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Steve Mellen's position revisited

Posted By: Timothy Chow
Date: Saturday, 3 April 2010, at 9:50 p.m.

Here is some belated analysis of a position that Steve Mellen posted a couple of weeks ago. This is a long post with several rollouts so you will need to keep scrolling down. Comments are interleaved with the rollouts.

First, let me give the rollout of Steve Mellen's original position, ATS and for money. As you can see, escaping the back checker is right by a mile in both cases, as JOH and Chase correctly surmised when Steve first posted the position.

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The score (after 0 games) is: Bot 0, fnurt 4 (match to 7 points)

fnurt to play 46

Bot	157
fnurt	131
Position ID: 2G7ggDBszpgDCA Match ID: cAn6AAAAIAAA

#		Ply	Move	Equity
•	1	R	22/16 13/9	+0.128
			0.590 0.212 0.033 - 0.410 0.130 0.006 +0.206 +0.128 0.002 0.003 0.002 - 0.002 0.001 0.000 0.005 0.010
	2	R	13/9 11/5*	-0.041 ( -0.169)
			0.538 0.236 0.052 - 0.462 0.170 0.015 +0.076 -0.041 0.002 0.003 0.003 - 0.002 0.002 0.001 0.007 0.013
	3	R	13/7 11/7	-0.116 ( -0.244)
			0.529 0.208 0.038 - 0.471 0.152 0.005 +0.049 -0.116 0.002 0.003 0.003 - 0.002 0.002 0.001 0.006 0.011
	4	R	13/3	-0.179 ( -0.307)
			0.512 0.189 0.038 - 0.488 0.155 0.006 +0.004 -0.179 0.002 0.002 0.003 - 0.002 0.002 0.000 0.006 0.011
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 847977657 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]

---

Unlimited game: fnurt to play 64

Bot	157
fnurt	131
Position ID: 2G7ggDBszpgDCA Match ID: cAkTAAAAAAAA

#		Ply	Move	Equity
•	1	R	22/16 13/9	+0.432
			0.598 0.183 0.014 - 0.402 0.125 0.006 +0.262 +0.432 0.001 0.002 0.001 - 0.001 0.001 0.000 0.003 0.009
	2	R	13/9 11/5*	+0.195 ( -0.236)
			0.542 0.219 0.020 - 0.458 0.169 0.014 +0.141 +0.195 0.001 0.001 0.001 - 0.001 0.001 0.000 0.004 0.010
	3	R	13/7 11/7	+0.140 ( -0.291)
			0.539 0.191 0.016 - 0.461 0.150 0.006 +0.127 +0.140 0.002 0.002 0.001 - 0.002 0.002 0.001 0.004 0.012
	4	R	13/3	+0.081 ( -0.351)
			0.519 0.180 0.017 - 0.481 0.150 0.007 +0.078 +0.081 0.001 0.002 0.001 - 0.001 0.002 0.000 0.004 0.011
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 847256159 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]

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It's an interesting question to ask how much the duplication of Bot's hitting 4's matters here. Below is a variant position where there is no such duplication; escaping is correct, but by a smaller margin (again, both ATS and for money). This is in accordance with what Chase predicted. This is not the end of the story, though...

---

The score (after 0 games) is: Bot 0, fnurt 4 (match to 7 points)

fnurt to play 56

Bot	157
fnurt	130
Position ID: 2G7ggDBsbpgDEA Match ID: cIn6AAAAIAAA

#		Ply	Move	Equity
•	1	R	23/17 13/8	+0.058
			0.580 0.202 0.028 - 0.420 0.137 0.006 +0.165 +0.058 0.002 0.003 0.002 - 0.002 0.002 0.000 0.005 0.010
	2	R	13/8 11/5*	-0.029 ( -0.086)
			0.545 0.235 0.049 - 0.455 0.168 0.014 +0.086 -0.029 0.002 0.003 0.003 - 0.002 0.002 0.001 0.006 0.011
	3	R	11/6 11/5*	-0.033 ( -0.091)
			0.551 0.225 0.046 - 0.449 0.143 0.005 +0.118 -0.033 0.002 0.003 0.003 - 0.002 0.002 0.000 0.006 0.011
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 847357123 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]

