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Something's got to give

Posted By: Timothy Chow
Date: Friday, 19 March 2010, at 2:12 a.m.

In Response To: Something's got to give (Timothy Chow)

This one had me puzzled for a while but GNU's temperature map gives some insights.

OTB, I played 18/17 18/13, thinking that my best chance was to race and minimize contact. The rollout shows that 18/17 18/13 is significantly worse than 18/12. This surprises me because in either case the same number of non-doublets (fourteen) hit and at least partially cover. So what distinguishes between the two plays? It seems that White has more bad rolls after 18/12. In particular, after 18/12, 3-1 and 5-1 force White to waste pips shuffling his checkers in his home board. (6-1 is also a bad roll but it is bad after either 18/17 18/13 or 18/12.) Paradoxically, keeping slightly more contact on this turn works out well for Blue's racing chances. This seems to be a position where general principles have to give way to actual enumeration of rolls. Alter the position slightly and everything changes. For example, shift a checker from White's 5-point to White's 6-point and 18/17 18/13 becomes better than 18/12.

gnubg	74
tchow	77
Position ID: u7WYAQB3awPAAA Match ID: cIkGABAAAAAA

#		Ply	Move	Equity
•	1	R	18/12	-0.479
			0.334 0.024 0.000 - 0.666 0.027 0.000 -0.335 -0.479 0.001 0.000 0.000 - 0.001 0.001 0.000 0.001 0.003
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 850648836 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	18/13 5/4	-0.492 ( -0.014)
			0.333 0.024 0.000 - 0.667 0.031 0.000 -0.340 -0.492 0.001 0.000 0.000 - 0.001 0.001 0.000 0.001 0.003
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 850648836 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	6/1 5/4	-0.537 ( -0.059)
			0.333 0.005 0.000 - 0.667 0.030 0.001 -0.360 -0.537 0.000 0.000 0.000 - 0.000 0.001 0.000 0.001 0.003
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 850648836 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	18/17 18/13	-0.560 ( -0.081)
			0.318 0.020 0.000 - 0.682 0.030 0.000 -0.375 -0.560 0.001 0.001 0.000 - 0.001 0.001 0.000 0.001 0.003
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 850648836 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

• Something's got to give
  Timothy Chow -- Thursday, 18 March 2010, at 1:42 a.m.
  • Something's got to give
    Chase -- Thursday, 18 March 2010, at 2:30 a.m.
  • Something's got to give
    nori -- Thursday, 18 March 2010, at 4:13 a.m.
  • Something's got to give
    Timothy Chow -- Friday, 19 March 2010, at 2:12 a.m.
    • Something's got to give
      storm -- Friday, 19 March 2010, at 9:48 a.m.
      • Something's got to give
        Timothy Chow -- Friday, 19 March 2010, at 3:22 p.m.