On Monday, July 3, 2023 at 1:18:52 PM UTC+1, Timothy Chow wrote:
XGID=a-BBBDAAA--------ccbbBbb--:2:-1:1:65:0:0:0:0:10
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O O | | O O X O O | +---+
| O O | | O O X O O | | 4 |
| O O | | | +---+
| | | |
| | | |
| |BAR| |
| | O | |
| | | X |
| | | X |
| | | X X X X |
| X X | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 101 O: 102 X-O: 0-0
Cube: 4, O own cube
X to play 65
Making home-board points during a blitz is usually the right strategy.
But XG says this is an exception. The trouble is that even after
making the 1pt, X still has a lot of work to do. The 6pt will be
hard to make, and O will probably be threatening to enter and turn
the game around for several rolls to come. Also, two of X's checkers
are behind O's four-prime, so he's in some danger of crunching his
board if he can't leap those checkers out.
If X jumps both checkers out now, then he'll certainly be unhappy if
O rolls a 6. But otherwise, most of his rolls will cover his 6pt, practically locking up the game. He won't have to worry about
escaping his back checkers. And finally, O's sixes from the bar
are pretty bad for him anyway. Obviously X doesn't want to get hit,
but if he does get hit, he still has a few return shots from the bar.
In the variant, X doesn't have as many ways to cover his 6pt, has
better outfield coverage if O enters with a 6, and is in less danger
of being forced to crunch his board.
1. Rollout¹ 21/16 21/15 eq:+0.005
Player: 60.17% (G:8.06% B:0.07%)
Opponent: 39.83% (G:18.93% B:1.81%)
Confidence: ±0.003 (+0.002..+0.008) - [100.0%]
2. Rollout¹ 7/1 6/1 eq:-0.086 (-0.092)
Player: 54.32% (G:6.23% B:0.03%)
Opponent: 45.68% (G:5.89% B:0.18%)
Confidence: ±0.004 (-0.090..-0.083) - [0.0%]
¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
eXtreme Gammon Version: 2.19.211.pre-release
-------
Variant
-------
XGID=a-BBBDAA-----A---ccbbBbb--:2:-1:1:65:0:0:0:0:10
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O | | O O X O O | +---+
| O O | | O O X O O | | 4 |
| O O | | | +---+
| | | |
| | | |
| |BAR| |
| | O | |
| | | X |
| | | X |
| | | X X X X |
| X | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 106 O: 102 X-O: 0-0
Cube: 4, O own cube
X to play 65
1. Rollout¹ 7/1 6/1 eq:-0.049
Player: 55.45% (G:6.31% B:0.03%)
Opponent: 44.55% (G:5.80% B:0.17%)
Confidence: ±0.007 (-0.057..-0.042) - [99.7%]
2. Rollout¹ 21/16 21/15 eq:-0.063 (-0.013)
Player: 57.89% (G:6.91% B:0.06%)
Opponent: 42.11% (G:19.14% B:1.78%)
Confidence: ±0.006 (-0.069..-0.056) - [0.3%]
¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
eXtreme Gammon Version: 2.19.211.pre-release
---
Tim Chow
The analysis could also mention that the correct play gives
the opponent big gammon chances. This explains why the correct
play gives only an equal game despite them only having 11/36 good rolls. However, the correct play is obvious at DMP.
This position makes a good illustration for Stick's DMP Rule, although that could be said to be cherry-picking.
Note that the correct play has a nice diversification aspect making
the covering of the 6 point (if not hit) more likely than it may first appear. As well as 1s and 2s to cover, 9s and 10s also cover with no duplication.
This means that 28 out of 36 (7/9) rolls cover the 6 point.
Paul
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