---

Unlimited game: fnurt to play 65

Bot	157
fnurt	130
Position ID: 2G7ggDBsbpgDEA Match ID: cAkXAAAAAAAA

#		Ply	Move	Equity
•	1	R	23/17 13/8	+0.331
			0.588 0.179 0.014 - 0.412 0.134 0.006 +0.228 +0.331 0.001 0.001 0.000 - 0.001 0.001 0.000 0.004 0.009
	2	R	11/6 11/5*	+0.296 ( -0.035)
			0.558 0.218 0.019 - 0.442 0.140 0.006 +0.206 +0.296 0.002 0.002 0.001 - 0.002 0.001 0.000 0.004 0.012
	3	R	13/8 11/5*	+0.167 ( -0.164)
			0.549 0.219 0.018 - 0.451 0.170 0.014 +0.151 +0.167 0.001 0.001 0.000 - 0.001 0.001 0.001 0.003 0.010
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 847944838 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]

---

Details matter! Below is another variant which differs from the above variant in a seemingly small way: fnurt now owns the 9 point instead of the 7 point. This modification weakens fnurt's position significantly, and now blitzing becomes a much more attractive alternative. Part of the message seems to be that if you have an advantage then you can think about consolidating it, but if you don't have an advantage then you need to look for ways to seize one.

Note that at 3-away/7-away, even the awkward-looking 9/4 9/3 rolls out well, although the rollout should really be extended.

---

The score (after 0 games) is: Bot 0, fnurt 4 (match to 7 points)

fnurt to play 56

Bot	157
fnurt	134
Position ID: 2G7ggDBsjpkDEA Match ID: cIn6AAAAIAAA

#		Ply	Move	Equity
•	1	R	9/4 9/3	-0.188
			0.505 0.179 0.024 - 0.495 0.149 0.006 -0.017 -0.188 0.001 0.002 0.002 - 0.001 0.001 0.000 0.004 0.007
	2	R	11/6 11/5*	-0.193 ( -0.005)
			0.507 0.208 0.038 - 0.493 0.156 0.006 +0.002 -0.193 0.001 0.002 0.002 - 0.001 0.001 0.000 0.004 0.009
	3	R	23/17 13/8	-0.198 ( -0.010)
			0.515 0.165 0.026 - 0.485 0.172 0.008 -0.031 -0.198 0.001 0.002 0.002 - 0.001 0.001 0.000 0.004 0.007
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 847671663 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]

---

Unlimited game fnurt to play 65

Bot	157
fnurt	134
Position ID: 2G7ggDBsjpkDEA Match ID: cAkXAAAAAAAA

#		Ply	Move	Equity
•	1	R	11/6 11/5*	+0.096
			0.515 0.192 0.016 - 0.485 0.152 0.009 +0.077 +0.096 0.002 0.002 0.001 - 0.002 0.002 0.000 0.004 0.012
	2	R	13/8 11/5*	+0.066 ( -0.030)
			0.501 0.198 0.017 - 0.499 0.196 0.018 +0.003 +0.066 0.001 0.001 0.001 - 0.001 0.001 0.001 0.004 0.010
	3	R	23/17 13/8	+0.052 ( -0.045)
			0.518 0.153 0.011 - 0.482 0.171 0.008 +0.019 +0.052 0.002 0.002 0.000 - 0.002 0.002 0.000 0.004 0.011
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 847958492 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]

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Messages In This Thread

• Steve Mellen's position revisited
  Timothy Chow -- Saturday, 3 April 2010, at 9:50 p.m.
  • Steve Mellen's position revisited
    Steve Mellen -- Sunday, 4 April 2010, at 2:33 a.m.