A lucky guess

[[e-mail]]

Here, there are only two candidate plays but I had no real idea
whether to go greedy or safe.
I guessed right but it really was a guess.
In fact during the review, I was expecting to be penalised.
There is a fair amount of equity at stake here with the wrong
play losing 0.04.
Wouldn't it be good if there was an expert reader of this forum
who knows about the issues here and who could explain to me
how to make the decision reliably rather than guessing?

Since I'm mathematically oriented, I wonder if there's someone
here who has a particular interest in mathematical games
(of which backgammon could be said to be one) and who has
contributed to journals of combinatorial game theory.?

Paul

XGID=aBBCCBB-----b--b-b-cb-c---:2:-1:1:53:3:2:0:11:10

X:Daniel O:XG Roller+
Score is X:3 O:2 11 pt.(s) match.
[phone]------19-20-21-22-23-24-+
| O O | | O O O | +---+
| O O | | O O O | | 4 |
| | | O O | +---+
| | | |
| | | |
| |BAR| |
| | O | |
| | | |
| | | X X |
| O | | X X X X X X |
| O | | X X X X X X |
[phone]-------6--5--4--3--2--1-+
Pip count X: 49 O: 124 X-O: 3-2/11
Cube: 4, O own cube
X to play 53

1. 4-ply 6/3 6/1 eq:+1.476
Player: 98.16% (G:57.60% B:0.06%)
Opponent: 1.84% (G:0.00% B:0.00%)

2. 4-ply 5/2 5/Off eq:+1.432 (-0.043)
Player: 95.68% (G:59.99% B:0.08%)
Opponent: 4.32% (G:0.00% B:0.00%)

3. 1-ply 6/1 3/Off eq:+0.932 (-0.543)
Player: 79.65% (G:52.69% B:0.17%)
Opponent: 20.35% (G:0.00% B:0.00%)

4. 1-ply 5/Off 3/Off eq:+0.913 (-0.563)
Player: 78.55% (G:53.96% B:0.25%)
Opponent: 21.45% (G:0.00% B:0.00%)

5. 1-ply 6/1 4/1 eq:+0.800 (-0.675)
Player: 76.83% (G:46.14% B:0.08%)
Opponent: 23.17% (G:0.00% B:0.00%)


eXtreme Gammon Version: 2.10, MET: Kazaross XG2

[Timothy Chow]

Post by ***@gmail.com
Here, there are only two candidate plays but I had no real idea
whether to go greedy or safe.
I guessed right but it really was a guess.

I think that if you have one checker closed out, then the only time
you would clear the 5pt instead of the 6pt with 5x is if x=1 and
you don't have a spare on the 4pt, as in the position below.


XGID=aBBDBBB-----b--b-b-cb-c---:2:-1:1:51:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
[phone]------19-20-21-22-23-24-+
| O O | | O O O | +---+
| O O | | O O O | | 4 |
| | | O O | +---+
| | | |
| | | |
| |BAR| |
| | O | |
| | | X |
| | | X |
| O | | X X X X X X |
| O | | X X X X X X |
[phone]-------6--5--4--3--2--1-+
Pip count X: 48 O: 124 X-O: 0-0
Cube: 4, O own cube
X to play 51

1. XG Roller++ 5/4 5/Off eq:+1.473
Player: 95.65% (G:57.49% B:0.05%)
Opponent: 4.35% (G:0.00% B:0.00%)

2. XG Roller++ 6/5 6/1 eq:+1.460 (-0.013)
Player: 96.08% (G:55.19% B:0.03%)
Opponent: 3.92% (G:0.00% B:0.00%)

eXtreme Gammon Version: 2.19.211.pre-release


At gammon go, you can occasionally find a position where it's a bit
better to clear the 5pt.


