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11/4 is not an error (IMO)

Posted By: Nack Ballard
Date: Tuesday, 21 November 2023, at 1:55 a.m.

In Response To: pay now? How come? (svilo)





White is Player 2

score: 0
pip: 78
Unlimited Game
Jacoby Beaver
pip: 27
score: 0

Blue is Player 1
XGID=-EE-a-B----------aabbbbbb-:1:-1:1:62:0:0:3:0:10
Backgammon by Paul Magriel, Chapter 14, Position 1

Above is X22's first position of Chapter 14. He poses the question of how Black should play 62. As is the case in most of the chapters in his book, there is no cube to be seen in Chapter 14 -- not even a blank square off to the side of the board.

If we assume that this is a money game and Black has not double-whoppered by failing to double, the cube is not in the center here. Magriel didn't indicate that it is. Nor did he indicate that it isn't. That was me who put it on the opponent's side, because that is its logical position.

I suppose that either we are to assume that:

(a) It is a money/NMS position and the cube is in its obvious position (owned by the opponent -- otherwise Black would have doubled instead of rolling); or

(b) It is a money/NMS game and we are to assume the cube is in it's most likely position -- the one that conforms to the way that two cube-savvy players would with high probability reach the position; or

(c) It is DMP; or

(d) The game is cubeless (with Gs and BGs counting).

I haven't read Paul's masterpiece in decades, so I don't remember if there was supposed to be an assumption or that the cube status goes addressed (except in chapters highlighting the cube). If I had to pick an assumption that seems most consistent with the tenor of his book, like it or not, I would go with "b" (the cube is in its most likely position).

With that in mind, let's move on to Magriel's fourth position in the same chapter, the feature position of Svilo's post:





White is Player 2

score: 0
pip: 126
Unlimited Game
Jacoby Beaver
pip: 76
score: 0

Blue is Player 1
XGID=-BBBBcC-B--B-----bbbbbb---:1:-1:1:61:0:0:3:0:10
Backgammon by Paul Magriel, Chapter 14, Position 4

1.Rollout111/4eq: -0.0886
Player:
Opponent:		50.10% (G:2.19% B:0.01%)
49.90% (G:5.54% B:0.14%)		Conf.: ±0.0024 (-0.0911...-0.0862) - [100.0%]
Duration: 21 minutes 03 seconds
2.Rollout18/7 8/2eq: -0.1114 (-0.0228)
Player:
Opponent:		50.17% (G:2.28% B:0.01%)
49.83% (G:6.78% B:0.24%)		Conf.: ±0.0041 (-0.1155...-0.1073) - [0.0%]
Duration: 18 minutes 03 seconds
1 1296 Games rolled with Variance Reduction.
Dice Seed: 70563229
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

I have put the cube on the opponent's side, because by either assumption "a" (obvious position) or assumption "b" most likely position), it clearly belongs there. In money or at NMS, this is a monster central double (and take), and with so many market-losing sequences, it is even an obvious redouble for competent players.

With that in mind, 11/4 would be the best play, just as the author claims.

For his excellent book Classic Backgammon Revisited, Jeremy Bagai selected a few renowned books, including PM's Backgammon. He went through them with a fine-tooth comb, rolled out the positions and logged the errors. I note that Jeremy did not include Magriel's 11/4 above. I hope that no one else publishes it as an error, either.

Nack

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