Game 4, move 50 : Forum 3-3

[diane]

Forum, blue, to move 3-3

fycACDj25gAAAA:QYmtACAACAAA

[ah_clem]

Spoiler

We want a gammon here, so a namby-pamby move like 6/off 6/3(2) is not the way to go.  We have a chance to take more than one checker off, so lets do it.

But, taking four off with 3/off(4) almost guarantees that we'll leave a shot.  We can bear off 3 checkers without leaving nearly as much of a target, and 7 checkers off is not much different than 8 off (it'll take the same number of rolls if we can bear off two checkers each time).

So that's my choice: 6/off 3/off(2).

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[dorbel]

Spoiler

I don't think clem is right here. I hope he won't take it personally if I point out that not "reading the numbers" as Robertie calls it, is his particular weakness. His play of 6/off, 3/off(2) leaves us stripped and with the 6pt still to clear. This is unlikely to cost us the game, but might cost us our gammon if White can hit us and keep us at bay long enough to run his men around. That play has 12 immediate shot numbers (6-5, 6-1, 5-4, 5-3, 5-2, 5-1). Some other numbers fail to clear the 6pt leaving us with extended jeopardy (3-1 and 2-1), while 6-2 and 4-2 leave us with an odd number on the highest point. I think if we can clear the 6pt safely, we should go with that, even at the expense of a big stack on the 3pt. I choose 6/3(3), 3/off, only 8 immediate shot numbers (6-3, 5-3, 4-3, 3-2), no extended jeopardy and even on the highest point. After that, we have ten men to bear off while White still needs a minimum of 66 pips (8 rolls on average) to save the gammon. That should be good enough.

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[ah_clem]

Spoiler

I'm not offended by any criticism of my ideas as long as they are reasonable and I can learn something.  Here's my thinking - tell me why it's wrong:

In this position, our opponent has no board at all.  Even if we're hit we'll enter and recirculate; we're far enough ahead in the  race and he has no hope of closing us out that we'll win the game almost always.  So what's to fear about getting hit?  Well, losing the gammon is to be feared, but the gammon is by no means certain.  He needs 12 transitions to save gammon, and the safe play leaves 10 transitions for us.  With him on roll, that's not that big a margin for error.  But if we're 8 transitions to go instead of 10, we're in the driver's seat.  Agreed that a stripped 6 point and a gap on the 5 leaves lots of shots, but we're playing for gammon vs single point win and it seems the extra gammon chance is worth the extra risk of leaving a shot.

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[diane]

Spoiler

I am with the safer play, but that may be because I got bitten by a Gammonbot this morning, and left  shot when it had no board and of course lost...    I do think that really, over the board, I will tend to go with the slightly riskier play to try and get the gammon, if there is a low chance of me losing because of it.
The question revolves around what are the gammon chances without taking this risk, and with taking it...because the reality is that we are only playing to distinguish a single win from a double and the match.

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[dorbel]

Spoiler

White does have a weak board, but recirculating is not always as easy as it looks. Just running round again takes two or three turns if things go well, never mind if we get hit, plus there is always the chance of dancing on a two point board, or rolling some root number that exposes a second checker. That's where our gammons will go.
We'll have two fewer checkers off after the safer play of course, but I think we will make those up anyway, as our bearoff will go faster later. After taking three men off, we take none off next turn with 4-3, 4-2, 3-2, 3-1 or 2-1 for example. Stripped positions with gaps are very bad for bearing off against an anchor. Stacking on the 3pt is ugly but better.

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[ah_clem]

Spoiler

I think what I was missing here is an accurate reckoning of how far each player has to go.  I said that we need 8 or 10 transitions depending on our choice of move and that blue needed 12 to save gammon.  That's correct in as far as it goes, but transitions are only a rough proxy.  A deeper analysis reveals that with three men on the 24, blue is not at all likely to make 12 transitions in the minimum of 6 rolls.  For our side, checkers on the 6 point will often need two  dice instead of one to come off, making the two checker-off difference less than it seems.  

So our gammon chances are much better than I had thought, even if we make the safer move.  Since the gammon is well in hand (but don't reach for the scoresheet yet) it makes since to make the safer move.

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[ah_clem]

rollout

Spoiler

With a 75% gammon chance, there's not much to recommend risky moves to increase those chances. Especially if the risky move decreases the gammon chances.



   1. Rollout          6/off 6/3(2)                 Eq.:  +2.472
      0.995 0.755 0.492 - 0.005 0.000 0.000 CL  +2.472 CF  +2.472
     [0.001 0.002 0.009 - 0.001 0.000 0.000 CL   0.005 CF   0.005]

   2. Rollout          6/off 3/off(2)               Eq.:  +2.408 ( -0.065)
      0.992 0.725 0.463 - 0.008 0.000 0.000 CL  +2.410 CF  +2.408
     [0.001 0.002 0.009 - 0.001 0.000 0.000 CL   0.005 CF   0.005]
       Full cubeful rollout with var.redn.
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