"Your point is that it would have been more precise for me to say, "If I declare the higher-scoring play to be the better play, what percentage of the time will I be correct, assuming that the DMP winning probabilities of the two plays are picked uniformly at random?" I agree that I was making that implicit assumption. With that assumption, though, what I said was correct. "
I still disagree. Let's say it is DMP and there are just two candidate plays. The statement "play A is better than play B with 95% confidence" means that if the plays were actually equal that the diffence in the rolled out values would only be that large or larger 5% of the time. This is not the same as saying there is a 95% chance that A is the better play.
For example some rollouts will involve situation where we believe one play to be superior. The RO quickly reaches 95% confidence. We then are quite sure it is correct (certainly more than 95%). For example what do you think the chance is that for an opening 31 that making the 5 point is better than splitting. You may be 99.9999% sure that it is. But if you do the following RO you don't want to change your answer to only about 99% (based on the 2.4 JSDs) do you? Your technique of asserting the best play based on a 95% confidence RO actually gets it right more than 95% of the time.
The score (after 0 games) is: gnubg 0, user 0 (match to 7 points)
Move number 2: user to play 13
| gnubg | 167 |
|---|---|
| |
| user | 167 |
Position ID: 4HPwATDgc/ABMA Match ID: cInsAAAAAAAA | |
| # | Ply | Move | Equity | |||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | R | 8/5 6/5 | +0.201383 | |||||||||||||||||||
| ||||||||||||||||||||||
| Full cubeful rollout with var.redn. | ||||||||||||||||||||||
| 134 games, Mersenne Twister dice gen. with seed 867982123 and quasi-random dice | ||||||||||||||||||||||
| Stop when best play is enough JSDs ahead: limit 3.2 (min. 324 games) | ||||||||||||||||||||||
| Play: 0-ply cubeful [expert] | ||||||||||||||||||||||
| Cube: 0-ply cubeful [expert] | ||||||||||||||||||||||
| 2 | R | 24/23 13/10 | +0.055182 ( -0.146201) | |||||||||||||||||||
| ||||||||||||||||||||||
| Full cubeful rollout with var.redn. | ||||||||||||||||||||||
| 133 games, Mersenne Twister dice gen. with seed 867982123 and quasi-random dice | ||||||||||||||||||||||
| Stop when best play is enough JSDs ahead: limit 3.2 (min. 324 games) | ||||||||||||||||||||||
| Play: 0-ply cubeful [expert] | ||||||||||||||||||||||
| Cube: 0-ply cubeful [expert] | ||||||||||||||||||||||
| 3 | 0 | 13/9 | -0.001933 ( -0.203316) | |||||||||||||||||||
| 0.496628 0.145331 0.007383 - 0.503372 0.139005 0.006489 | ||||||||||||||||||||||
| 4 | 0 | 13/10 6/5 | -0.003447 ( -0.204830) | |||||||||||||||||||
| 0.500172 0.145310 0.008305 - 0.499828 0.148288 0.008802 | ||||||||||||||||||||||
| 5 | 0 | 24/20 | -0.005912 ( -0.207295) | |||||||||||||||||||
| 0.500101 0.125114 0.005943 - 0.499899 0.132557 0.003575 | ||||||||||||||||||||||