and over again, you're going to increase your chances of seeing it at least once. If you stop as soon as you hit 3 jsds, you're effectively looking for the rare event after every single trial, rather than just at the very end. Granted, you're not taking forty thousand independent "looks" because if the plays are very close after the 1578th trial then they're still going to be close after the 1579th trial. But it should be intuitively clear that the chances of at least one rare event occurring somewhere over a large range will be noticeably higher than the chances of its occurring specifically at the very end.

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