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Rollout and analysis

Posted By: Timothy Chow
Date: Wednesday, 7 April 2010, at 11:56 p.m.

In Response To: Bear 2 or clear the 6? (Timothy Chow)

Over the board, I "cleared from the rear and didn't ask questions." I should have asked some questions. Specifically:

1. What is my immediate shot jeopardy? As Daniel Murphy points out, clearing from the rear creates one more blotting roll than bearing two.

2. What is my long-term shot jeopardy? Leaving a gap creates longer-term shot jeopardy that most people tend to underestimate. But again as Daniel hinted, since White is crunched already, he will probably be forced to leave soon anyway, thereby reducing my long-term shot jeopardy.

3. Does bearing 2 win enough extra gammons to matter? This is an unlimited game so gammons of course matter, and the question is whether the extra gammons matter. Here the gammon is neither in the bag nor absurdly unlikely, so the two extra checkers off make a significant difference.

All the above factors point in the same direction, so the choice is clear: Bearing 2 is much better than clearing the 6 point.

Just to emphasize the importance of considering long-term shot jeopardy, though, let me point out that if we switch to double match point and give White extra timing, then clearing the 6 point becomes correct. See the rollout below.

---

Unlimited game: tchow to play 44

gnubg	79
tchow	64
Position ID: 7+4AADDudhsAAA Match ID: QgkSAAAAKAAA

#		Ply	Move	Equity
•	1	R	7/3(2) 4/off(2)	+0.951
			0.932 0.109 0.002 - 0.068 0.000 0.000 +0.974 +0.951 0.001 0.001 0.000 - 0.001 0.000 0.000 0.002 0.002
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 848129799 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	7/3(2) 6/2(2)	+0.899 ( -0.052)
			0.927 0.067 0.001 - 0.073 0.000 0.000 +0.922 +0.899 0.001 0.001 0.000 - 0.001 0.000 0.000 0.001 0.001
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 848129799 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]

---

The score (after 0 games) is: gnubg 0, tchow 0 (match to 1 point, post-Crawford play)

gnubg	108
tchow	64
Position ID: tu0GADDudhsAAA Match ID: cAkyAAAAAAAA

#		Ply	Move	Equity
•	1	R	7/3(2) 6/2(2)	+0.613
			0.807 0.373 0.043 - 0.193 0.000 0.000 +0.613 +0.613 0.001 0.008 0.003 - 0.001 0.000 0.000 0.002 0.002
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 849101644 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	7/3(2) 4/off(2)	+0.591 ( -0.022)
			0.796 0.432 0.039 - 0.204 0.000 0.000 +0.591 +0.591 0.001 0.009 0.002 - 0.001 0.000 0.000 0.002 0.002
			Full cubeful rollout with var.redn.
			1296 games, Mersenne Twister dice gen. with seed 849101644 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

• Bear 2 or clear the 6?
  Timothy Chow -- Wednesday, 7 April 2010, at 12:12 a.m.
  • Bear 2 or clear the 6?
    Daniel Murphy -- Wednesday, 7 April 2010, at 12:31 a.m.
    • Bear 2 or clear the 6?
      lenny -- Wednesday, 7 April 2010, at 2:31 a.m.
  • Rollout and analysis
    Timothy Chow -- Wednesday, 7 April 2010, at 11:56 p.m.
    • Rollout and analysis
      Daniel Murphy -- Thursday, 8 April 2010, at 2:49 a.m.
      • Rollout and analysis
        Timothy Chow -- Thursday, 8 April 2010, at 4:14 a.m.