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Rollout: Safe or bold?

Posted By: Timothy Chow
Date: Saturday, 27 February 2010, at 10:30 p.m.

In Response To: Safe or bold? (Timothy Chow)

Even after studying this position a while, I find it a tricky one. Varying the position in seemingly small ways can change which play comes out on top. First, let me give the rollout (but keep scrolling down past the rollout because I continue the discussion afterwards).

gnubg	79
tchow	120
Position ID: c3cHABCzNSMCGA Match ID: UYkFAEAAAAAA

#		Ply	Move	Equity
•	1	R	8/7 8/5	-0.295
			0.390 0.029 0.001 - 0.610 0.260 0.014 -0.463 -0.295 0.001 0.001 0.000 - 0.001 0.001 0.001 0.003 0.005
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 844124577 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	11/10 8/5	-0.334 ( -0.039)
			0.382 0.027 0.001 - 0.618 0.270 0.015 -0.493 -0.334 0.001 0.001 0.000 - 0.001 0.002 0.001 0.003 0.005
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 844124577 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	14/13 8/5	-0.340 ( -0.045)
			0.380 0.027 0.001 - 0.620 0.277 0.016 -0.504 -0.340 0.001 0.001 0.000 - 0.001 0.001 0.001 0.003 0.005
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 844124577 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	14/11 5/4	-0.355 ( -0.059)
			0.322 0.017 0.000 - 0.678 0.145 0.005 -0.489 -0.355 0.001 0.001 0.000 - 0.001 0.002 0.000 0.003 0.004
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 844124577 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]
	5	R	5/2*/1	-0.410 ( -0.115)
			0.310 0.012 0.000 - 0.690 0.169 0.005 -0.543 -0.410 0.001 0.001 0.000 - 0.001 0.002 0.000 0.003 0.004
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 844124577 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]
	6	R	14/11 6/5	-0.412 ( -0.117)
			0.328 0.020 0.000 - 0.672 0.219 0.009 -0.552 -0.412 0.001 0.001 0.000 - 0.001 0.002 0.000 0.003 0.004
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 844124577 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]
	7	R	11/8 5/4	-0.422 ( -0.127)
			0.292 0.014 0.000 - 0.708 0.138 0.003 -0.544 -0.422 0.001 0.001 0.000 - 0.001 0.002 0.000 0.003 0.004
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 844124577 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]

So the rollout says that the bold play 8/7 8/5 wins. But before we start trying to justify it, let's look at some variants. In the position below, I didn't bother doing a 2-ply rollout, but a 0-ply rollout puts the safe play 14/11 5/4 slightly ahead of 8/7 8/5.

gnubg	78
tchow	118
Position ID: c3cHAAibNSMCGA Match ID: UYkFAEAAAAAA

#		Ply	Move	Equity
	1	R	14/11 5/4	-0.558
			0.245 0.011 0.000 - 0.755 0.148 0.004 -0.650 -0.558 0.002 0.001 0.000 - 0.002 0.002 0.001 0.003 0.005
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 849665829 and quasi-random dice
			Play: 0-ply cubeful [expert]
			Cube: 0-ply cubeful [expert]
	2	R	8/7 8/5	-0.575 ( -0.017)
			0.295 0.013 0.000 - 0.705 0.290 0.016 -0.703 -0.575 0.002 0.001 0.000 - 0.002 0.002 0.001 0.004 0.006
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 849665829 and quasi-random dice
			Play: 0-ply cubeful [expert]
			Cube: 0-ply cubeful [expert]

Now suppose we take away Blue's deuce-point anchor, as well as the option to make a new outfield point. Then, again according to a 0-ply rollout, 5/2*/1 is GNU's clear favorite, and 8/7 8/5 looks like a double whopper. Keep scrolling down.

