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Rollout: 4-2 to play

Posted By: Timothy Chow
Date: Sunday, 2 May 2010, at 10:34 p.m.

In Response To: 4-2 to play (Timothy Chow)

OTB I played 15/13 9/5 thinking that it couldn't be bad to make the 5 point. However, the rollout definitely prefers 15/11 13/11. I'm not completely sure I understand this position, but here are some observations. It's not just an issue of being behind in the race and wanting to block White. If I drag all of White's deep checkers back to the 6-, 7-, and 8-points, giving Black something like a 10- to 15-pip race lead, then 15/9 becomes more attractive but GNU still hates 15/13 9/5.

What I think is going on is that neither side is likely to leave a shot soon, so Blue's goal is to build up his board smoothly in preparation for the moment when White gets squeezed off the anchor. In particular, it is not so critical to make points immediately if there is a more flexible play that will ultimately produce a better board over the next few rolls. The trouble with 15/13 9/5 is that it strips a valuable spare from the 9 point. In contrast, 15/11 13/11 leaves the spare there and also gives us a useful option for playing 6-5, 6-3, or 6-2 (by breaking the 11 point). It's hard to verify directly that 15/11 13/11 yields more flexibility because there are so many options to check, but I think this is what's going on. Those who are familiar with Kit Woolsey's article "Breaking Up is Hard to Do" will know that paradoxically, sometimes the best way to build a board is to break a point you already have in order to slot a new point. I suspect that a similar principle is at work here.

One might worry that 15/11 13/11 creates Too Many Points and that the 11 point will be hard to clear without leaving a shot. This might be the case in the modified position I suggested above, when Blue is much further ahead in the race, and perhaps that explains why 15/9 is more attractive in that case. But here, the danger of leaving a shot on the 11 point is largely illusory. Blue has plenty of time and spare checkers. He'd need a very unlucky sequence of 6-1's or 6-4's to blot on the 11 point.

Finally, for comparison, at the end of this post I give a rollout of another position that came up recently where again I made what seemed to me to be the "natural" play, making the 5 point and the 4 point. Again, this was apparently a mistake, and I think that the point was that flexibility trumped making points immediately.

gnubg	121
tchow	132
Position ID: W8zCwQDQZ4cTAA Match ID: cAkKAAAAEAAA

#		Ply	Move	Equity
•	1	R	15/11 13/11	-0.074
			0.475 0.022 0.001 - 0.525 0.024 0.000 -0.052 -0.074 0.001 0.001 0.000 - 0.001 0.001 0.000 0.002 0.003
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 855506883 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	15/13 9/5	-0.117 ( -0.043)
			0.461 0.021 0.001 - 0.539 0.015 0.000 -0.072 -0.117 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 855506883 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	15/9	-0.123 ( -0.049)
			0.459 0.021 0.001 - 0.541 0.015 0.000 -0.075 -0.123 0.001 0.001 0.000 - 0.001 0.001 0.000 0.002 0.003
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 855506883 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]

---

Here's the other position I promised. Note: there were several other plays that rolled out better than my play, but I have only displayed GNU's top two plays along with my own.

Unlimited game: tchow to play 23

gnubg	134
tchow	118
Position ID: tF3B4ABSzxkHAA Match ID: cAkNAEAAOAAA

#		Ply	Move	Equity
•	1	R	13/8	+0.600
			0.691 0.014 0.000 - 0.309 0.015 0.000 +0.382 +0.600 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 855536251 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	13/10 6/4	+0.596 ( -0.003)
			0.690 0.015 0.000 - 0.310 0.016 0.000 +0.377 +0.596 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 855536251 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	8/5 6/4	+0.556 ( -0.043)
			0.680 0.017 0.000 - 0.320 0.018 0.001 +0.359 +0.556 0.001 0.001 0.000 - 0.001 0.000 0.000 0.001 0.003
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 855536251 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

• 4-2 to play
  Timothy Chow -- Saturday, 1 May 2010, at 1:07 a.m.
  • 4-2 to play
    Casper van der Tak -- Saturday, 1 May 2010, at 6:59 a.m.
  • 4-2 to play
    mamabear -- Saturday, 1 May 2010, at 11:39 a.m.
  • 4-2 to play
    Seth -- Saturday, 1 May 2010, at 11:44 a.m.
  • 4-2 to play
    Martin -- Saturday, 1 May 2010, at 12:59 p.m.
  • Rollout: 4-2 to play
    Timothy Chow -- Sunday, 2 May 2010, at 10:34 p.m.
    • Rollout: 4-2 to play
      Daniel Murphy -- Monday, 3 May 2010, at 2:36 a.m.