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Rollouts: Firing squad quiz

Posted By: Timothy Chow
Date: Tuesday, 11 May 2010, at 1:25 a.m.

In Response To: Firing squad quiz (Timothy Chow)

Position 1

Blue has a stronger board and a slight race lead, so it's thematic to get those back checkers going. This is a typical position where many players are afraid to leap into the outfield for fear of getting hit, but really, when is Blue going to get a better opportunity to get the back checkers moving? The rollout might need to be extended if we want to be sure which 2 GNU thinks is best, but 24/18 is clear for the 6.

gnubg	158
tchow	155
Position ID: mGfkASjYZswBMA Match ID: cAkZABAAIAAA

#		Ply	Move	Equity
•	1	R	24/18 13/11	+0.426
			0.604 0.195 0.012 - 0.396 0.130 0.005 +0.281 +0.426 0.002 0.002 0.001 - 0.002 0.001 0.000 0.004 0.012
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 869827751 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	24/16	+0.397 ( -0.028)
			0.600 0.179 0.010 - 0.400 0.127 0.005 +0.258 +0.397 0.002 0.002 0.001 - 0.002 0.001 0.000 0.005 0.012
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 869827751 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	24/22 24/18	+0.386 ( -0.040)
			0.597 0.191 0.014 - 0.403 0.137 0.005 +0.256 +0.386 0.002 0.002 0.001 - 0.002 0.002 0.000 0.005 0.013
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 869827751 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	13/5	+0.356 ( -0.070)
			0.575 0.225 0.012 - 0.425 0.136 0.008 +0.243 +0.356 0.002 0.002 0.000 - 0.002 0.002 0.000 0.004 0.014
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 869827751 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	24/22 11/5	+0.347 ( -0.079)
			0.574 0.214 0.011 - 0.426 0.128 0.007 +0.239 +0.347 0.002 0.002 0.001 - 0.002 0.002 0.001 0.004 0.012
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 869827751 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]

---

Position 2

It's a closer call here because White has a stronger board than in Position 1 and more attackers, plus Blue is no longer ahead in the race. (In case you haven't figured it out, I got here from Position 1 by playing 24/16 and getting hit.) Hanging back on the ace-point anchor is not a serious error here, but GNU still seems to prefer bar/18 by a small margin. It's not so much that Blue wants to race here, but his back checkers are in danger of getting primed so it's worth considerable risk to try to establish an advanced anchor or at least escape one checker. Plus Blue usually gets a decent number of return shots if he is hit.

gnubg	141
tchow	156
Position ID: bM6SASjYZswBUA Match ID: cAkHABAAIAAA

#		Ply	Move	Equity
•	1	R	bar/18	-0.038
			0.520 0.169 0.013 - 0.480 0.243 0.010 -0.031 -0.038 0.001 0.001 0.000 - 0.001 0.001 0.000 0.002 0.007
			Full cubeful rollout with var.redn.
			5184 games, Mersenne Twister dice gen. with seed 869341591 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	bar/24 8/2*	-0.054 ( -0.016)
			0.497 0.191 0.015 - 0.503 0.220 0.025 -0.046 -0.054 0.001 0.001 0.000 - 0.001 0.001 0.001 0.002 0.007
			Full cubeful rollout with var.redn.
			5184 games, Mersenne Twister dice gen. with seed 869341591 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	bar/24 11/5	-0.061 ( -0.024)
			0.489 0.171 0.011 - 0.511 0.197 0.016 -0.054 -0.061 0.001 0.001 0.000 - 0.001 0.001 0.000 0.002 0.006
			Full cubeful rollout with var.redn.
			5184 games, Mersenne Twister dice gen. with seed 869341591 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]

---

Position 3

Calling this a "firing-squad problem" risks being chastised by Stick for a "lying subject line" because the real decision here is whether attempting to make the 5 point is worth the risk of getting another checker sent back. If not then bar/18 falls out by default despite its getting hit on all 36 rolls. According to the rollout, 8/5 is hugely correct. I can't say I have enough experience with this kind of situation to confirm that the rollout result is right, but it is certainly clear that Blue will have a tough time bringing this home safely without making another useful point, and now is probably his best chance to make that point.

gnubg	148
tchow	100
Position ID: zGamBAzHPB8AQA Match ID: cAkOAEAAMAAA

#		Ply	Move	Equity
•	1	R	bar/21 8/5	-0.564
			0.340 0.139 0.006 - 0.660 0.174 0.007 -0.355 -0.564 0.001 0.001 0.000 - 0.001 0.001 0.000 0.002 0.007
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 843656021 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	bar/18	-0.750 ( -0.186)
			0.296 0.104 0.003 - 0.704 0.148 0.005 -0.454 -0.750 0.001 0.001 0.000 - 0.001 0.001 0.000 0.003 0.007
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 843656021 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]

