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Rollout

Posted By: Timothy Chow
Date: Monday, 29 December 2014, at 12:19 a.m.

In Response To: A position that is neither fish nor fowl (Timothy Chow)

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: 129
Unlimited Game
pip: 155
score: 0

Blue is Player 1
XGID=--Ba-aC-BA--cD--Ac-cB--bb-:0:0:1:64:0:0:0:0:10
Blue to play 64

1.Rollout116/10 13/9eq: -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 seconds
2.Rollout116/10 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 seconds
1 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10


Variant:





White is Player 2

score: 0
pip: 131
Unlimited Game
pip: 155
score: 0

Blue is Player 1
XGID=-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 13/9eq: -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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