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Rollout: I didn't know that I didn't know how to play this kind of position

Posted By: Timothy Chow
Date: Thursday, 5 August 2010, at 12:29 a.m.

In Response To: I didn't know that I didn't know how to play this kind of position (Timothy Chow)

Thanks to Stick's comments and some playing around with variant positions, I think I understand this position much better now.

The Danger Zone is the 7 point through the 11 point, which is in direct-shot range of White's stack. This zone is dangerous for two reasons: First, of course, White can hit a blot in the Danger Zone indirectly from the bar; second, if White enters without hitting, any checkers in the Danger Zone are at risk of being hit on White's next roll. The latter possibility means that Blue is not too happy leaving checkers in the Danger Zone even if they make a point and are thus not at risk of being hit from the bar.

The worst point for Blue to leave a checker on is the 11 point because it is the hardest to safety. As we move from the 11 point to the 7 point, the number of ways to clear increases, so the points get less bad. The 6 point is optimal. Deeper home-board points get progressively worse since they are less flexible and are wasteful of pips for the gammon race.

Beyond the 11 point, the 12 point is the best point. Being the 7-away point, it is not in direct shot range, but it is optimally poised for leaping over the Danger Zone without having to dawdle there. Points get progressively worse as you move further back from the edge of the Danger Zone.

In the first position, we obviously cover with the 4 and have to find a 5. If you visualize the Danger Zone, then you see that there are two checkers in it, with the one on the 11 point being particularly poorly positioned. We would rather take checkers out of the Danger Zone than put checkers into it. Playing 11/6 take a checker from the worst point to the best point so it is the best play. The fact that 11/6 leaves more indirect shots than the alternative 16/11 is outweighed by the fact that 16/11 puts another checker onto our worst point, creating long-term danger.

In the second position, again we see that we have two checkers on our worst point, the 11 point. Clearing the 11 point is the best play.

Finally, for good measure, I've included a third variant position. In the variant, after covering with the 3, we have to find a 5. I haven't rolled it out, but evaluations suggest that 11/6 is very close to 17/12. Both plays take a checker from a bad point to a much better point.

---

gnubg	171
tchow	99
Position ID: hnMG4EFrcyImAA Match ID: QYkSAAAAiAAA

#		Ply	Move	Equity
•	1	R	11/2	+1.185
			0.853 0.561 0.003 - 0.147 0.019 0.001 +1.250 +1.185 0.001 0.002 0.001 - 0.001 0.001 0.000 0.004 0.005
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 896096548 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 6/2	+1.139 ( -0.046)
			0.845 0.535 0.003 - 0.155 0.019 0.000 +1.209 +1.139 0.001 0.002 0.001 - 0.001 0.001 0.000 0.004 0.005
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 896096548 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	8/3 6/2	+1.085 ( -0.100)
			0.821 0.546 0.004 - 0.179 0.025 0.001 +1.165 +1.085 0.001 0.002 0.001 - 0.001 0.001 0.000 0.004 0.005
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 896096548 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	14/9 6/2	+1.067 ( -0.118)
			0.820 0.543 0.004 - 0.180 0.032 0.002 +1.152 +1.067 0.001 0.002 0.001 - 0.001 0.001 0.000 0.004 0.007
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 896096548 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	171
tchow	81
Position ID: hnMG4EHbzdAIAA Match ID: QYkVAAAAiAAA

#		Ply	Move	Equity
•	1	R	11/8 11/6	+1.467
			0.895 0.738 0.004 - 0.105 0.011 0.000 +1.519 +1.467 0.001 0.002 0.001 - 0.001 0.001 0.000 0.003 0.005
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 897449455 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	11/6 10/7	+1.432 ( -0.035)
			0.886 0.722 0.003 - 0.114 0.014 0.000 +1.484 +1.432 0.001 0.002 0.001 - 0.001 0.001 0.000 0.004 0.005
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 897449455 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	14/6	+1.419 ( -0.048)
			0.884 0.712 0.004 - 0.116 0.008 0.000 +1.475 +1.419 0.001 0.002 0.001 - 0.001 0.000 0.000 0.004 0.005
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 897449455 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	14/9 10/7	+1.364 ( -0.103)
			0.873 0.692 0.003 - 0.127 0.013 0.000 +1.428 +1.364 0.001 0.002 0.001 - 0.001 0.001 0.000 0.004 0.005
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 897449455 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]

---

Variant position:

gnubg	168
tchow	100
Position ID: hjsG4EFbcyRGAA Match ID: QYkVAAAAiAAA

Messages In This Thread

• I didn't know that I didn't know how to play this kind of position
  Timothy Chow -- Wednesday, 4 August 2010, at 12:19 a.m.
  • I didn't know that I didn't know how to play this kind of position
    Stick -- Wednesday, 4 August 2010, at 12:46 a.m.
    • I didn't know that I didn't know how to play this kind of position
      Timothy Chow -- Wednesday, 4 August 2010, at 12:56 a.m.
      • I didn't know that I didn't know how to play this kind of position
        Stick -- Wednesday, 4 August 2010, at 2:14 a.m.
        • I didn't know that I didn't know how to play this kind of position
          neilkaz -- Wednesday, 4 August 2010, at 3:13 a.m.
          • We agree. Pay now - a matter of efficiency
            svilo -- Thursday, 5 August 2010, at 12:25 a.m.
    • I didn't know that I didn't know how to play this kind of position
      trichard -- Thursday, 5 August 2010, at 3:56 p.m.
      • I didn't know that I didn't know how to play this kind of position
        Stick -- Thursday, 5 August 2010, at 7:09 p.m.
      • Variant with super strong board
        Timothy Chow -- Saturday, 7 August 2010, at 10:40 p.m.
  • Rollout: I didn't know that I didn't know how to play this kind of position
    Timothy Chow -- Thursday, 5 August 2010, at 12:29 a.m.