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41$-31H-41E-61U-52P-52X-64 — XGR++ and GnuBg Trunc

Posted By: Taper_Mike
Date: Friday, 23 August 2013, at 11:46 a.m.

In Response To: 501 Essential Backgammon Problems #32 -- Rollout (Stick)

XGR++ and GnuBg Trunc
Both Better Than 1k XG Rollout

Stick wrote:

Just to show variance at work between my shorter 1k and your 10k rollout. Can have a sizeable effect on the magnitude of our errors.

It has taken me years, and the experience of working with thousands of rollouts, to really appreciate this fact.

If we can use Igor’s 10k rollout as a measuring stick, then both XGR++ and the corresponding 360-trial, GnuBg 5-ply trunc (below) yield more accurate results than a full 1k rollout with XG. This is not news to me, but it may come as a surprise to the many posters who continue to trust their 1k rollouts.

Note that Stick’s 1k rollout reached 100% confidence. That confidence applies to the top play being best, but has very little to do with the precise margins between the top play and the other candidates. In a long rollout, for instance, the second-best play might end up trailing by 0.001 rather than the 0.047 in Stick’s rollout. Were such an outcome to occur, it should make you question the accuracy of the original 1k rollout. As far as the confidence measure is concerned, however, that result would bolster the original claim of 100% confidence.

If all you need to know is which play is best, then a short rollout (with high confidence) is fine. If you are interested to know how close the second play is, then you generally need something with many more trials.

Mike

41$-31H-41E-61U-52P-52X-64 — Unlimited Games

Bot	Seed	Equity	Nacbracs	Link
GnuBg 0.xx 2-ply Trunc	724778382	+66.556	[Z U12 R15] /0.360t	Taper_Mike (below)
XG 2.10 XGR++ Eval	[XGR++ seed]	+130.9	[Z U17 R22] "&e	Taper_Mike (below)
XG 2.10 3-ply, Cubes: XGR	57408517	+144	[Z U25 R27] "<=10	Igor Erovenko
XG 2.10 3-ply, Cubes: XGR	60045198	+159	[Z R47 U54] "<=1*0.648	Stick

Key: Z = Reverse split = H = Hit [bar/21*, 13/7], R = Run [bar/21*/15], U = Up [bar/21*, 24/18]

Red = Crappy 1k rollout

Explanation of nacbracs

---

XGR++ Eval

		White is Player 2 score: 0 pip: 154 Unlimited Game Jacoby Beaver pip: 174 score: 0 Blue is Player 1
XGID=-a--BAB-C---fD---c-d-a--BA:0:0:1:64:0:0:3:0:10
Blue to play 64

1.	XG Roller++	Bar/21* 13/7	eq: +0.1309
	Player: Opponent: 52.46% (G:15.94% B:0.66%) 47.54% (G:12.33% B:0.72%)
2.	XG Roller++	Bar/21* 24/18	eq: +0.1143 (-0.0167)
	Player: Opponent: 52.46% (G:14.11% B:0.63%) 47.54% (G:12.05% B:0.56%)
3.	XG Roller++	Bar/21* 21/15	eq: +0.1088 (-0.0222)
	Player: Opponent: 52.32% (G:14.79% B:0.66%) 47.68% (G:12.52% B:0.74%)

Eval by Taper_Mike 2013-Aug-23 eXtreme Gammon Version: 2.10.199.2658 41$-31H-41E-61U-42P-52X-64-tm.xgp [Z U17 R22] "&e

eXtreme Gammon Version: 2.10

---

360-Trial GnuBg Trunc

The score (after 0 games) is: Opponent 0, Player 0

Move number 7: Player to play 64

Opponent	154
Player	174
Position ID: yHPwAyBYc/AAWA Match ID: cAkTAAAAAAAA

#		Ply	Move	Equity
•	1	R	bar/21* 13/7	+0.066556
			0.509599 0.158457 0.007321 - 0.490401 0.134847 0.008345 +0.041786 +0.066556 0.000796 0.001005 0.000141 - 0.000796 0.000812 0.000187 0.002220 0.004398
			Truncated cubeful rollout (depth 5) with var.redn.
			360 games, Mersenne Twister dice gen. with seed 724778382 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]
			Different evaluations after 2 plies:
			Play: 1-ply cubeful prune
			keep the first 0 0-ply moves and up to 8 more moves within equity 0.16
			Cube: 2-ply cubeful prune [world class]
	2	R	bar/21* 24/18	+0.054548 ( -0.012008)
			0.507826 0.141387 0.005968 - 0.492174 0.126482 0.005659 +0.030866 +0.054548 0.000721 0.000969 0.000177 - 0.000721 0.000788 0.000122 0.002134 0.004028
			Truncated cubeful rollout (depth 5) with var.redn.
			360 games, Mersenne Twister dice gen. with seed 724778382 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]
			Different evaluations after 2 plies:
			Play: 1-ply cubeful prune
			keep the first 0 0-ply moves and up to 8 more moves within equity 0.16
			Cube: 2-ply cubeful prune [world class]
	3	R	bar/21*/15	+0.051552 ( -0.015004)
			0.508694 0.147308 0.006677 - 0.491306 0.135225 0.007779 +0.028369 +0.051552 0.000744 0.000977 0.000141 - 0.000744 0.000709 0.000156 0.002086 0.004107
			Truncated cubeful rollout (depth 5) with var.redn.
			360 games, Mersenne Twister dice gen. with seed 724778382 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]
			Different evaluations after 2 plies:
			Play: 1-ply cubeful prune
			keep the first 0 0-ply moves and up to 8 more moves within equity 0.16
			Cube: 2-ply cubeful prune [world class]

Annotation

Truncated Rollout by Taper_Mike
2013-Aug-23
Version GNU Backgammon 0.90-mingw 20120806
41$-31H-41E-61U-52P-52X-64-tm.sgf
[Z U12 R15] /0.360t

Messages In This Thread

• 501 Essential Backgammon Problems #32
  Igor -- Saturday, 17 August 2013, at 4:16 p.m.
  • 501 Essential Backgammon Problems #32
    Taper_Mike -- Saturday, 17 August 2013, at 7:01 p.m.
  • 501 Essential Backgammon Problems #32 -- Rollout + Variant
    Igor -- Tuesday, 20 August 2013, at 3:31 p.m.
    • 501 Essential Backgammon Problems #32 -- Rollout
      Stick -- Tuesday, 20 August 2013, at 4:27 p.m.
      • 501 Essential Backgammon Problems #32 -- Rollout
        Igor -- Tuesday, 20 August 2013, at 4:32 p.m.
        • 501 Essential Backgammon Problems #32 -- Rollout
          Stick -- Wednesday, 21 August 2013, at 1:09 a.m.
          • 41$-31H-41E-61U-52P-52X-64 — XGR++ and GnuBg Trunc
            Taper_Mike -- Friday, 23 August 2013, at 11:46 a.m.