I recently gave a quick tutorial about how to interpret XG's new rollout statistics, but did not give any indication of what these statistics are good for. Here I will give one application: Finding out how many games and gammons each player wins.
You might be puzzled by this remark, because don't the bots already tell us the win/gammon breakdown? Well, they do, sort of, but what they actually give is an approximation of the cubeless wins and gammons. To illustrate the difference, let's look at a position that neilkaz recently mentioned, namely 42P-63S-66. Neil posted the position at 4a8a, but for simplicity, let's change the score to 2a3a. Here's a rollout of the blitzing play 13/7*/1*(2):
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| XGID=-a--B-DaB---dE-a-c-e----B-:0:0:1:66:1:0:0:3:10 | |||||
| Blue to play 66 | |||||
| 1. | Rollout1 | 13/7*(2) 7/1*(2) | eq: +0.970 | |||
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| 1 5184 Games rolled with Variance Reduction. Dice Seed: 271828 Moves: 3-ply, cube decisions: XG Roller Search interval: Large | ||||||
eXtreme Gammon Version: 2.19.208.pre-release, MET: Kazaross XG2
If you take these numbers at face value, you might think that Blue wins a gammon about 46% of the time. However, this is not the case. Let's look at the rollout stats (I've corrected the typos that I mentioned before):
13/7*(2) 7/1*(2) Non VR Equity: +0.996 (Cost: +75.03%)
Cube Win BG Win G Win S Cash Pass Lose S Lose G Lose BG D/T D/P Take % D/T D/P Take %
1 174 1,566 712 523 22 3 307 712 30.13% 1,877 523 78.21%
2 21 425 434 767 201 29 307 100.00%
4 3 62 154 75 11 2
Blue wins an undoubled gammon (or backgammon) an estimated 1566+174 out of 5184 trials, or about 1/3 of the time. Even if you count the gammons with the cube on 2 or 4, Blue wins a gammon only about 43% of the time. The cubeless estimates are not even a good estimate of that, and in any case, the gammons ATS that we really care about are the undoubled gammons. Until now, we had no way to extract from XG the percentage of undoubled gammons. This is obviously important information when trying to understand how aggressively to play for the gammon at a score where the opponent can kill our gammons by sending the cube over. We may not want to go all-out for a gammon if it turns out that, too often, the cube gets turned.
Here's another example at 2a3a where the cubeless numbers are misleading. This may not be the world's best example but it's the first reasonable example that I found in my files.
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| XGID=-a-aBBDBB----A-A-cbdb-b-A-:0:0:1:65:1:0:0:3:10 | |||||
| Blue to play 65 | |||||
| 1. | Rollout1 | 13/7 6/1* | eq: +0.240 | |||
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| 2. | Rollout1 | 7/1* 6/1 | eq: +0.182 (-0.058) | |||
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| 1 2592 Games rolled with Variance Reduction. Dice Seed: 271828 Moves: 3-ply, cube decisions: XG Roller Search interval: Large | ||||||
eXtreme Gammon Version: 2.19.208.pre-release, MET: Kazaross XG2
PoH is the gammon go play, and you might think that it would be the play here too since our gammon value is 1. Admittedly, the opponent also wins some gammons, but if we just look at the cubeless estimates of the above two plays (by the way, I'm not claiming that these are the only two candidates here—I'm just using these two plays for illustrative purposes), it looks like PoH wins about 12.2% net gammons while the other play wins only 9.5% net gammons. With a gammon value of 1, shouldn't that make up for the 2.8% extra wins, more or less?
Let's look at the rollout stats:
13/7 6/1* Non VR Equity: +0.264 (Cost: +65.84%)
Cube Win BG Win G Win S Cash Pass Lose BG Lose G Lose S D/T D/P Pass % D/T D/P Pass %
1 33 260 591 345 16 232 591 28.19% 1,115 345 76.37%
2 7 114 349 469 142 34 232 100.00%
4 7 44 120 50 11
7/1* 6/1 Non VR Equity: +0.183 (Cost: +64.83%)
Cube Win BG Win G Win S Cash Pass Lose BG Lose G Lose S D/T D/P Pass % D/T D/P Pass %
1 22 402 394 472 72 9 133 394 25.24% 1,088 472 69.74%
2 5 171 284 463 128 37 133 100.00%
4 1 21 70 38 3
The non VR equity isn't as close to the VR equity as we might like, so more trials are probably in order, but we can already note some things. After PoH, if we tot up all of Blue's wins, we see that Blue actually wins only about 53% of the time, and wins an undoubled gammon only about 16% of the time. On the other hand, the other play wins about 59% of the time and wins an undoubled gammon about 11% of the time. Without going into all the rest of the details we can already see that this is giving us a clearer picture of what is actually happening.