BGonline.org Forums

Race cubes - rollouts

Posted By: Daniel Murphy
Date: Saturday, 2 June 2007, at 7:57 p.m.

In Response To: Race cubes (Daniel Murphy)

Forumette's Theorem: The number of responses to a problem is proportional to the cube root of the number of diagrams shown in the problem.

Moving right along, at 3-away all both positions are of course huge double/passes. At 5-away all both positions are takes. For money the first one is a take, the second is a pass.

---

First position, money game rollout:

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

Move number 7: White on roll, cube decision?

White	72
Blue	80
Position ID: bbsFEQC1200AAA Match ID: MAEAAAAAAAAA

Cube decision
Rollout cubeless equity		+0.5570
Cubeful equities:
1.	Double, take	+0.9779
2.	Double, pass	+1.0000	+0.0221
3.	No double	+0.8439	-0.1340
Proper cube action:		Double, take
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Centered 1-cube 0.7785 0.0000 0.0000 - 0.2215 0.0000 0.0000 +0.5570 +0.8439 Standard error 0.0001 0.0000 0.0000 - 0.0001 0.0000 0.0000 0.0002 0.0012 Player Blue owns 2-cube 0.7781 0.0000 0.0000 - 0.2219 0.0000 0.0000 +1.1122 +0.9779 Standard error 0.0001 0.0000 0.0000 - 0.0001 0.0000 0.0000 0.0004 0.0017
Full cubeful rollout with var.redn.
718 games, Mersenne Twister dice gen. with seed 1061815761 and quasi-random dice
Play: 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0.12
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

---

Second position, 5-away all rollout:

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

Move number 4: White on roll, cube decision?

White	71
Blue	80
Position ID: bbsFEQC1u00AAA Match ID: MAHgACAAEAAA

Cube decision
Rollout cubeless equity		+0.5885	(Money: +0.5885)
Cubeful equities:
1.	Double, take	+0.9929
2.	Double, pass	+1.0000	+0.0071
3.	No double	+0.8609	-0.1320
Proper cube action:		Double, take
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Centered 1-cube 0.7942 0.0000 0.0000 - 0.2058 0.0000 0.0000 +0.5885 +0.8609 Standard error 0.0001 0.0000 0.0000 - 0.0001 0.0000 0.0000 0.0002 0.0011 Player Blue owns 2-cube 0.7941 0.0000 0.0000 - 0.2059 0.0000 0.0000 +1.1411 +0.9929 Standard error 0.0001 0.0000 0.0000 - 0.0001 0.0000 0.0000 0.0006 0.0021
Full cubeful rollout with var.redn.
864 games, Mersenne Twister dice gen. with seed 1061815761 and quasi-random dice
Play: 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0.12
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

---

Second, position, money game rollout:

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

Move number 8: White on roll, cube decision?

White	71
Blue	80
Position ID: bbsFEQC1u00AAA Match ID: MAEAAAAAAAAA

Cube decision
Rollout cubeless equity		+0.5885
Cubeful equities:
1.	Double, pass	+1.0000
2.	Double, take	+1.0514	+0.0514
3.	No double	+0.8768	-0.1232
Proper cube action:		Double, pass
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Centered 1-cube 0.7942 0.0000 0.0000 - 0.2058 0.0000 0.0000 +0.5885 +0.8768 Standard error 0.0001 0.0000 0.0000 - 0.0001 0.0000 0.0000 0.0002 0.0014 Player Blue owns 2-cube 0.7939 0.0000 0.0000 - 0.2061 0.0000 0.0000 +1.1757 +1.0514 Standard error 0.0001 0.0000 0.0000 - 0.0001 0.0000 0.0000 0.0005 0.0022
Full cubeful rollout with var.redn.
432 games, Mersenne Twister dice gen. with seed 1061815761 and quasi-random dice
Play: 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0.12
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

A raw "10% +2" formula for White's takepoint, usually a good guide, doesn't work here. White's position is more efficient, but only by a little. Chase estimated EPC as 79 (8 pips wasted) and 88 (8 wasted), a difference of 9. The actual numbers (according to GNUBG**) are 79.841 (8.841 wasted) and 88.698 (8.698 wasted), a difference of 8.857.

Some 71-80 pip races are takes, some are passes.

This one is borderline:

White's pip count	71	Blue's pip count	80White's raw lead	9
White's EPC	79.759	Blue's EPC	88.296	White's EPC lead	8.537
White's wastage8.759	Blue's wastage	8.296

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

Move number 19: White on roll, cube decision?

White	71
Blue	80
Position ID: td1KAQC1u00AAA Match ID: MAEAAAAAAAAA

• White doubles

Cube decision
Rollout cubeless equity		+0.5654
Cubeful equities:
1.	Double, pass	+1.0000
2.	Double, take	+1.0012	+0.0012
3.	No double	+0.8586	-0.1414
Proper cube action:		Double, pass
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Centered 1-cube 0.7827 0.0000 0.0000 - 0.2173 0.0000 0.0000 +0.5654 +0.8586 Standard error 0.0001 0.0000 0.0000 - 0.0001 0.0000 0.0000 0.0002 0.0020 Player Blue owns 2-cube 0.7823 0.0000 0.0000 - 0.2177 0.0000 0.0000 +1.1291 +1.0012 Standard error 0.0002 0.0000 0.0000 - 0.0002 0.0000 0.0000 0.0006 0.0031
Full cubeful rollout with var.redn.
216 games, Mersenne Twister dice gen. with seed 1061942415 and quasi-random dice
Play: 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0.12
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

**Notice that White's position in the last two diagrams is the same but Blue's is different. I don't know why GNUBG reports two different EPCs for White.

Messages In This Thread

• Race cubes
  Daniel Murphy -- Friday, 1 June 2007, at 6:07 p.m.
  • Correction - score is 2-2/7
    Daniel Murphy -- Friday, 1 June 2007, at 7:00 p.m.
    • Correction - score is 2-2/7
      neilkaz -- Saturday, 2 June 2007, at 2:46 a.m.
  • Race cubes
    Chase -- Friday, 1 June 2007, at 7:29 p.m.
  • Race cubes - rollouts
    Daniel Murphy -- Saturday, 2 June 2007, at 7:57 p.m.
    • Race cubes - rollouts
      Chase -- Saturday, 2 June 2007, at 8:52 p.m.
    • Race cubes - rollouts
      neilkaz -- Sunday, 3 June 2007, at 4:38 a.m.