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BGonline.org Forums
a bias in rollouts
Posted By: Tom Keith In Response To: a bias in rollouts (Stick)
Date: Friday, 2 May 2008, at 1:24 p.m.
Leads me to believe such a bias is either non existant or not worth worrying about.
I don't think Bob is saying that it is something you (normally) have to worry about.
Here is an example where it might apply. At the bottom of this page, I calculate that if you win the opening roll, your average cubeless equity is +.0393. One of the numbers that goes into this average is a value of +.0053 for an opening 3-2. This value assumes the correct way to play 3-2 is 13/11, 13/10. But my rollout shows very little difference between 13/11, 13/10 and 24/21, 13/11. It could be that the reason 13/11, 13/10 won the rollout was simply because it happened to have luckier dice.
In general, candidates with luckier rolls during a rollout will have higher equities than those with poor rolls. So the lucky candidates will tend to be the winner more often than they should. Since only the winning candidate's equity goes into the calculation of absolute equity, and the candidates with lucky dice tend to win more often, this has a positive bias on the final result.
Normally you don't care about absolute equity. You just want to know which play is best. So this effect is not of interest. But it could mean, for example, that the gammon rate I calculated on the same page is a little higher than it should be. If I reran the rollouts 1,000,000 times for each candidate and redid the calculation, it is more likely than not that the new result would be lower than the one I calculated.
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