BGonline.org Forums

New XG rollout statistics: Use case #1

Posted By: Timothy Chow
Date: Tuesday, 17 February 2015, at 9:07 p.m.

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):

 White is Player 2 score: 0 pip: 158 3 point match pip: 161 score: 1 Blue is Player 1
XGID=-a--B-DaB---dE-a-c-e----B-:0:0:1:66:1:0:0:3:10
Blue to play 66

1.Rollout113/7*(2) 7/1*(2) eq: +0.970
 Player:Opponent: 69.16% (G:46.06% B:3.80%)30.84% (G:7.62% B:0.80%) Conf.: ± 0.008 (+0.962...+0.978)Duration: 1 hour 59 minutes
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.

 White is Player 2 score: 0 pip: 124 3 point match pip: 124 score: 1 Blue is Player 1
XGID=-a-aBBDBB----A-A-cbdb-b-A-:0:0:1:65:1:0:0:3:10
Blue to play 65

1.Rollout113/7 6/1* eq: +0.240
 Player:Opponent: 58.66% (G:20.85% B:1.69%)41.34% (G:11.46% B:1.35%) Conf.: ± 0.010 (+0.230...+0.250) - [100.0%]Duration: 29 minutes 57 seconds
2.Rollout17/1* 6/1eq: +0.182 (-0.058)
 Player:Opponent: 55.84% (G:25.39% B:1.43%)44.16% (G:13.18% B:1.89%) Conf.: ± 0.008 (+0.173...+0.190) - [0.0%]Duration: 23 minutes 03 seconds
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.

Post Response

Subject:
Message: