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hard 2-2 with 6-prime -- more RO's

Posted By: Daniel Murphy
Date: Monday, 30 July 2012, at 2:09 a.m.

In Response To: hard 2-2 with 6-prime (Petter Bengtsson)

I notice that the equities displayed in Petter's XG rollout are cubeless^*, not cubeful. E.g.:

7/1* 5/3	(0.9216 + 0.1376 + 0.0062) - (0.0784 + 0.0089 + 0.0001) =	0.9780
8/6 8/2	(0.9526 + 0.0491 + 0.0014) - (0.0474 + 0.0004 + 0.0000) =	0.9553
8/2 7/5	(0.9291 + 0.0415 + 0.0012) - (0.0709 + 0.0025 + 0.0000) =	0.8984

Here's a cubeful Gnubg 2-ply rollout showing "cubeless" and cubeful equities:

Unlimited, no Jacoby, Blue to play 2-2

White	72
Blue	80
Position ID: t94GACDabjcAAA Match ID: cAkJAAAAAAAE

#		Ply	Move	Equity
•	1	R	7/1* 5/3	+1.071770
			0.908385 0.126032 0.005164 - 0.091615 0.005629 0.000038 +0.942301 +1.071770 0.000853 0.001402 0.000277 - 0.000853 0.000231 0.000007 0.002219 0.002136
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 691138810 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	8/2 8/6	+1.016745 ( -0.055025)
			0.936831 0.050717 0.001464 - 0.063169 0.001666 0.000000 +0.924176 +1.016745 0.000481 0.000841 0.000158 - 0.000481 0.000064 0.000004 0.001243 0.000999
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 691138810 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]

And here's a cubeful Gnubg rollout with White holding the cube:

Unlimited, Blue to play 2-2

White	72
Blue	80
Position ID: t94GACDabjcAAA Match ID: QQkJAAAAAAAE

Alert: doubtful move ( -0.011)

#		Ply	Move	Equity
	1	R	7/1* 5/3	+0.947518
			0.922477 0.127967 0.005337 - 0.077523 0.006700 0.000099 +0.971460 +0.947518 0.000805 0.001329 0.000263 - 0.000805 0.000367 0.000019 0.002065 0.002419
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 691138810 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	8/2 8/6	+0.936364 ( -0.011155)
			0.951970 0.047195 0.001429 - 0.048030 0.000381 0.000000 +0.952185 +0.936364 0.000456 0.000761 0.000125 - 0.000456 0.000109 0.000027 0.001133 0.001318
			Full cubeful rollout with var.redn.
			2592 games, Mersenne Twister dice gen. with seed 691138810 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]

Why aren't the two plays that close with a centered cube? It seems that with a centered cube (no Jacoby), 7/1* 5/3 is a virtually free shot at generating extra gammons. After 8/2 8/6, Gnubg 2-ply as Blue almost always plays on Too Good for at least one more roll (Blue cashes if White rolls 3--3, 3-1 or 1-1 which safety both home board blots and decrease gammon chances by a lot). After 7/1* 5/3, Gnubg 2-ply as Blue plays on Too Good if White enters (hitting, and often exposing 1 or 2 blots in White's home board)), but if White fans, Gnubg 2-ply as Blue doubles White out to avoid, with much reduced gammon chances, a few awkward rolls:

Unlimited, Blue to play 2-2

White	73
Blue	72
Position ID: t94GAEB12zYAAA Match ID: cAkAAAAAAAAE

Cube decision
Rollout cubeless equity		+0.873062
Cubeful equities:
1.	Double, pass	+1.000000
2.	Double, take	+1.744823	+0.744823
3.	No double	+0.988746	-0.011254
Proper cube action:		Double, pass
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Centered 1-cube 0.904950 0.062824 0.002403 - 0.095050 0.002056 0.000010 +0.873062 +0.988746 Standard error 0.000529 0.000953 0.000246 - 0.000529 0.000091 0.000002 0.001407 0.001464 Player White owns 2-cube 0.917540 0.066904 0.002982 - 0.082460 0.008442 0.000132 +1.792782 +1.744823 Standard error 0.000775 0.001391 0.000309 - 0.000775 0.000597 0.000054 0.003794 0.004610
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 691138810 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]

---

^*Or "cubeless," quasicubeless or pseudocubeless.

Messages In This Thread

• hard 2-2 with 6-prime
  Robert Andersson -- Sunday, 29 July 2012, at 12:17 a.m.
  • hard 2-2 with 6-prime
    John O'Hagan -- Sunday, 29 July 2012, at 1:08 a.m.
    • hard 2-2 with 6-prime
      Dmitriy Obukhov -- Sunday, 29 July 2012, at 1:11 a.m.
      • hard 2-2 with 6-prime
        Robert Andersson -- Sunday, 29 July 2012, at 1:45 a.m.
        • hard 2-2 with 6-prime
          Dmitriy Obukhov -- Sunday, 29 July 2012, at 4:19 a.m.
  • hard 2-2 with 6-prime
    Chuck Bower -- Sunday, 29 July 2012, at 1:19 a.m.
  • hard 2-2 with 6-prime
    Robert Andersson -- Sunday, 29 July 2012, at 11:53 a.m.
    • hard 2-2 with 6-prime
      Petter Bengtsson -- Sunday, 29 July 2012, at 12:13 p.m.
      • hard 2-2 with 6-prime
        Robert Andersson -- Sunday, 29 July 2012, at 1:06 p.m.
      • hard 2-2 with 6-prime -- more RO's
        Daniel Murphy -- Monday, 30 July 2012, at 2:09 a.m.
    • hard 2-2 with 6-prime
      John O'Hagan -- Sunday, 29 July 2012, at 2:42 p.m.