---

Position 4

Here 13/7 is clear. Again it's thematic that since Blue is way ahead in the race and White has a weak board, there's no time like the present to make a bolt for it with 22/18. One might still wonder whether it's right to step into a triple shot; if we're ahead in the race, isn't it important to "play safe"? But leaving a blot up front isn't safe either and still risks losing the race lead. After 22/18, White typically has to break a point to hit and also has a blot on the five point, so 22/18 is not really that unsafe.

gnubg	179
tchow	157
Position ID: 0DNjwDDg6+ABDA Match ID: cAkTAAAAAAAA

#		Ply	Move	Equity
•	1	R	22/18 13/7	+0.018
			0.509 0.141 0.007 - 0.491 0.142 0.005 +0.019 +0.018 0.001 0.001 0.000 - 0.001 0.001 0.000 0.004 0.009
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 850999931 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	13/9 13/7	-0.010 ( -0.028)
			0.494 0.150 0.009 - 0.506 0.132 0.006 +0.010 -0.010 0.001 0.001 0.001 - 0.001 0.001 0.000 0.004 0.010
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 850999931 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	13/7 8/4	-0.040 ( -0.058)
			0.489 0.138 0.006 - 0.511 0.132 0.005 -0.016 -0.040 0.001 0.001 0.000 - 0.001 0.001 0.000 0.004 0.009
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 850999931 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]

---

Position 5

Here Blue is not ahead in the race so bar/18 does not accomplish much. Often your opponent will not want to hit from a stripped midpoint, but here White has a bar-point anchor which makes White more willing to break the midpoint. It is the bar-point anchor that White is more reluctant to break. The simple 14/11 is safe and constructive, and tops the rollout.

gnubg	119
tchow	138
Position ID: mjuDwQDYzsEFQA Match ID: UQkOAAAAEAAA

#		Ply	Move	Equity
•	1	R	bar/21 14/11	-0.355
			0.351 0.073 0.004 - 0.649 0.266 0.003 -0.490 -0.355 0.001 0.001 0.000 - 0.001 0.002 0.000 0.004 0.006
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 847738154 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	bar/21 8/5	-0.409 ( -0.054)
			0.339 0.076 0.004 - 0.661 0.289 0.003 -0.535 -0.409 0.001 0.001 0.000 - 0.001 0.002 0.000 0.004 0.005
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 847738154 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	bar/21 6/3	-0.454 ( -0.099)
			0.335 0.078 0.004 - 0.665 0.322 0.006 -0.576 -0.454 0.001 0.001 0.000 - 0.001 0.002 0.001 0.004 0.006
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 847738154 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	bar/18	-0.488 ( -0.133)
			0.318 0.061 0.003 - 0.682 0.307 0.003 -0.611 -0.488 0.001 0.001 0.000 - 0.001 0.002 0.000 0.004 0.005
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 847738154 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]

---

Position 6

Here 13/8 is a natural-looking way to play the 5, and many players would not even consider using the 5 to play 23/18. Blue is behind in the race so what does 23/18 accomplish? The answer is that if Blue is missed then Blue stands to gain either a more advanced anchor or an extra builder for the priming game. Sticking a checker in White's face also prevents White from freely deploying builders in the outfield for White's prime. Because Blue has equal board strength and more checkers back, Blue need not worry unduly about getting hit. The pure play of 23/18 13/11 rolls out on top.

gnubg	153
tchow	171
Position ID: sM/EATCwc/AAFg Match ID: cIkKAFAAAAAA

#		Ply	Move	Equity
•	1	R	23/18 13/11	+0.074
			0.521 0.138 0.006 - 0.479 0.140 0.005 +0.041 +0.074 0.001 0.001 0.000 - 0.001 0.001 0.000 0.003 0.008
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 854385988 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	23/16	+0.003 ( -0.071)
			0.504 0.130 0.006 - 0.496 0.143 0.006 -0.004 +0.003 0.001 0.001 0.000 - 0.001 0.001 0.000 0.003 0.008
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 854385988 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	23/18 8/6	-0.010 ( -0.084)
			0.499 0.134 0.006 - 0.501 0.145 0.007 -0.012 -0.010 0.001 0.001 0.000 - 0.001 0.002 0.001 0.005 0.010
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 854385988 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	23/21 13/8	-0.021 ( -0.095)
			0.496 0.134 0.006 - 0.504 0.147 0.006 -0.022 -0.021 0.001 0.001 0.000 - 0.001 0.001 0.000 0.003 0.008
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 854385988 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]

