Discussion:
Boxcars at 5-away/4-away
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Tim Chow
2020-07-21 03:08:51 UTC
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XGID=-BA--bC-C--B-C--Acdcc-----:1:1:1:66:2:3:0:7:10

X:Player 1 O:Player 2
Score is X:2 O:3 7 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X X O O | | O O |
| X O O | | O O |
| X O O | | O O |
| O | | |
| | | |
| |BAR| |
| | | |
| | | |
| X | | X | +---+
| X X | | X O X | | 2 |
| X X | | X O X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 123 O: 125 X-O: 2-3/7
Cube: 2, X own cube
X to play 66

---
Tim Chow
Paul Epstein
2020-07-21 10:30:03 UTC
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Post by Tim Chow
XGID=-BA--bC-C--B-C--Acdcc-----:1:1:1:66:2:3:0:7:10
X:Player 1 O:Player 2
Score is X:2 O:3 7 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X X O O | | O O |
| X O O | | O O |
| X O O | | O O |
| O | | |
| | | |
| |BAR| |
| | | |
| | | |
| X | | X | +---+
| X X | | X O X | | 2 |
| X X | | X O X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 123 O: 125 X-O: 2-3/7
Cube: 2, X own cube
X to play 66
---
Tim Chow
Access to the cube is important here. The action will probably
be D/P or a very marginal take, so the idea is to minimize the opponent's
jokers. I don't see a completely safe play.
If we leave a blot on the midpoint, the hits from 22 and 62 are blocked
but we still leave the jokers of 53 and 44.
13/7(3) 8/2 minimizes jokers and has a bonus of making the two point.
The only shot it leaves is 65.
When Tim variantizes by giving the opponent the cube, we will see that the
above play is wrong because of the difficulty in safetying the 16 point.
With access to the cube, we don't need to worry about this because
we cash the position before that becomes an issue.

13/7(3) 8/2 for the given position.
13/7(2) 16/4 when Tim variantizes by giving Oppy the cube.

Confidence level -- 99% [confidence that I'm talking nonsense, that is.]

Paul
Peter
2020-07-21 10:59:01 UTC
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Post by Tim Chow
XGID=-BA--bC-C--B-C--Acdcc-----:1:1:1:66:2:3:0:7:10
X:Player 1 O:Player 2
Score is X:2 O:3 7 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X X O O | | O O |
| X O O | | O O |
| X O O | | O O |
| O | | |
| | | |
| |BAR| |
| | | |
| | | |
| X | | X | +---+
| X X | | X O X | | 2 |
| X X | | X O X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 123 O: 125 X-O: 2-3/7
Cube: 2, X own cube
X to play 66
---
Tim Chow
Leave 16 where it is, mend the blot, 13/7(3).
That's what I'd do, anyway.
Tim Chow
2020-07-21 17:07:05 UTC
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Post by Peter
Leave 16 where it is, mend the blot, 13/7(3).
That's what I'd do, anyway.
Does the match score influence your play?

---
Tim Chow
Peter
2020-07-21 17:28:49 UTC
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Post by Tim Chow
Post by Peter
Leave 16 where it is, mend the blot, 13/7(3).
That's what I'd do, anyway.
Does the match score influence your play?
No.
Paul Epstein
2020-07-21 19:50:44 UTC
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Post by Tim Chow
Post by Peter
Leave 16 where it is, mend the blot, 13/7(3).
That's what I'd do, anyway.
Does the match score influence your play?
Mine's a yes for sure. I prefer 13/7(2) 16/4 at DMP where we have minimal
problems scrambling home if our blot is missed.
It's not that easy to safety the 16 point blot if we're not able to cash the
game.

Paul
Tim Chow
2020-07-21 17:07:08 UTC
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Post by Peter
Leave 16 where it is, mend the blot, 13/7(3).
That's what I'd do, anyway.
Does the match score influence your play?

---
Tim Chow
Peter
2020-07-21 17:30:06 UTC
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Post by Tim Chow
Post by Peter
Leave 16 where it is, mend the blot, 13/7(3).
That's what I'd do, anyway.
Does the match score influence your play?
No.

Is the prob. from your OTB play?
Tim Chow
2020-07-23 14:34:43 UTC
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Post by Peter
Post by Tim Chow
Post by Peter
Leave 16 where it is, mend the blot, 13/7(3).
That's what I'd do, anyway.
Does the match score influence your play?
No.
Is the prob. from your OTB play?
It's from playing against the bot, which is where 99% of these positions
come from. Once in a while I'll post something from a chouette.

---
Tim Chow
Tim Chow
2020-07-24 16:34:47 UTC
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XGID=-BA--bC-C--B-C--Acdcc-----:1:1:1:66:2:3:0:7:10

X:Player 1 O:Player 2
Score is X:2 O:3 7 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X X O O | | O O |
| X O O | | O O |
| X O O | | O O |
| O | | |
| | | |
| |BAR| |
| | | |
| | | |
| X | | X | +---+
| X X | | X O X | | 2 |
| X X | | X O X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 123 O: 125 X-O: 2-3/7
Cube: 2, X own cube
X to play 66

Paul nailed this one. My variant below is for money, but XG does narrowly
prefer 16/4 13/7(2) over 13/7(3) 8/2 ATS if O owns the cube (on 2 or 4).

