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It was a small error... Rollout

Posted By: Daniel Murphy
Date: Tuesday, 6 November 2012, at 7:48 p.m.

In Response To: It was a small error... Rollout (Taper_Mike)

Well, I think you're right that the zugzwang idea doesn't really apply here. As the Wikipedia article goes on to point out, it's not just that a player is forced to make a move when he'd rather not make a move at all (which, since that's not legal, he can accomplish by making a trivial move that does not affect the equity of his position), but that the condition of zugzwang means that any play he chooses makes his position worse.

In the backgammon position, Blue can force White to ... to try to enter? But Blue's hit does not force him to make a play that makes his position worse. In fact White is a lot better off when he responds to 16/12 2/1* with a hit, than if White had hit after 16/11. And that's balanced by his being worse off in other sequences, particularly the 9 fanning numbers.

A study of similar "Should Blue open up a second blot? Is the tempo gained worth the risk?" positions would be interesting. I know that in my experience, exposing a second blot turned out to be wrong more often than I thought, but that doesn't tell you much besides that I previously thought that exposing a second blot was right more often than it was. Mike's position is a good example of those kinds of errors, perhaps -- even with White only having a 2 point board, 2/1* is just barely better. Give White a 3-point board, and it's definitely not:

The score (after 0 games) is: White 0, Blue 0

Move number 5: Blue to play 41

White77

5X5X2X ' ' ' ' '1O ' ' '

1X6O2O ' '2O ' '2X ' ' '
Blue46
Position ID: 3zcAGCB+YwACAA Match ID: QQkGAAAAAAAA

• Blue moves 16/11

# Ply Move Equity
1 R 16/11 +0.841890
0.8910410.0965210.001660-0.1089590.0000000.000000 +0.880262 +0.841890
0.0014230.0015010.000276-0.0014230.0000000.000000 0.003049 0.003678
Full cubeful rollout with var.redn.
452 games, Mersenne Twister dice gen. with seed 699422448 and quasi-random dice
Play: world class 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0.16
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]
2 R 16/12 2/1* +0.809879 ( -0.032011)
0.8531230.1556510.001324-0.1468770.0000000.000000 +0.863221 +0.809879
0.0018250.0020930.000254-0.0018250.0000000.000000 0.003817 0.004937
Full cubeful rollout with var.redn.
450 games, Mersenne Twister dice gen. with seed 699422448 and quasi-random dice
Play: world class 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0.16
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

Notice that the "cubeless" numbers would suggest that hitting is clearly right, since "cubeless" that play wins 6.16% more gammons and loses only 2.28% fewer games. Cubeful action must tell a different story.

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