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Rollout
Posted By: Timothy Chow In Response To: A position that is neither fish nor fowl (Timothy Chow)
Date: Monday, 29 December 2014, at 12:19 a.m.
Before getting to the position, I want to briefly digress on the topic of classifying positions. Certain classes of positions are characterized by how many checkers each player has back and whether they are anchored. For example:
Blue 0 checkers back; White 0 checkers back: race
Blue 0 checkers back; White 1 checker back (or possibly 2 checkers back, unanchored): containment
Blue 0 checkers back; White 2 checkers back, anchored: holding game
Blue 2 checkers back, anchored; White 2 checkers back, anchored: mutual holding game
This leaves several categories of positions that don't have names. For example, what if Blue has 2 checkers back, anchored and White has 1 checker back? I believe that the way to understand such positions is to recognize that Blue is normally aiming for a containment position (White 1 checker back, Blue 0 checkers back) while White is normally aiming for a holding game (White 0 checkers back, Blue 2 checkers back, anchored). Thus the strategy centers around White's straggler, which Blue is trying to contain. One tricky thing about such positions is that Magriel's safe/bold criteria are not as helpful as they usually are. Magriel says that Blue can play boldly, which is usually true, but usually the key question that Blue faces is not whether to play safely or boldly, but whether a bold attacking play or a bold priming play does a better job of containing White's straggler.
In the current position, Blue has 2 checkers back, anchored, while White has 2 checkers back, unanchored, and White is significantly ahead in the pip count. The strategy here is similar, in that White is trying to scramble the stragglers home and Blue is trying to contain them, but here White has the additional option of anchoring and converting to a mutual holding game. The question Blue faces is, is attacking or priming the better containment strategy here?
Examining people's responses, I think that only David Presser recognized the tactical subtlety of this problem. According to the rollout, hitting is a whopper, but in the variant position with White's rear straggler on the 1pt, XGR++ slightly prefers hitting. I like David's suggested explanations for the difference but welcome further comments.
White is Player 2
score: 0
pip: 129Unlimited Game pip: 155
score: 0
Blue is Player 1XGID=--Ba-aC-BA--cD--Ac-cB--bb-:0:0:1:64:0:0:0:0:10 Blue to play 64
1. Rollout1 16/10 13/9 eq: -0.075
Player:
Opponent:47.61% (G:12.58% B:0.40%)
52.39% (G:12.88% B:0.27%)Conf.: ± 0.013 (-0.088...-0.061) - [100.0%]
Duration: 22 minutes 38 seconds2. Rollout1 16/10 9/5* eq: -0.175 (-0.100)
Player:
Opponent:46.49% (G:12.95% B:0.40%)
53.51% (G:17.60% B:0.33%)Conf.: ± 0.013 (-0.188...-0.162) - [0.0%]
Duration: 23 minutes 04 seconds1 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG RollereXtreme Gammon Version: 2.10
Variant:
White is Player 2
score: 0
pip: 131Unlimited Game pip: 155
score: 0
Blue is Player 1XGID=-aB--aC-BA--cD--Ac-cB--bb-:0:0:1:64:0:0:0:0:10 Blue to play 64
1. XG Roller++ 16/10 9/5* eq: -0.105
Player:
Opponent:47.81% (G:13.72% B:0.41%)
52.19% (G:16.93% B:0.30%)2. XG Roller++ 16/10 13/9 eq: -0.114 (-0.010)
Player:
Opponent:46.85% (G:10.41% B:0.32%)
53.15% (G:11.91% B:0.21%)eXtreme Gammon Version: 2.10
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