Game 3 move 6 The Herd to play 6-3

[ah_clem]

Zorba takes the cube offer and we have a 6-3 to play.

[ah_clem]

Spoiler

We've got that big stack on the 13 saying "move me". With him only having half a roll, unstacking two checkers looks enticing.  If he misses us, we're almost certain to make another blocking  point and be well on our way to Gammon City.  If he hits, he has to use both numbers to do so and we'll have counterplay with the blot in his homeboard.   I count 6-1 6-2 5-2 5-3 and 5-5 as hitting numbers for a total of nine.  5-5 is pretty bad for us, but the others are not. 

After 13/7 13/10, we pretty much coast to a single point win with good gammon chances 75% of the time.  The other 75% we're back to even.  Looks like good odds to me.

The one thing holding me back is that at this match score a doubled gammon "wastes" a point so that makes me less certain about this move.  So what about the others?  13/4 may well be correct due to the match score, but ti seems passive.  I don't see the wisdom in leaving a direct shot.  That leaves 13/7 6/3.

13/7 6/3 only leaves one less shot (5-5). It bears an extra builder on the blot on the one point at the expense of one less builder aimed at the 5 point. Which is more important? Pointing on his head on the 1 or making the 5?  While I'd gladly point on the blot on the ace point, the 5 point is probably of more strategic importance.  I'll stay with bringing down two.

13/7 13/10.

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[NIHILIST]

Spoiler

The problem with your play is that it could result in a sequence where we get hit, we roll an airball entering number or fan and now we're in real trouble with extra blots exposed; plus, it turns 5-5 for him into a truly devastating roll. It seems that your play introduces too much volatility into a position we just want to quietly bring home.

I think we just play quietly here with 13-4.

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Bob

[ah_clem]

Spoiler

The problem with your play is that it could result in a sequence where we get hit, we roll an airball entering number or fan and now we're in real trouble with extra blots exposed; plus, it turns 5-5 for him into a truly devastating roll. It seems that your play introduces too much volatility into a position we just want to quietly bring home.

I think we just play quietly here with 13-4.

The quiet play certainly seems viable and it looks like that's the way the Herd is going.  Applying Magriel's safe vs bold criteria we see:

we have more homeboard points -> bold
he has a blot in his homeboard -> bold
we're ahead in the race -> safe
we're ahead in the match -> safe
he has more checkers back than us -> safe

So, this would imply that the safe play is correct by a "vote" of 3-2.  But it neglects the fact that he only has half a roll here.  That tips it toward bold for me.  YMMV. 

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[r_monk]

Spoiler

13/10 13/7 for me too. However, very much in doubt.

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[ah_clem]

gnubg results

Spoiler

2-ply analysis likes bringing down two form the bar by .043.  0-ply rollout likes the safe play by .005.

For both settings, the bold play wins more games and more gammons, but loses more gammons. 

I'll start a 2-ply rollout and see what that says.



/////////// 2 ply analysis ////////////////////////////////////

    1. Cubeful 2-ply    13/10 13/7                   Eq.:  +0.357
       0.720 0.250 0.016 - 0.280 0.074 0.003
        2-ply cubeful prune [world class]
    2. Cubeful 2-ply    13/4                         Eq.:  +0.314 ( -0.043)
       0.707 0.222 0.011 - 0.293 0.059 0.001
        2-ply cubeful prune [world class]
    3. Cubeful 2-ply    13/7 6/3                     Eq.:  +0.274 ( -0.083)
       0.694 0.237 0.014 - 0.306 0.074 0.002
        2-ply cubeful prune [world class]


/////////////////////// 0 ply rollout //////////////////////////////////////

    1. Rollout          13/4                         Eq.:  +0.357
       0.715 0.227 0.032 - 0.285 0.057 0.003 CL  +0.521 CF  +0.357
      [0.002 0.003 0.003 - 0.002 0.001 0.001 CL   0.005 CF   0.007]

    2. Rollout          13/10 13/7                   Eq.:  +0.353 ( -0.005)
       0.717 0.250 0.046 - 0.283 0.071 0.005 CL  +0.515 CF  +0.353
      [0.002 0.003 0.004 - 0.002 0.001 0.001 CL   0.005 CF   0.007]

    3. Rollout          13/7 6/3                     Eq.:  +0.302 ( -0.055)
       0.699 0.244 0.037 - 0.301 0.071 0.004 CL  +0.476 CF  +0.302
      [0.002 0.003 0.003 - 0.002 0.001 0.001 CL   0.005 CF   0.007]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 903967096 and quasi-random dice
        Play: 0-ply cubeful [expert]
        Cube: 0-ply cubeful [expert]

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[ah_clem]

2-ply gnubg rollout

Spoiler

two ply rollout favors the bold play, but not by much.  Looks like about a wash to me.




    1. Rollout          13/10 13/7                   Eq.:  +0.361
       0.719 0.262 0.052 - 0.281 0.071 0.008 CL  +0.546 CF  +0.361
      [0.002 0.004 0.004 - 0.002 0.001 0.002 CL   0.004 CF   0.006]

    2. Rollout          13/4                         Eq.:  +0.353 ( -0.008)
       0.717 0.237 0.037 - 0.283 0.061 0.004 CL  +0.538 CF  +0.353
      [0.002 0.004 0.004 - 0.002 0.001 0.001 CL   0.004 CF   0.006]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 903967096 and quasi-random dice
        Play:  2-ply cubeful prune [world class]
        keep the first 0 0-ply moves and up to 8 more moves within equity 0.1
        Skip pruning for 1-ply moves.
        Cube: 2-ply cubeful prune [world class]

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