Here is an example from a real rollout.
I rolled out 64R 65
The sample size is large enough so that it is reasonable to think the sampling distributions are normal. So based on the rollouts we think that play A has an equity of .011 We realize this is not an exact answer though and can say we think it is N(.011,.032) Similarly we can think that play B is N(-.069,.035).
Based on that how sure should we be that play A is better than play B? A-B also has a normal distribution. It's mean is .011 - -.069 = .08 Think that if you had to give a single value for how much better A is than B you should guess the difference in the equity estimates. A - B has variance equal to the sum of the individual variances. Because of the dice streams being the same this is not quite the case, but the reported gnu values ignore that. So we obtain as variance .032^2 + .035^2 = .002249. Taking the square root gives the std. dev of .047
How likely is it that the rollout got it wrong? In other words that A - B is actually negative? If A - B is N(.08, .047) that is something which is 1.702 deviations below the mean. That 1.702 value is what gnu reports as the JSD. You can then use a normal distribution table to find what the probability is. (I won't get into here why it is actaully called a confidence instead of a probability).
The score (after 0 games) is: gnubg 0, user 0 (match to 7 points)
Move number 3: user to play 56
| gnubg | 157 |
|---|---|
| |
| user | 167 |
Position ID: 4HPhQSDgc/ABMA Match ID: cIn6AAAAAAAA | |
| # | Ply | Move | Equity | |||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | R | 13/7* 6/1* | +0.011 | |||||||||||||||||||
| ||||||||||||||||||||||
| Full cubeful rollout with var.redn. | ||||||||||||||||||||||
| 332 games, Mersenne Twister dice gen. with seed 867958357 and quasi-random dice | ||||||||||||||||||||||
| Stop when best play is enough JSDs ahead: limit 3.1 (min. 324 games) | ||||||||||||||||||||||
| Play: 0-ply cubeful prune [expert] | ||||||||||||||||||||||
| Cube: 0-ply cubeful prune [expert] | ||||||||||||||||||||||
| 2 | R | 13/8 13/7* | -0.069 ( -0.080) | |||||||||||||||||||
| ||||||||||||||||||||||
| Full cubeful rollout with var.redn. | ||||||||||||||||||||||
| 332 games, Mersenne Twister dice gen. with seed 867958357 and quasi-random dice | ||||||||||||||||||||||
| Stop when best play is enough JSDs ahead: limit 3.1 (min. 324 games) | ||||||||||||||||||||||
| Play: 0-ply cubeful prune [expert] | ||||||||||||||||||||||
| Cube: 0-ply cubeful prune [expert] | ||||||||||||||||||||||
| 3 | 0 | 24/13 | -0.149 ( -0.160) | |||||||||||||||||||
| 0.465 0.092 0.002 - 0.535 0.130 0.002 | ||||||||||||||||||||||
| 4 | 0 | 24/18 13/8 | -0.175 ( -0.186) | |||||||||||||||||||
| 0.459 0.105 0.003 - 0.541 0.149 0.003 | ||||||||||||||||||||||
| 5 | 0 | 13/7*/2 | -0.175 ( -0.186) | |||||||||||||||||||
| 0.455 0.126 0.005 - 0.545 0.159 0.008 | ||||||||||||||||||||||