Discussion:
Score-based checkerplay decision
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Tim Chow
2020-05-19 22:59:01 UTC
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XGID=-B-DAaB-D---ba-bAbbe---A--:0:0:1:43:1:4:0:7:10

X:Player 1 O:Player 2
Score is X:1 O:4 7 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O O X O O | | O X |
| O O O | | O |
| | | O |
| | | O |
| | | O |
| |BAR| |
| | | |
| X | | X |
| X | | X |
| O X | | X X X |
| O X | | X O X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 101 O: 138 X-O: 1-4/7
Cube: 1
X to play 43

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Tim Chow
Tim Chow
2020-05-21 22:13:56 UTC
Permalink
XGID=-B-DAaB-D---ba-bAbbe---A--:0:0:1:43:1:4:0:7:10

X:Player 1 O:Player 2
Score is X:1 O:4 7 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O O X O O | | O X |
| O O O | | O |
| | | O |
| | | O |
| | | O |
| |BAR| |
| | | |
| X | | X |
| X | | X |
| O X | | X X X |
| O X | | X O X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 101 O: 138 X-O: 1-4/7
Cube: 1
X to play 43

Trailing in the match, X might be expected to go for the gammonish hitting
play. But the cube is still centered. If O dances then X massively
overshoots his market. XG plays 23/16 ATS. But note that XG hits and
covers for money.

1. Rollout¹ 23/16 eq:+0.691
Player: 63.03% (G:18.01% B:0.19%)
Opponent: 36.97% (G:7.85% B:0.59%)
Confidence: ±0.013 (+0.678..+0.705) - [100.0%]

2. Rollout¹ 16/13* 8/4 eq:+0.632 (-0.059)
Player: 58.66% (G:30.20% B:0.33%)
Opponent: 41.34% (G:6.17% B:0.29%)
Confidence: ±0.013 (+0.619..+0.645) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.207.pre-release, MET: Kazaross XG2

-----
Money
-----

XGID=-B-DAaB-D---ba-bAbbe---A--:0:0:1:43:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O O X O O | | O X |
| O O O | | O |
| | | O |
| | | O |
| | | O |
| |BAR| |
| | | |
| X | | X |
| X | | X |
| O X | | X X X |
| O X | | X O X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 101 O: 138 X-O: 0-0
Cube: 1
X to play 43

1. Rollout¹ 16/13* 8/4 eq:+0.537
Player: 58.56% (G:30.06% B:0.33%)
Opponent: 41.44% (G:6.30% B:0.25%)
Confidence: ±0.010 (+0.528..+0.547) - [100.0%]

2. Rollout¹ 23/16 eq:+0.486 (-0.052)
Player: 63.51% (G:17.28% B:0.18%)
Opponent: 36.49% (G:7.97% B:0.41%)
Confidence: ±0.013 (+0.473..+0.499) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.207.pre-release

---
Tim Chow
Tom Martin
2020-06-25 21:40:44 UTC
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Interesting - the hitting play is presumably wrong because with the opponent at 3-away, gammons are less valuable, right? Try rolling it out as 6-away 4-away. GNU's 4-ply evaluations show hitting as even worse! Although a rollout closes a big gap in the evaluations, how can gammons be even less valuable when your opponent is 4-away?
Tom Martin
2020-06-25 22:12:59 UTC
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Oops - my brain was on backwards. Gammons are reduced in value when WE are at 3-away.

Still, I'm trying to think of a good reason why the money rollout is so different from 6-away, 3-away. The market loss theory seems a bit questionable.
Tom Martin
2020-06-25 23:57:18 UTC
Permalink
OK, I found some numbers in Lamford's Improve your Backgammon that say our opponent should pass at this score a little more quickly than for money. I wouldn't think the 3% difference in equity would create quite as big a swing, but it easily could, I suppose.

So Tim's answer was correct - at this score we do indeed lose our market more readily than for money.

Extra credit - why should our opponent drop more quickly?
Tom Martin
2020-06-26 01:31:39 UTC
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BTW, the 3% number is not really accurate. I got it by comparing this score's takepoint to that at the beginning of a 9-point match for positions with 25% gammon chances (well under this one's). But even in the first game of such a match, the takepoint is still 4% less than money if gammon chances are 25%. So the posted position's takepoint is really over 7% less than money!

Now you know why I don't play matches...
Tom Martin
2020-07-08 18:38:32 UTC
Permalink
It turns out that Lamford's takepoints for gammonish positions aren't supported by other writers like John O'Hagan and Phil Simborg.

The approximate 3% difference due to the match score is likely correct, but the big area of contention is how to play at the start of a match. Lamford says to adjust by 4%, the two above say no more than 1% for 5 point and longer matches, which feels right to me.

If anyone is looking for the most reliable numbers, I suggest https://sites.google.com/site/backgammonlessons/new-take-points-and-pog
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