Game 3, move 18: Herd to move 6-2

[diane]

r_monk danced with 4-6, Herd up again..

s+0SAkCbtwEQGA:UQm5AAAAGAAA

[stiefnu]

[spoiler]Coming out with the 6 while we have the chance looks good, then maybe running it to the 15 pt to dupe the 3s is a possibility but why risk another shot? Perhaps playing safe with the 2 is better. 23/17, 4/2[/spoiler]

[ah_clem]

[spoiler]17/9 seems "safe" but 36 and 32 are pretty devastating and even if he misses, we still have the problem of getting our runners out.  However, neither are particular gammonish.  Playing off the 23 gives us more chances to win, but leads to more  gammons:  3-5 and 3-4 hit our blot and 3-6 3-3  and 3-2 put it behind a five prime.

Since we're just trying to win a single point here, I'm going to go with the play that gives him a 4/36 chance of icing us vs the 9/36 chance.  Yes this throws away some winning chances, but I'll actually be happy to get out of this game without being gammoned.



[/spoiler]

[diane]

[spoiler]Since we're just trying to win a single point here, I'm going to go with the play that gives him a 4/36 chance of icing us vs the 9/36 chance.  Yes this throws away some winning chances, but I'll actually be happy to get out of this game without being gammoned.[/spoiler]

To save me the counting headache...which one was that - cos you were being quite persuasive 

[ah_clem]

To save me the counting headache...which one was that - cos you were being quite persuasive 

[spoiler]17/11 4/2[/spoiler]

[ah_clem]

[spoiler]
Let's take another look at this in the cool light of day.

NOTE: updated, as I hosed the shotcount before

play            return shots              shots for us if he misses

17/9            2 (36)                    11 (any 5)
             

23/17 4/2    4 (35 34 )                 22 (any 5 plus 11 21 31 41 61)

23/15         7 (31 33 34 35)             29 (as above plus 32 33 34 36)

17/11 4-2    0                            11 (any 5)


Of course, the shot count is not the whole story (even if I managed to get it right this time, which is not a given). If we preserve the anchor, we're faced with the ongoing problem of how to get those checkers home.  But of the two anchor-preserving plays it seems that the one that leaves no return shots would be better.

And if we're going to abandon the anchor, giving him three more shots in order to gain 7 shots for us seems like a slight advantage (at this match score where gammons count for him but not for us - at an even match score, it's a clear advantage) so it looks to me like  23/15 has a slight edge over 23/17, 4/2.

The question then becomes whether to play safe by preserving the anchor, or bold by moving off the anchor.  The match score and the cube setting clearly indicate safe play.  The other "Magriel Factors" are neutral: race is about even, same number of homeboard points, same number of homeboard blots.  So that led me to vote for the safe play that leaves no return shots, 17/11 4-2.

The thing is, if we don't move from the anchor now, when are we going to? Sitting on the 23 point seems like waiting around to lose.  With him on the bar against a 5 point board, there's not going to be a better opportunity to move them out.  What to do?

Let's compute the equities and see what that says. We'll simplify 23/15 by assuming a return shot is a gammon loss for us and anything else is a win.

return hit -> gammon loss -> score 3-4 -> equity == .3
no return hit -> win -> equity == 1

So the equity for 23/15 is .3(7/36) + 1(29/36) == .058 + .806 == .864

The winning chances for 17/11 4/2 is harder to calculate - all I can do is eyeball it and make an estimate.  Let's say we're 60% to win.  That gives

win -> match equity == 1
lose -> score 3-2 ->  match equity ==.6

The equity for 17/11 4/2 is 1(.6) + .6(.4) = .6 + .24 = .84

Looks pretty close. I'm going to stick with the safe move, but I'm not sure it's correct.

[/spoiler]

[ah_clem]

rollout

[spoiler]

The Herd gets it right here. 

I way overestimated r_monk's gammon chances (among other errors).

    1. Rollout          23/17 4/2                    Eq.:  +0.319
       0.713 0.491 0.048 - 0.287 0.076 0.001 CL  +0.319 CF  +0.319
      [0.002 0.007 0.003 - 0.002 0.001 0.000 CL   0.004 CF   0.004]

    2. Rollout          23/15                        Eq.:  +0.219 ( -0.100)
       0.705 0.521 0.062 - 0.295 0.129 0.008 CL  +0.219 CF  +0.219
      [0.002 0.007 0.004 - 0.002 0.001 0.001 CL   0.004 CF   0.004]

    3. Rollout          17/9                         Eq.:  +0.106 ( -0.213)
       0.618 0.430 0.048 - 0.382 0.090 0.004 CL  +0.106 CF  +0.106
      [0.002 0.007 0.003 - 0.002 0.002 0.001 CL   0.004 CF   0.004]

    4. Rollout          17/11 4/2                    Eq.:  +0.077 ( -0.242)
       0.604 0.403 0.039 - 0.396 0.091 0.004 CL  +0.077 CF  +0.077
      [0.002 0.007 0.003 - 0.002 0.002 0.000 CL   0.004 CF   0.004]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 901453930 and quasi-random dice
        Play: 0-ply cubeful prune [expert]
        Cube: 0-ply cubeful prune [expert]
[/spoiler]