---

Position 7

During the game I was hating life and expecting to be gammoned unless I managed to roll a joker that would let me hit and cover. I was taken off guard by this roll and did not see anything to do with it except bar/18. However, an objective assessment shows that Blue now has the advantage and White is the one who may soon be hating life. White still has two checkers behind a prime and a bunch of outfield blots to try to clean up. Playing 4/1 looks awkward, putting a checker out of play where it is either vulnerable to getting hit or has to drag another checker over to cover it, but it leaves White with nothing to attack and a bunch of vulnerable and poorly placed checkers. No reason to face a firing squad here. I didn't roll out bar/21 7/4 but it's a 0.250 whopper on eval and I doubt that a rollout will reverse that verdict.

gnubg	153
tchow	171
Position ID: sM/EATCwc/AAFg Match ID: cIkKAFAAAAAA

#		Ply	Move	Equity
•	1	R	23/18 13/11	+0.074
			0.521 0.138 0.006 - 0.479 0.140 0.005 +0.041 +0.074 0.001 0.001 0.000 - 0.001 0.001 0.000 0.003 0.008
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 854385988 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	23/16	+0.003 ( -0.071)
			0.504 0.130 0.006 - 0.496 0.143 0.006 -0.004 +0.003 0.001 0.001 0.000 - 0.001 0.001 0.000 0.003 0.008
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 854385988 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	23/18 8/6	-0.010 ( -0.084)
			0.499 0.134 0.006 - 0.501 0.145 0.007 -0.012 -0.010 0.001 0.001 0.000 - 0.001 0.002 0.001 0.005 0.010
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 854385988 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	23/21 13/8	-0.021 ( -0.095)
			0.496 0.134 0.006 - 0.504 0.147 0.006 -0.022 -0.021 0.001 0.001 0.000 - 0.001 0.001 0.000 0.003 0.008
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 854385988 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]

---

Position 8

One of the trickiest positions for me. If we were to move one of Blue's checkers from the 6 point back to the midpoint, then 13/7 would be much more attractive. Blue would be further behind in the race and the extra spare on the midpoint could be put to good use in a priming attempt. But 13/7 is less attractive in the given position since the race is equal and 13/7 strips the midpoint. Bar/18 is the lesser of two evils here. I'm still surprised at how much worse GNU thinks 13/7 is. I think that part of the issue is that even though White hits with most rolls, many of these hits leave White with a scattered position that is not all that much stronger than what White would have anyway if Blue were to play 13/7 and be missed. And of course if White hits after 13/7 then Blue is in serious trouble.

gnubg	141
tchow	145
Position ID: sM+SCSDgc4cDQA Match ID: cAkHAEAAKAAA

#		Ply	Move	Equity
•	1	R	bar/18	-0.315
			0.434 0.094 0.006 - 0.566 0.191 0.005 -0.229 -0.315 0.002 0.001 0.000 - 0.002 0.002 0.000 0.004 0.010
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 851945072 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	bar/24 9/3	-0.423 ( -0.108)
			0.403 0.095 0.004 - 0.597 0.178 0.007 -0.280 -0.423 0.001 0.001 0.000 - 0.001 0.002 0.000 0.003 0.010
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 851945072 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	bar/24 13/7	-0.436 ( -0.121)
			0.397 0.096 0.005 - 0.603 0.180 0.008 -0.294 -0.436 0.001 0.001 0.000 - 0.001 0.002 0.001 0.004 0.011
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 851945072 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

• Firing squad quiz
  Timothy Chow -- Sunday, 9 May 2010, at 9:12 p.m.
  • Firing squad quiz
    John O'Hagan -- Sunday, 9 May 2010, at 9:59 p.m.
  • Firing squad quiz
    Chase -- Sunday, 9 May 2010, at 11:27 p.m.
    • Where the problems came from
      Timothy Chow -- Sunday, 9 May 2010, at 11:46 p.m.
      • Where the problems came from
        Chase -- Monday, 10 May 2010, at 12:03 a.m.
  • Firing squad quiz
    Ian Shaw -- Monday, 10 May 2010, at 12:42 p.m.
  • Rollouts: Firing squad quiz
    Timothy Chow -- Tuesday, 11 May 2010, at 1:25 a.m.
    • Sorry...wrong diagram for Position 7
      Timothy Chow -- Tuesday, 11 May 2010, at 1:33 a.m.