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Blue's 22 play before the ho-hum 61

Posted By: Nack Ballard
Date: Monday, 30 June 2014, at 6:48 a.m.

In Response To: Blue's 22 play before the ho-hum 61 (Robert Chow)





White is Player 2

score: 0
pip: 88
Unlimited Game
Jacoby Beaver
pip: 127
score: 0

Blue is Player 1
XGID=---BBBC---A-dC----Babbbbb-:1:-1:1:22:0:0:3:0:10

43S-44P-21@-55J-55C-52I-62P-33P-31P-11E-C-21D-55R-22


1.Rollout113/11 6/2 4/2eq: -0.5309
Player:
Opponent:		33.26% (G:2.88% B:0.07%)
66.74% (G:3.07% B:0.12%)		Conf.: ±0.0010 (-0.5319...-0.5298) - [99.9%]
Duration: 5 hours 02 minutes
2.Rollout113/11 10/8 6/2eq: -0.5331 (-0.0023)
Player:
Opponent:		32.96% (G:2.78% B:0.07%)
67.04% (G:2.34% B:0.04%)		Conf.: ±0.0010 (-0.5341...-0.5321) - [0.1%]
Duration: 4 hours 21 minutes
3.Rollout210/2eq: -0.5344 (-0.0035)
Player:
Opponent:		32.89% (G:2.80% B:0.07%)
67.11% (G:2.38% B:0.03%)		Conf.: ±0.0012 (-0.5356...-0.5332) - [0.0%]
Duration: 2 hours 32 minutes
4.Rollout213/7 4/2eq: -0.5349 (-0.0040)
Player:
Opponent:		33.42% (G:3.15% B:0.08%)
66.58% (G:4.64% B:0.27%)		Conf.: ±0.0012 (-0.5361...-0.5336) - [0.0%]
Duration: 2 hours 41 minutes
1 41472 Games rolled with Variance Reduction.
Dice Seed: 1019915
Moves: 3-ply, cube decisions: XG Roller

2 31104 Games rolled with Variance Reduction.
Dice Seed: 1019915
Moves: 3-ply, cube decisions: XG Roller

Tim's and Robert's theories make sense. Somehow I forgot that the checker plays are 3-ply, not XGR++!

Below is a table of Blue's equities when White's responds with rolls of 51, 41, 32 and 31, to each of three double 2s moves. The columns are: (1) roll, (2) 3-ply play, (3) XGR++ play, (4) XGR++ eval of the 3-ply play, (5) XGR++ eval of the XGR++ play if different from 3-ply, (6) Total of the four 3-ply equities, (7) cost compared to best performing play, and (8) column 7 divided by 18. The under-number in column 8 is the rollout margin.

---------------------------------------------------------------

.........MOVES...........XGR++ EVALS
....3-ply.....XGR++......3-ply.XGR++...Total (cost)...div18

13/11 6/2 4/2

51..13/8 6/5..13/8 6/5...-.401........-1.740 (-.000) -.0000
41..13/8......5/4 5/1... -.423 -.464.................-.0000 ro
32..13/8......5/3 5/2... -.423 -.462
31..5/1...... 5/1........-.493

13/11 10/8 6/2

51..13/8 6/5..13/8 6/5...-.379........-1.776 (-.036) -.0020
41..5/4 5/1...5/4 5/1... -.467.......................-.0023 ro
32..6/1.......5/3 5/2... -.439 -.466
31..5/1.......5/1....... -.491

13/7 4/2

51..13/8 6/5..13/8 6/5...-.462........-1.854 (-.114) -.0063
41..13/8......5/4 5/1... -.464 -.473.................-.0040 ro
32..13/8......13/8 ......-.464
31..13/9......5/1....... -.464 -.498

---------------------------------------------------------------

When White's 3-ply play and XGR++ play both leave a shot, Blue's natural 13/11 10/8 6/2 play does best. For example, vs 51, it gains .022 (compared to the board-compromising 13/11 6/2 4/2). However, the 3-ply errors induced by the (presumably inferior) 13/11 6/2 4/2 more than make up for that, placing it (unfairly) atop the rollout.

The net costs (unfairly) charged to 13/11 10/8 6/2 are -.0020, which is very close to its -.0023 margin in the rollout.

Despite inducing the most 3-ply error ((.009 + .034)/18), 13/7 4/2 is unable to make up for its loss (from a double-blotted board) when White leaves a shot. I'm not sure what accounts for the difference between its already optimistic -.0063 and its rollout margin of -.0040. One possibility is that this peculiar move manages to induce additional 3-ply errors on White's subsequent roll(s).

Nack

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