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Containment checker play, take 2

Posted By: Timothy Chow
Date: Tuesday, 29 December 2009, at 2:40 a.m.

O.K., I rolled out the position I posted before and now have some followup comments and questions. This is a pretty long message so keep scrolling down as you read.

First, here's the original position as I first posed it, with the cube in the center and assuming money play with Jacoby. As Stick and others pointed out, the cube is not likely to be in the center in real life, and the Jacoby rule distorts things because Black is not going to be gammoned if White hits a fly shot. Thus it is not too surprising that the play 16/11 15/11 comes out on top despite the 3 indirect shots.

gnubg	76
tchow	101
Position ID: 2+4GAEDbNkiUAA Match ID: cIkSAAAAAAAA

#		Ply	Move	Equity
•	1	R	16/11 15/11	+0.676
			0.678 0.012 0.000 - 0.322 0.086 0.001 +0.282 +0.676 0.001 0.000 0.000 - 0.001 0.001 0.000 0.002 0.005
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 840362659 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	16/12 15/10	+0.640 ( -0.036)
			0.685 0.011 0.000 - 0.315 0.034 0.000 +0.346 +0.640 0.001 0.000 0.000 - 0.001 0.001 0.000 0.002 0.005
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 840362659 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	18/14 15/10	+0.595 ( -0.082)
			0.667 0.011 0.000 - 0.333 0.052 0.001 +0.293 +0.595 0.001 0.000 0.000 - 0.001 0.001 0.000 0.002 0.005
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 840362659 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]

If, more realistically, we give Black the cube, then the safer 16/12 15/10 narrowly squeaks into first place.

gnubg	76
tchow	101
Position ID: 2+4GAEDbNkiUAA Match ID: UYkSAAAAAAAA

#		Ply	Move	Equity
•	1	R	16/12 15/10	+0.633
			0.682 0.012 0.000 - 0.318 0.033 0.000 +0.343 +0.633 0.001 0.000 0.000 - 0.001 0.001 0.000 0.002 0.004
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 840416385 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 15/11	+0.618 ( -0.015)
			0.675 0.012 0.000 - 0.325 0.094 0.001 +0.267 +0.618 0.001 0.000 0.000 - 0.001 0.001 0.000 0.002 0.004
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 840416385 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	18/14 15/10	+0.596 ( -0.037)
			0.671 0.011 0.000 - 0.329 0.048 0.001 +0.304 +0.596 0.001 0.000 0.000 - 0.001 0.001 0.000 0.003 0.004
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 840416385 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]

Rich Munitz suggested considering this position at DMP, and if we do that, again 16/12 15/10 comes out slightly on top.

gnubg	76
tchow	101
Position ID: 2+4GAEDbNkiUAA Match ID: UYkyAAAAAAAA

#		Ply	Move	Equity
•	1	R	16/12 15/10	+0.365
			0.683 0.068 0.000 - 0.317 0.059 0.000 +0.365 +0.365 0.001 0.004 0.000 - 0.001 0.004 0.001 0.002 0.002
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 840055197 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 15/11	+0.355 ( -0.010)
			0.678 0.071 0.000 - 0.322 0.127 0.000 +0.355 +0.355 0.001 0.005 0.000 - 0.001 0.005 0.000 0.002 0.002
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 840055197 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	18/14 15/10	+0.344 ( -0.022)
			0.672 0.060 0.000 - 0.328 0.075 0.000 +0.344 +0.344 0.001 0.004 0.000 - 0.001 0.004 0.011 0.002 0.002
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 840055197 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]

Unfortunately, I feel that I'm still not getting that good a sense of the correct location of the boundary between too bold and too safe. Here's another position that might clarify the issue a bit better. What's the correct money-play (or DMP, if you prefer) decision here?

The score (after 0 games) is: gnubg 0, tchow 0

Move number 4: tchow to play 62

gnubg	76
tchow	101
Position ID: 2+4GAEDbNoiSAA Match ID: UQkLAAAAAAAA

Messages In This Thread

• Containment checker play, take 2
  Timothy Chow -- Tuesday, 29 December 2009, at 2:40 a.m.
  • Containment checker play, take 2
    Stick -- Tuesday, 29 December 2009, at 2:48 a.m.
    • Containment checker play, take 2
      Nack Ballard -- Wednesday, 30 December 2009, at 4:27 a.m.
  • Addendum
    Timothy Chow -- Tuesday, 29 December 2009, at 2:50 a.m.
    • Addendum
      Daniel Murphy -- Tuesday, 29 December 2009, at 3:41 a.m.
      • Addendum
        Timothy Chow -- Tuesday, 29 December 2009, at 3:40 p.m.
  • Containment checker play, take 2
    Chuck Bower -- Tuesday, 29 December 2009, at 2:12 p.m.
    • Containment checker play, take 2
      Timothy Chow -- Tuesday, 29 December 2009, at 3:51 p.m.
      • Containment checker play, take 2
        Chuck Bower -- Tuesday, 29 December 2009, at 4:30 p.m.
        • The slotting option
          Chuck Bower -- Wednesday, 30 December 2009, at 2:30 a.m.
          • The slotting option
            Timothy Chow -- Wednesday, 30 December 2009, at 5:16 p.m.
            • The slotting option
              Chuck Bower -- Wednesday, 30 December 2009, at 6:15 p.m.
      • Containment checker play, take 2
        Rich Munitz -- Wednesday, 30 December 2009, at 6:33 p.m.
  • Rollout
    Timothy Chow -- Saturday, 2 January 2010, at 9:05 p.m.