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Rollout

Posted By: Timothy Chow
Date: Thursday, 24 December 2009, at 4:43 p.m.

In Response To: Money game: Blue to play 53 (Timothy Chow)

OTB I ticked off the safe-versus-bold checklist: behind in the race, stronger board, more checkers back. So I decided that I wanted to maintain contact and didn't need to worry excessively about leaving blots, especially since 2's and 4's are duplicated. Anchoring avoids bad accidents but is tantamount to resigning oneself to a losing race in which the opponent has cube access. I played 13/10 13/8.

The rollout, however, shows Stick's intuition to be correct: Anchoring comes out clearly on top.

Still, I wasn't satisfied. What was wrong with my reasoning? I tried fiddling around with the position a little. For example, I tried moving two checkers from my 4-point back to my 5-point, strengthening my board and putting myself 2 more pips behind in the race. In this modified position, my play 13/10 13/8 floats to the top of the rollout (see second diagram below), clearly ahead of anchoring.

Moving all three checkers from the 4-point back to the 5-point produces a rollout that doesn't quite make sense (see third diagram below) since it suggests that White is then too good (?!) after any play. I interpret this to mean that GNU 2-ply doesn't realize that Blue must drop.

The conclusion seems to be that Blue is in dire straits in all three positions. Seemingly small changes in the race and/or the strength of Blue's board will dictate which straw to grasp at—an inferior race or a risky attempt to get a shot and hit it.

gnubg	124
tchow	145
Position ID: xOdxBgDsDPgRBA Match ID: cIkVANAAGAAA

#		Ply	Move	Equity
•	1	R	21/16 13/10	-0.875
			0.242 0.001 0.000 - 0.758 0.003 0.000 -0.517 -0.875 0.001 0.000 0.000 - 0.001 0.000 0.000 0.002 0.004
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 839227481 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]
	2	R	16/11 13/10	-0.931 ( -0.056)
			0.266 0.022 0.001 - 0.734 0.105 0.001 -0.551 -0.931 0.001 0.001 0.000 - 0.001 0.002 0.001 0.003 0.008
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 839227481 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]
	3	R	13/10 13/8	-0.952 ( -0.077)
			0.261 0.022 0.001 - 0.739 0.105 0.002 -0.561 -0.952 0.001 0.001 0.000 - 0.001 0.002 0.000 0.003 0.007
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 839227481 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]

gnubg	124
tchow	147
Position ID: xOdxBgCsDfgRBA Match ID: cIkVANAAGAAA

#		Ply	Move	Equity
•	1	R	13/10 13/8	-0.947
			0.267 0.024 0.001 - 0.733 0.114 0.002 -0.556 -0.947 0.001 0.001 0.000 - 0.001 0.002 0.000 0.003 0.008
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 840463696 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]
	2	R	16/11 13/10	-0.954 ( -0.008)
			0.261 0.022 0.001 - 0.739 0.100 0.001 -0.557 -0.954 0.001 0.001 0.000 - 0.001 0.002 0.000 0.003 0.008
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 840463696 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]
	3	R	13/5	-0.975 ( -0.029)
			0.259 0.025 0.001 - 0.741 0.113 0.001 -0.570 -0.975 0.001 0.001 0.000 - 0.001 0.002 0.000 0.003 0.008
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 840463696 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]
	4	R	21/16 13/10	-0.976 ( -0.029)
			0.220 0.001 0.000 - 0.780 0.002 0.000 -0.561 -0.976 0.001 0.000 0.000 - 0.001 0.000 0.000 0.002 0.004
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 840463696 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]

gnubg	124
tchow	148
Position ID: xOdxBgDMDfgRBA Match ID: cIkVANAAGAAA

#		Ply	Move	Equity
•	1	R	13/10 13/8	-1.002
			0.254 0.024 0.001 - 0.746 0.114 0.002 -0.583 -1.002 0.001 0.001 0.000 - 0.001 0.002 0.000 0.003 0.007
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 839259744 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]
	2	R	16/11 13/10	-1.014 ( -0.012)
			0.251 0.022 0.001 - 0.749 0.110 0.001 -0.585 -1.014 0.001 0.001 0.000 - 0.001 0.002 0.000 0.003 0.007
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 839259744 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]
	3	R	21/16 13/10	-1.022 ( -0.019)
			0.211 0.001 0.000 - 0.789 0.003 0.000 -0.579 -1.022 0.001 0.000 0.000 - 0.001 0.001 0.002 0.002 0.004
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 839259744 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]

Messages In This Thread

• Money game: Blue to play 53
  Timothy Chow -- Saturday, 19 December 2009, at 7:46 p.m.
  • Money game: Blue to play 53
    Stick -- Saturday, 19 December 2009, at 7:55 p.m.
    • Money game: Blue to play 53
      neilkaz -- Sunday, 20 December 2009, at 3:04 a.m.
  • Money game: Blue to play 53
    Chuck Bower -- Sunday, 20 December 2009, at 2:51 a.m.
  • Money game: Blue to play 53
    Nack Ballard -- Sunday, 20 December 2009, at 3:09 a.m.
  • Rollout
    Timothy Chow -- Thursday, 24 December 2009, at 4:43 p.m.