XGID=aBBCCBB------b-b-b-cb-c---:0:0:1:53:0:1:1:2:10

Score is X:0 O:1 2 pt.(s) match.
[phone]------19-20-21-22-23-24-+
| O O O | | O O O |
| O O O | | O O O |
| | | O O |
| | | |
| | | |
| |BAR| |
| | O | |
| | | |
| | | X X |
| | | X X X X X X |
| | | X X X X X X |
[phone]-------6--5--4--3--2--1-+
Pip count X: 49 O: 122 X-O: 0-1/2 Crawford
Cube: 1
X to play 53

1. Rollout¹ 5/2 5/Off eq:+1.956
Player: 95.33% (G:52.47% B:0.39%)
Opponent: 4.67% (G:0.00% B:0.00%)
Confidence: ±0.003 (+1.953..+1.959) - [99.9%]

2. Rollout¹ 6/3 6/1 eq:+1.950 (-0.006)
Player: 98.11% (G:49.37% B:0.25%)
Opponent: 1.89% (G:0.00% B:0.00%)
Confidence: ±0.003 (+1.947..+1.953) - [0.1%]

¹ 2592 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.211.pre-release, MET: Kazaross XG2

---
Tim Chow

[[e-mail]]

Post by Timothy Chow

Post by ***@gmail.com
Here, there are only two candidate plays but I had no real idea
whether to go greedy or safe.
I guessed right but it really was a guess.

I think that if you have one checker closed out, then the only time
you would clear the 5pt instead of the 6pt with 5x is if x=1 and
you don't have a spare on the 4pt, as in the position below.
XGID=aBBDBBB-----b--b-b-cb-c---:2:-1:1:51:0:0:0:0:10
Score is X:0 O:0. Unlimited Game
[phone]------19-20-21-22-23-24-+
| O O | | O O O | +---+
| O O | | O O O | | 4 |
| | | O O | +---+
| | | |
| | | |
| |BAR| |
| | O | |
| | | X |
| | | X |
| O | | X X X X X X |
| O | | X X X X X X |
[phone]-------6--5--4--3--2--1-+
Pip count X: 48 O: 124 X-O: 0-0
Cube: 4, O own cube
X to play 51
1. XG Roller++ 5/4 5/Off eq:+1.473
Player: 95.65% (G:57.49% B:0.05%)
Opponent: 4.35% (G:0.00% B:0.00%)
2. XG Roller++ 6/5 6/1 eq:+1.460 (-0.013)
Player: 96.08% (G:55.19% B:0.03%)
Opponent: 3.92% (G:0.00% B:0.00%)
eXtreme Gammon Version: 2.19.211.pre-release
At gammon go, you can occasionally find a position where it's a bit
better to clear the 5pt.
XGID=aBBCCBB------b-b-b-cb-c---:0:0:1:53:0:1:1:2:10
Score is X:0 O:1 2 pt.(s) match.
[phone]------19-20-21-22-23-24-+
| O O O | | O O O |
| O O O | | O O O |
| | | O O |
| | | |
| | | |
| |BAR| |
| | O | |
| | | |
| | | X X |
| | | X X X X X X |
| | | X X X X X X |
[phone]-------6--5--4--3--2--1-+
Pip count X: 49 O: 122 X-O: 0-1/2 Crawford
Cube: 1
X to play 53
1. Rollout¹ 5/2 5/Off eq:+1.956
Player: 95.33% (G:52.47% B:0.39%)
Opponent: 4.67% (G:0.00% B:0.00%)
Confidence: ±0.003 (+1.953..+1.959) - [99.9%]
2. Rollout¹ 6/3 6/1 eq:+1.950 (-0.006)
Player: 98.11% (G:49.37% B:0.25%)
Opponent: 1.89% (G:0.00% B:0.00%)
Confidence: ±0.003 (+1.947..+1.953) - [0.1%]
¹ 2592 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
eXtreme Gammon Version: 2.19.211.pre-release, MET: Kazaross XG2
---
Tim Chow

Thanks, Tim.
Presumably the closer the gammon percentage is to 50, the better the greedy plays are.
Here, it's a significant error to play greedy even though the gammon percentage is
uncannily close to 50/50.
So yes, it must be rare -- I didn't know that.
It's quite common to give yourself a positional weakness to increase your gammon count
but maybe not this way.

Paul