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Race%? Shot E% Take?

Posted By: Ian Shaw
Date: Tuesday, 17 May 2011, at 9:50 a.m.

In Response To: Race%? Shot E% Take? (Mr Majestyk)

I don't know any theory that would allow one to calculate the probability of clearing as 16/(114+9). I think you have to look at rolls that clear, leave a shot or (in essence) repeat the position. Douglas Zare gave this some treatment in a GV article.

Gnubg has a very similar rollout result to XG. I also noted some of the stats, which might throw more light on the situation.

White hit in 16.44% of games (1278/7776). White doesn't win with every hit, of course (and gnubg doesn't report a "wins with hit, wins without hit" breakdown") but it does give an idea of the hitting potential.

White	130
Blue	114
Position ID: tLvAAQM4b2MGAA Match ID: cAmgADAAEAAE

• Blue doubles

Cube decision
Rollout cubeless equity		+0.4514	(Money: +0.4373)
Cubeful equities:
1.	Double, take	+0.9938
2.	Double, pass	+1.0000	+0.0062
3.	No double	+0.8750	-0.1188
Proper cube action:		Double, take
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Centered 1-cube 0.7216 0.0158 0.0008 - 0.2784 0.0217 0.0007 +0.4514 +0.8750 Standard error 0.0004 0.0003 0.0002 - 0.0004 0.0010 0.0002 0.0009 0.0019 Player White owns 2-cube 0.7293 0.0173 0.0013 - 0.2707 0.0254 0.0010 +0.9938 +0.9938 Standard error 0.0004 0.0003 0.0002 - 0.0004 0.0012 0.0002 0.0022 0.0022
Full cubeful rollout with var.redn.
7776 games, Mersenne Twister dice gen. with seed 888004444 and quasi-random dice
Play: world class 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0.16
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

You calculated 2.94% shot equity. This would imply that White wins 2.94/16.44 = 17.9% of games in which she hits. I find it hard to believe that White is a 5:1 underdog after hitting.

My estimate of 20% race equity implies (after seeing the rollout) that White wins 7% after hits. 7/16 gives 44% White wins after hitting, which seems much more reasonable to me.

The rollout below attempts to assess the race equity. White's pipcount remains at 130; Blue's has been adjusted upward by the previously estimated 2 pips to allow for the fact that in the original position Blue won't be able to fill the five point smoothly. White wins 21.1% in this straight race.

paul	130
ian	116
Position ID: qGP3AQA4byMHAA Match ID: cAmgADAAEAAE

Cube decision
Rollout cubeless equity		+0.577	(Money: +0.577)
Cubeful equities:
1.	Double, pass	+1.000
2.	Double, take	+1.414	+0.414
3.	No double	+0.955	-0.045
Proper cube action:		Double, pass
Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Centered 1-cube 0.789 0.000 0.000 - 0.211 0.000 0.000 +0.577 +0.955 Standard error 0.000 0.000 0.000 - 0.000 0.000 0.000 0.000 0.001 Player paul owns 2-cube 0.788 0.000 0.000 - 0.212 0.000 0.000 +1.414 +1.414 Standard error 0.000 0.000 0.000 - 0.000 0.000 0.000 0.000 0.000
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 887492603 and quasi-random dice
Play: 0-ply cubeful [expert]
Cube: 0-ply cubeful [expert]

Messages In This Thread

• Race%? Shot E% Take?
  Mr Majestyk -- Wednesday, 11 May 2011, at 8:49 p.m.
  • Race%? Shot E% Take?
    Lucas Bauer -- Wednesday, 11 May 2011, at 10:13 p.m.
    • Race%? Shot E% Take?
      Stick -- Wednesday, 11 May 2011, at 11:00 p.m.
      • Race%? Shot E% Take?
        Timothy Chow -- Thursday, 12 May 2011, at 4:33 a.m.
        • Race%? Shot E% Take?
          Stick -- Thursday, 12 May 2011, at 12:35 p.m.
  • Technicality of Gaps in Contact Races
    Mr Majestyk -- Thursday, 12 May 2011, at 10:30 a.m.
  • You have the score reversed *NM*
    Michael Nielsen -- Thursday, 12 May 2011, at 11:01 a.m.
    • Oops, that was a response to Timothy *NM*
      Michael Nielsen -- Thursday, 12 May 2011, at 11:02 a.m.
  • Race%? Shot E% Take?
    Ian Shaw -- Friday, 13 May 2011, at 8:46 a.m.
    • Race%? Shot E% Take?
      Mr Majestyk -- Friday, 13 May 2011, at 12:17 p.m.
      • Race%? Shot E% Take?
        Ian Shaw -- Friday, 13 May 2011, at 4:31 p.m.
        • Race%? Shot E% Take?
          Mr Majestyk -- Friday, 13 May 2011, at 8:02 p.m.
        • Race%? Shot E% Take?
          Mr Majestyk -- Saturday, 14 May 2011, at 9:52 a.m.
      • Race%? Shot E% Take?
        Bob Koca -- Friday, 13 May 2011, at 11:09 p.m.
      • Race%? Shot E% Take?
        Ian Shaw -- Tuesday, 17 May 2011, at 9:50 a.m.