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Rollout Result/Gnu/Post on Forum

Posted By: Daniel Murphy
Date: Monday, 29 March 2010, at 12:24 a.m.

In Response To: Rollout Result/Gnu/Post on Forum (Seth)

You're comparing two plays, one of which, your rollout says, is a double whopper. I'd answer your three questions thus: (1) Yes (2) Yes, and (3) No, unless 2- and 3-ply are both wrong ;)

Notice the 95% confidence intervals (as Zorba recently reminded us, multiply the SD's that Gnubg reports by 1.96 to get the confidence intervals) for the two plays ...

(A) 21/11 6/1*(2): +0.177 ±0.061

(B) 21/6 13/8: -0.030 ± 0.089

... which is Gnubg telling you that if you extended your rollout indefinitely, the equity of (A) is unlikely to be less than +0.116, and the equity of (B) is unlikely to be more than +0.059. So ... 108 trials is enough for this position, if you're only concerned with finding the best play, and you don't care to know if with Gnubg 0-/2-ply the second best play is a triple whopper, double whopper, or "only" a large error.

---

For your second position,

(A) 8/2* -0.461 ±0.053

(B) 13/8 6/5 -0.602 ±0.092

since -0.461 - 0.053 = -0.514, and -0.602 + 0.092 = -0.510, the 95% confidence intervals overlap slightly, and that generally tells me that more trials would be a good idea. But for the position I wouldn't bother, since it seems clear that leaving 18 shots ought be to a lot better than leaving 24.

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