1. Rollout¹ 13/7(3) 8/2 eq:+0.931
Player: 70.27% (G:2.34% B:0.05%)
Opponent: 29.73% (G:2.21% B:0.06%)
Confidence: ±0.003 (+0.928..+0.934) - [100.0%]

2. Rollout¹ 13/7(2) 13/1 eq:+0.898 (-0.033)
Player: 68.45% (G:1.95% B:0.01%)
Opponent: 31.55% (G:2.47% B:0.06%)
Confidence: ±0.003 (+0.895..+0.901) - [0.0%]

3. Rollout¹ 16/4 13/7(2) eq:+0.880 (-0.051)
Player: 70.17% (G:2.30% B:0.02%)
Opponent: 29.83% (G:2.28% B:0.12%)
Confidence: ±0.003 (+0.878..+0.883) - [0.0%]

4. Rollout¹ 16/4 13/1 eq:+0.830 (-0.102)
Player: 66.32% (G:1.91% B:0.05%)
Opponent: 33.68% (G:2.91% B:0.20%)
Confidence: ±0.009 (+0.821..+0.838) - [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=-BA--bC-C--B-C--Acdcc-----:1:1:1:66:0:0:0:0:10

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-+
| X X O O | | O O |
| X O O | | O O |
| X O O | | O O |
| O | | |
| | | |
| |BAR| |
| | | |
| | | |
| X | | X | +---+
| X X | | X O X | | 2 |
| X X | | X O X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 123 O: 125 X-O: 0-0
Cube: 2, X own cube
X to play 66

1. Rollout¹ 16/4 13/7(2) eq:+0.799
Player: 71.78% (G:1.66% B:0.03%)
Opponent: 28.22% (G:2.19% B:0.08%)
Confidence: ±0.009 (+0.790..+0.808) - [100.0%]

2. Rollout¹ 13/7(3) 8/2 eq:+0.749 (-0.051)
Player: 71.11% (G:2.36% B:0.04%)
Opponent: 28.89% (G:2.36% B:0.07%)
Confidence: ±0.009 (+0.740..+0.758) - [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
Paul Epstein
2020-07-25 13:44:52 UTC
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Post by Tim Chow
XGID=-BA--bC-C--B-C--Acdcc-----:1:1:1:66:2:3:0:7:10
X:Player 1 O:Player 2
Score is X:2 O:3 7 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X X O O | | O O |
| X O O | | O O |
| X O O | | O O |
| O | | |
| | | |
| |BAR| |
| | | |
| | | |
| X | | X | +---+
| X X | | X O X | | 2 |
| X X | | X O X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 123 O: 125 X-O: 2-3/7
Cube: 2, X own cube
X to play 66
Paul nailed this one. My variant below is for money, but XG does narrowly
prefer 16/4 13/7(2) over 13/7(3) 8/2 ATS if O owns the cube (on 2 or 4).
1. Rollout¹ 13/7(3) 8/2 eq:+0.931
Player: 70.27% (G:2.34% B:0.05%)
Opponent: 29.73% (G:2.21% B:0.06%)
Confidence: ±0.003 (+0.928..+0.934) - [100.0%]
2. Rollout¹ 13/7(2) 13/1 eq:+0.898 (-0.033)
Player: 68.45% (G:1.95% B:0.01%)
Opponent: 31.55% (G:2.47% B:0.06%)
Confidence: ±0.003 (+0.895..+0.901) - [0.0%]
3. Rollout¹ 16/4 13/7(2) eq:+0.880 (-0.051)
Player: 70.17% (G:2.30% B:0.02%)
Opponent: 29.83% (G:2.28% B:0.12%)
Confidence: ±0.003 (+0.878..+0.883) - [0.0%]
4. Rollout¹ 16/4 13/1 eq:+0.830 (-0.102)
Player: 66.32% (G:1.91% B:0.05%)
Opponent: 33.68% (G:2.91% B:0.20%)
Confidence: ±0.009 (+0.821..+0.838) - [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=-BA--bC-C--B-C--Acdcc-----:1:1:1:66:0:0:0:0:10
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-+
| X X O O | | O O |
| X O O | | O O |
| X O O | | O O |
| O | | |
| | | |
| |BAR| |
| | | |
| | | |
| X | | X | +---+
| X X | | X O X | | 2 |
| X X | | X O X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 123 O: 125 X-O: 0-0
Cube: 2, X own cube
X to play 66
1. Rollout¹ 16/4 13/7(2) eq:+0.799
Player: 71.78% (G:1.66% B:0.03%)
Opponent: 28.22% (G:2.19% B:0.08%)
Confidence: ±0.009 (+0.790..+0.808) - [100.0%]
2. Rollout¹ 13/7(3) 8/2 eq:+0.749 (-0.051)
Player: 71.11% (G:2.36% B:0.04%)
Opponent: 28.89% (G:2.36% B:0.07%)
Confidence: ±0.009 (+0.740..+0.758) - [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
I'm not sure whether I would have got the money play right or not.
The issue depends on whether we should be concerned about the long-term
difficulties in safetying the 16 point checker.
For money, the equity is quite far from 1.
This indicates that O will usually have a take and so the difficulty
in bringing the 16 checker to safety needs to be considered, so 16/4.
If we (wrongly) thought that the money equity was 0.95, then we would
play 13/7(3) to avoid jokers, expecting an immediate cash.

For the original problem, the equity is a massive 0.931, indicating
a cash if the opponent doesn't roll a joker so we give Oppy two shots
instead of 3.

Paul

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