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Cubeless games in cubeful rollouts #2

Posted By: Daniel Murphy
Date: Sunday, 4 September 2011, at 1:17 a.m.

In Response To: Cubeless games in cubeful rollouts (Daniel Murphy)

Below, a second position. Again, I'm presenting displays (using Timothy Chow's labels) of "traditional statistics" (which include cubeless equity and cubeless or "cubeless" or "pseudocubeless" game outcomes) and "actual statistics" (the actual outcomes of every trial in the rollout).

The first position was simple -- no gammons or backgammons, and no takable redoubles. Here there are no gammons, but there are redoubles and more -- some games end with the cube on 32.

Money game. Blue on roll.

White	49
Blue	56
Position ID: dQcAAG23OwAAAA Match ID: UQkAAAAAAAAA

"Traditional statistics"

Cube decision
Rollout cubeless equity		+0.5448
Cubeful equities:
1.	Double, take	+0.9542
2.	Double, pass	+1.0000	+0.0458
3.	No double	+0.9308	-0.0234
Proper cube action:		Redouble, take
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Player Blue owns 2-cube 0.7724 0.0000 0.0000 - 0.2276 0.0000 0.0000 +0.5448 +0.9308 Standard error 0.0036 0.0000 0.0000 - 0.0036 0.0000 0.0000 0.0073 0.0186 Player White owns 4-cube 0.7723 0.0000 0.0000 - 0.2277 0.0000 0.0000 +1.0892 +0.9542 Standard error 0.0040 0.0000 0.0000 - 0.0040 0.0000 0.0000 0.0160 0.0213
Full cubeful rollout without var.redn.
10000 games, Mersenne Twister dice gen. with seed 1010101010 and quasi-random dice
Play: 4-ply cubeful prune
keep the first 0 0-ply moves and up to 8 more moves within equity 0.16
Skip pruning for 1-ply moves.
keep the first 0 2-ply moves and up to 2 more moves within equity 0.08
Skip pruning for 3-ply moves.
Cube: 4-ply cubeful prune

"Actual statistics"

Cube decision
Cubeful equities:
1.	Double, take	+0.9542
2.	Double, pass	+1.0000	+0.0487
3.	No double	+0.9308	-0.0234
Proper cube action:		Redouble, take
Rollout details
Win Win Double value Win Extra Value Lose Lose Double value Lose Extra value Cubeful Player Blue owns 2-cube 0.7986 0.5522 0.0201 - 0.2014 0.1376 0.0487 +0.9308 Standard error 0.0036 0.0000 0.0000 - 0.0036 0.0000 0.0000 0.0186 Player White owns 4-cube 0.7562 0.0233 0.0034 - 0.2438 0.0638 0.0018 +0.9542 Standard error 0.0040 0.0000 0.0000 - 0.0040 0.0000 0.0000 0.0213
Full cubeful rollout without var.redn.
10000 games, Mersenne Twister dice gen. with seed 1010101010 and quasi-random dice
Play: 4-ply cubeful prune
keep the first 0 0-ply moves and up to 8 more moves within equity 0.16
Skip pruning for 1-ply moves.
keep the first 0 2-ply moves and up to 2 more moves within equity 0.08
Skip pruning for 3-ply moves.
Cube: 4-ply cubeful prune

The table below shows exactly how often how many points were won in the rollout:

No Redouble

Blue	Wins	White
22.63%	2 points	01.51%
55.22%	4 points	13.76%
01.75%	8 points	04.75%
00.25%	16 points	00.10%
00.01%	32 points	00.02%
79.86%	Total	20.14%

Double/Take

Blue	Wins	White
00.00%	2 points	00.00%
72.95%	4 points	17.82%
02.33%	8 points	06.38%
00.31%	16 points	00.16%
00.03%	32 points	00.02%
75.62%	Total	24.38%

---

Pay no attention to how close the Double / No Double decision is. Gnubg underestimates Blue's cubeless GWC (there's no getting away from it!) by about 5% in the starting position. Here are evaluations of the starting position, of the next turn, and the next:

Blue on roll

White	49
Blue	56
Position ID: dQcAAG23OwAAAA Match ID: UQkAAAAAAAAA

Cube decision
2-ply cubeless equity		+0.4543
	0.7272 0.0000 0.0000 - 0.2728 0.0000 0.0000
Cubeful equities:
1.	No double	+0.7244
2.	Double, pass	+1.0000	+0.2756
3.	Double, take	+0.7237	-0.0007
Proper cube action:		No redouble, take (0.2%)

Blue on roll after 6-1 ... fan

White	49
Blue	49
Position ID: dQcAAG13GwAAAA Match ID: UQkAAAAAAAAA

Cube decision
2-ply cubeless equity		+0.4615
	0.7308 0.0000 0.0000 - 0.2692 0.0000 0.0000
Cubeful equities:
1.	No double	+0.7749
2.	Double, pass	+1.0000	+0.2251
3.	Double, take	+0.7512	-0.0237
Proper cube action:		No redouble, take (9.5%)

Blue on roll after 6-1 ... fan ... 5-4 ... fan

White	49
Blue	40
Position ID: dQcAAN3uDAAAAA Match ID: UQkAAAAAAAAA

Cube decision
2-ply cubeless equity		+0.5647
	0.7824 0.0000 0.0000 - 0.2176 0.0000 0.0000
Cubeful equities:
1.	Double, take	+0.9916
2.	Double, pass	+1.0000	+0.0084
3.	No double	+0.8201	-0.1715
Proper cube action:		Redouble, take

Messages In This Thread

• Cubeless games in cubeful rollouts
  Daniel Murphy -- Friday, 2 September 2011, at 3:16 p.m.
  • Cubeless games in cubeful rollouts
    Timothy Chow -- Friday, 2 September 2011, at 4:56 p.m.
  • Cubeless games in cubeful rollouts
    Neil Robins -- Saturday, 3 September 2011, at 4:49 a.m.
    • Cubeless games in cubeful rollouts
      Timothy Chow -- Saturday, 3 September 2011, at 5:28 p.m.
      • Cubeless games in cubeful rollouts
        Daniel Murphy -- Saturday, 3 September 2011, at 7:09 p.m.
        • Cubeless games in cubeful rollouts
          Timothy Chow -- Sunday, 4 September 2011, at 6:37 p.m.
          • Cubeless games in cubeful rollouts
            Neil Robins -- Monday, 5 September 2011, at 7:53 a.m.
            • Cubeless games in cubeful rollouts
              Timothy Chow -- Tuesday, 6 September 2011, at 12:41 a.m.
  • Cubeless games in cubeful rollouts #2
    Daniel Murphy -- Sunday, 4 September 2011, at 1:17 a.m.