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XG Error analysis question - 2nd position

Posted By: Daniel Murphy
Date: Monday, 19 September 2011, at 4:29 a.m.

In Response To: XG Error analysis question (joe freedman)

First, the usual rollout presentation, in EMG and ME:

The score (after 0 games) is: White 2, Blue 4 (match to 7 points). Blue on roll.

White	85
Blue	49
Position ID: 23YDBCD+zgsAAA Match ID: UQngACAAIAAE

Cube decision
Rollout cubeless equity		+0.6976	(Money: +0.7389)
Cubeful equities:
1.	Double, take	+0.9727
2.	Double, pass	+1.0000	+0.0273
3.	No double	+0.8746	-0.0981
Proper cube action:		Redouble, take
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Player Blue owns 2-cube 0.8428 0.0519 0.0018 - 0.1572 0.0004 0.0000 +0.6976 +0.8746 Standard error 0.0003 0.0015 0.0004 - 0.0003 0.0000 0.0000 0.0006 0.0011 Player White owns 4-cube 0.8373 0.1300 0.0053 - 0.1627 0.0006 0.0000 +1.2095 +0.9727 Standard error 0.0004 0.0027 0.0004 - 0.0004 0.0002 0.0000 0.0015 0.0021
Full cubeful rollout with var.redn.
10000 games, Mersenne Twister dice gen. with seed 928994868 and quasi-random dice
Play: supremo 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

Cube decision
Rollout cubeless MWC		79.025%	(Money: +0.7389)
Cubeful equities:
1.	Double, take	83.727%
2.	Double, pass	84.194%	0.467%
3.	No double	82.050%	-1.677%
Proper cube action:		Redouble, take
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Player Blue owns 2-cube 0.8428 0.0519 0.0018 - 0.1572 0.0004 0.0000 79.025% 82.050% Standard error 0.0003 0.0015 0.0004 - 0.0003 0.0000 0.0000 0.011% 0.020% Player White owns 4-cube 0.8373 0.1300 0.0053 - 0.1627 0.0006 0.0000 87.776% 83.727% Standard error 0.0004 0.0027 0.0004 - 0.0004 0.0002 0.0000 0.026% 0.035%
Full cubeful rollout with var.redn.
10000 games, Mersenne Twister dice gen. with seed 928994868 and quasi-random dice
Play: supremo 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

Compare that to the actual results (where a pass is a pass!) of the same rollout, obtained with Gnubg's "show statistics" feature:

No Double
	Blue Wins 2 pts	Blue Wins 3 pts	White Wins 2 pts	White wins 4 pts	White wins 5 pts
2-cube	65.96%	00.14%	03.89%	00.05%	00.00%
4-cube	00.00%	13.85%	00.00%	00.02%	00.00%
8-cube	00.00%	10.43%	00.00%	00.00%	05.65%
Totals	65.06%	24.42%	03.89%	00.07%	05.65%
Double/Take
	Blue Wins 2 pts	Blue Wins 3 pts	White wins 2 pts	White wins 4 pts	White wins 5 pts
4-cube	00.00%	51.85%	00.00%	00.00%	00.00%
8-cube	00.00%	31.69%	00.00%	00.00%	16.46%
Totals	00.00%	83.54%	00.00%	00.00%	16.46%

No Double MWC = (0.6506 * 0.841941) + 0.2442 + (0.0389 * 0.50) + (0.007 * 0.248821) = 81.31%

Double/Take MWC = 83.54%

Summarizing GWC and MWC:

No Double GWC	No Double MWC	Double/pass MWC	Double/Take GWC	Double/Take MWC
89.48%	81.31%	84.194%	83.54%	83.54%

Messages In This Thread

• XG Error analysis question
  joe freedman -- Sunday, 18 September 2011, at 1:42 p.m.
  • XG Error analysis question
    Bob Koca -- Sunday, 18 September 2011, at 2:58 p.m.
  • XG Error analysis question
    Daniel Murphy -- Sunday, 18 September 2011, at 3:55 p.m.
  • Links
    Timothy Chow -- Sunday, 18 September 2011, at 6:44 p.m.
  • XG Error analysis question
    joe freedman -- Sunday, 18 September 2011, at 10:18 p.m.
    • XG Error analysis question
      Daniel Murphy -- Sunday, 18 September 2011, at 10:38 p.m.
    • XG Error analysis question
      Daniel Murphy -- Sunday, 18 September 2011, at 11:02 p.m.
  • XG Error analysis question - 2nd position
    Daniel Murphy -- Monday, 19 September 2011, at 4:29 a.m.