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A Fifth Play is Possibly Best at Another Score

Posted By: Paul Weaver
Date: Saturday, 16 June 2012, at 11:01 a.m.

In Response To: 63S-32, the only second roll T4 (Nack Ballard)

Nack finds this situation very interesting, when four different plays are correct in the same position at four different scores. I am also fascinated by the subject. Is it possible that five, six, or seven plays could be correct in the same position at different scores? Maybe one day we will have the firepower to know the answer.

This is only a 3-ply rollout, and the number of trials is currently only 7660, but it enough to suggest that at this score and cube situation (super gammon go), a fifth play may be best.

I certainly admit that this is only of theoretical and not practical interest. How could White own a 4-cube so early in the game? Very unlikely, but I suppose Nack could find a sequence of rolls and plays that would lead to this position with White owning a 4-cube. And if it could happen once, it could happen to you a thousand games in a row, so you might want to be prepared.

I interuppted the rollout and made this post because I am going out for the day, but I will let the rollout run to 20K. After I post this 20K rollout, maybe someone with nothing better to do with his life and his computer will want to do a 4-ply 200K rollout of 63S-32 at this score.





White is Player 2

score: 6
pip: 158
8 point match
pip: 167
score: 0

Blue is Player 1
XGID=-a----EaC---dE-a-c-e----B-:2:-1:1:32:0:6:0:8:10
Blue to play 32

1.Rollout113/11 8/5eq: +0.353
Player:
Opponent:		42.68% (G:12.36% B:0.74%)
57.32% (G:21.54% B:3.99%)		Conf.: ± 0.005 (+0.348...+0.358) - [56.9%]
Duration: 1 hour 05 minutes
2.Rollout113/10 6/4eq: +0.351 (-0.001)
Player:
Opponent:		43.05% (G:12.15% B:0.86%)
56.95% (G:21.62% B:4.09%)		Conf.: ± 0.005 (+0.346...+0.357) - [33.0%]
Duration: 1 hour 06 minutes
3.Rollout26/1* eq: +0.349 (-0.003)
Player:
Opponent:		42.75% (G:12.25% B:0.69%)
57.25% (G:20.13% B:3.24%)		Conf.: ± 0.005 (+0.344...+0.354) - [10.0%]
Duration: 1 hour 06 minutes
4.Rollout224/21 13/11eq: +0.343 (-0.010)
Player:
Opponent:		43.40% (G:11.77% B:0.80%)
56.60% (G:21.51% B:3.20%)		Conf.: ± 0.005 (+0.338...+0.348) - [0.0%]
Duration: 1 hour 04 minutes
5.Rollout324/22 13/10eq: +0.341 (-0.011)
Player:
Opponent:		42.98% (G:11.93% B:0.74%)
57.02% (G:21.34% B:2.72%)		Conf.: ± 0.005 (+0.336...+0.346) - [0.0%]
Duration: 1 hour 02 minutes
6.Rollout424/21 6/4eq: +0.332 (-0.020)
Player:
Opponent:		43.29% (G:11.56% B:0.84%)
56.71% (G:21.94% B:3.25%)		Conf.: ± 0.006 (+0.326...+0.338) - [0.0%]
Duration: 46 minutes 25 seconds
1 7664 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

2 7663 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

3 7662 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

4 5184 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.03, MET: Kazaross XG2

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