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My first rollouts ever posted

Posted By: Nack Ballard
Date: Sunday, 31 January 2010, at 5:00 a.m.

In Response To: Rollout (Timothy Chow)

White	149
Blue to play 22 for Money	139

#		Ply	Move	Equity
•	1	R	24/22 13/11(3)	+0.096
			53.4 7.8 0.2 - 46.6 10.1 0.3 +0.044 +0.096 0.1 0.1 0.0 - 0.1 0.1 0.0 0.002 0.004
			Full cubeful rollout with var.redn.
			5184 games, Mersenne Twister dice gen. with seed 844444444 and quasi-random dice
			Play: 2-ply cubeful prune [world class]
			keep the first 0 0-ply moves and up to 12 more moves within equity 0.16
			Skip pruning for 1-ply moves.
			Cube: 2-ply cubeful prune [world class]
	2	R	24/20 13/11(2)	+0.064 ( -0.032)
			52.4 8.1 0.2 - 47.6 10.9 0.3 +0.020 +0.064 0.1 0.1 0.0 - 0.1 0.1 0.0 0.002 0.004
			Full cubeful rollout with var.redn.
			5184 games, Mersenne Twister dice gen. with seed 844444444 and quasi-random dice
			Play: 2-ply cubeful prune [world class]
			keep the first 0 0-ply moves and up to 12 more moves within equity 0.16
			Skip pruning for 1-ply moves.
			Cube: 2-ply cubeful prune [world class]

While I've quoted a lot of data from rollouts, and I've posted a lot of diagrams, these are the first (diagrammed) rollouts I've posted.

The above position is a confirmation of Tim's rollout that shows that, after playing 24/22 13/11(2) with three of the deuces, for the fourth ace playing a spare to the 11pt is clearly better than coming up to the 20pt. Our equities are almost identical: Tim's are .095 and .064 after 1296 trials; mine are .096 and .064 after 5184 trials.

Why is 13/11 clearly (.032) better than 22/20 for the fourth ace? Is it because 13/11 helps Blue's position, or is it because 22/20 hurts Blue's position?

To demonstrate what is going on, I created an alternate position below where Blue starts out with one fewer deuce -- midpoint spare back to 15pt (alternatively it can be reached by Tim's game sequence 41Z-62R-61R-32H-65$-51n-65P-547-62R-22 but with 54 replaced by 61), then determined Blue's equity after 15/11 13/11 24/22. It is identical to the equity achieved by (illegally) playing three deuces (24/22 13/11(2)) in the main position (above).

Here is a summary of the three key equities:

.068 - Equity if playing NO fourth deuce
.096 - Equity if playing 13/11 as fourth deuce
.064 - Equity if playing 22/20 as fourth deuce

What this tells us is that playing 13/11 as the fourth deuce helps Blue's position by .028 (from .068 to .096), whereas playing 22/20 hurts Blue's position but only by a mere .004 (the difference between .068 to .064).

In other words, the fourth deuce 13/11 helps Blue a lot (relatively speaking), whereas 22/20 has very little effect on his equity. If you want to understand why the 13/11 spare is so strong and the 22/20 up-play is about net neutral, read my earlier post (made before subjecting the position to bot analysis).

(The second play of the bottom rollout provides some supplemental information: the importance of coming up with the first deuce, 24/22. It is .082 better than 13/11. This is consistent with Tim's post-rollout observations that playing 24/22, thereby getting within a 6-launch of the outfield is the critical back checker deuce.)

Nack

[P.S. I've found that to figure out the equity of a position, the bots report a more dependable equity if you force a checker play to reach the position rather than set it up as a cube decision for the other side. At this time, I know of no logical reason for that to be the case; nevertheless it seems true based on my many observations. That's why I didn't roll out the Tim-three-deuce play as a cube decision and compare that to the checker rollout of the other two plays (or to another cube decision rollout); it would be a relatively unreliable comparison.]

Blue to play 22: This is like playing only three 2s in the other position

#		Ply	Move	Equity
•	1	R	24/22 15/11 13/11	+0.068
			53.0 7.2 0.2 - 47.0 10.3 0.3 +0.027 +0.068 0.1 0.1 0.0 - 0.1 0.1 0.0 0.002 0.004
			Full cubeful rollout with var.redn.
			5184 games, Mersenne Twister dice gen. with seed 888888888 and quasi-random dice
			Play: 2-ply cubeful prune [world class]
			keep the first 0 0-ply moves and up to 12 more moves within equity 0.16
			Skip pruning for 1-ply moves.
			Cube: 2-ply cubeful prune [world class]
	2	R	15/11 13/11(2)	-0.014 ( -0.082)
			50.6 7.2 0.2 - 49.4 10.6 0.3 -0.023 -0.014 0.1 0.1 0.0 - 0.1 0.1 0.0 0.002 0.004
			Full cubeful rollout with var.redn.
			5184 games, Mersenne Twister dice gen. with seed 888888888 and quasi-random dice
			Play: 2-ply cubeful prune [world class]
			keep the first 0 0-ply moves and up to 12 more moves within equity 0.16
			Skip pruning for 1-ply moves.
			Cube: 2-ply cubeful prune [world class]

Messages In This Thread

• Money game 2-2 to play
  Timothy Chow -- Thursday, 28 January 2010, at 3:01 a.m.
  • Money game 2-2 to play
    Stick -- Thursday, 28 January 2010, at 4:39 a.m.
    • The flexibility of nactation
      Timothy Chow -- Thursday, 28 January 2010, at 5:29 a.m.
      • The flexibility of nactation
        Nack Ballard -- Thursday, 28 January 2010, at 10:46 a.m.
  • Money game 2-2 to play
    Nack Ballard -- Thursday, 28 January 2010, at 9:54 a.m.
    • Money game 2-2 to play
      Stick -- Thursday, 28 January 2010, at 1:20 p.m.
  • Rollout
    Timothy Chow -- Friday, 29 January 2010, at 3:52 p.m.
    • My first rollouts ever posted
      Nack Ballard -- Sunday, 31 January 2010, at 5:00 a.m.
      • My first rollouts ever posted
        Stick -- Sunday, 31 January 2010, at 8:56 a.m.
      • My first rollouts ever posted
        Matt Cohn-Geier -- Sunday, 31 January 2010, at 1:05 p.m.
      • My first rollouts ever posted
        Stick -- Sunday, 31 January 2010, at 6:26 p.m.
        • About rollout seed
          eXtreme Gammon -- Sunday, 31 January 2010, at 8:01 p.m.