gnubg	79
tchow	113
Position ID: c3cHABCzNSPQAA Match ID: UYkFAEAAAAAA

#		Ply	Move	Equity
	1	R	5/2*/1	-0.081
			0.429 0.008 0.000 - 0.571 0.116 0.002 -0.253 -0.081 0.002 0.000 0.000 - 0.002 0.002 0.000 0.004 0.005
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 849665829 and quasi-random dice
			Play: 0-ply cubeful [expert]
			Cube: 0-ply cubeful [expert]
	2	R	18/15 5/4	-0.138 ( -0.057)
			0.425 0.010 0.000 - 0.575 0.166 0.004 -0.309 -0.138 0.002 0.000 0.000 - 0.002 0.002 0.001 0.004 0.006
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 849665829 and quasi-random dice
			Play: 0-ply cubeful [expert]
			Cube: 0-ply cubeful [expert]
	3	R	11/8 5/4	-0.164 ( -0.083)
			0.385 0.008 0.000 - 0.615 0.096 0.001 -0.319 -0.164 0.002 0.000 0.000 - 0.002 0.001 0.000 0.004 0.005
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 849665829 and quasi-random dice
			Play: 0-ply cubeful [expert]
			Cube: 0-ply cubeful [expert]
	4	4	17/14 5/4	-0.169 ( -0.088)
			0.409 0.013 0.000 - 0.591 0.136 0.003
	5	4	6/5 6/3	-0.188 ( -0.107)
			0.405 0.013 0.000 - 0.595 0.146 0.004
	6	4	5/1	-0.288 ( -0.207)
			0.372 0.008 0.000 - 0.628 0.163 0.004
	7	4	8/7 8/5	-0.324 ( -0.242)
			0.405 0.019 0.000 - 0.595 0.280 0.010

I've experimented with other variations, too, but this will do for now. Evidently, several factors have to be weighed carefully against each other: the consequences of getting hit; the quality of the outfield points; which five points we're making in our home board.

The deuce-point anchor makes a significant difference to how boldly we can play. Despite White's five-point board, leaving a direct shot with 8/7 8/5 is not fatal as long as we have that anchor. Without it, we are forced to play more safely, either by picking and passing, or lifting the blot and arranging our outfield checkers in the most effective manner. The deuce-point anchor doesn't automatically mean that 8/7 8/5 is best, though; there is still a downside to getting hit. It makes a difference that 8/7 8/5 completes Blue's second-best five-point board. The four-point prime not only helps contain White immediately, blocking low numbers, but has strong future value, if White partially escapes that rear checker but gets hit back. To put it another way, several factors have to come together to make 8/7 8/5 right. They're all present in the diagrammed position, however, so 8/7 8/5 is the right play.

OTB, I thought that White's five-point board meant I had to play safe, and I played 5/2*/1. However, although this gains some time, the problem is that putting a checker out of play, and passing up the opportunity to make the valuable 5-point, is very costly. Blue is not that desperate yet and can afford to be more aggressive.

Messages In This Thread

• Safe or bold?
  Timothy Chow -- Friday, 19 February 2010, at 2:23 a.m.
  • Safe or bold?
    Paul Weaver -- Friday, 19 February 2010, at 3:16 a.m.
    • Safe or bold?
      Timothy Chow -- Friday, 26 February 2010, at 2:39 a.m.
      • Safe or bold?
        Matt Cohn-Geier -- Friday, 26 February 2010, at 3:01 a.m.
        • Safe or bold?
          Timothy Chow -- Friday, 26 February 2010, at 3:43 a.m.
  • Safe or bold?
    Joe Russell -- Friday, 19 February 2010, at 3:34 a.m.
  • Safe or bold?
    David -- Friday, 19 February 2010, at 3:35 a.m.
    • Safe or bold?
      Joe Russell -- Friday, 19 February 2010, at 3:53 a.m.
  • Rollout: Safe or bold?
    Timothy Chow -- Saturday, 27 February 2010, at 10:30 p.m.
    • Rollout: Safe or bold?
      Philippe Michel -- Sunday, 28 February 2010, at 8:43 p.m.
      • Rollout: Safe or bold?
        Timothy Chow -- Monday, 1 March 2010, at 2:49 a.m.