Game 6, move 19 and 20 : Forum 6-6 to play

[diane]

Again a few 'next rolls - but this one seemed worth a conversation maybe...if not I will move it along

Forum, blue, to move 6-6

dgAAgNu2AQQIAA:8Am7ACAAIAAA

[ah_clem]

Spoiler

The only real question is whether we escape the backman now and avoid backgammon, or stay and try to win a single point.

Even if we are able to hit a shot, our winning chances are still pretty small, so I don't think it's worth  risking a backgammon for those small odds.  So move the runner up to the 18.  How we play the other three 6's doesn't matter.

If gammons meant anything, I'd probably stay and try to get a checker off, but at this match score it's not worth risking a backgammon to save a meaningless gammon.


I voted 24/12, 16/10, 7/1 because it's the first on the list.  I'll change to whatever play is leading as long as it's not 16/10, 7/1 (2)

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[dorbel]

16/10, 7/1(2) is an illegal play, although a very good one of course. Can we have 16/4, 7/1(2) please?

Spoiler

Running the back man now in order "to save the backgammon" is an enormous blunder. Only 2-1 and 1-1 don't leave a shot and even if White rolls one of those, or we get a shot and miss it, we are still a huge favourite to escape the bg. This is still a winnable game, let's stay back and try to win it with 16/4, 7/1(2)

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[diane]

16/10, 7/1(2) is an illegal play, although a very good one of course. Can we have 16/4, 7/1(2) please?

oopsy daisy....

[diane]

Spoiler

Running the back man now in order "to save the backgammon" is an enormous blunder. Only 2-1 and 1-1 don't leave a shot and even if White rolls one of those, or we get a shot and miss it, we are still a huge favourite to escape the bg. This is still a winnable game, let's stay back and try to win it with 16/4, 7/1(2)

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That was very much my feeling - for once I seem to have it right 

[ah_clem]

Spoiler

Spoiler

Running the back man now in order "to save the backgammon" is an enormous blunder. Only 2-1 and 1-1 don't leave a shot and even if White rolls one of those, or we get a shot and miss it, we are still a huge favourite to escape the bg. This is still a winnable game, let's stay back and try to win it with 16/4, 7/1(2)

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You're probably right again, since that seems to be the trend when we disagree.  The thing is, "because Dorbel says so" doesn't help me when I'm playing on my own, so I have to try to figure it out myself.  Here's my take:

Let's assume we get a shot and are able to close him out.  What are our winning chances with him having only three checkers to bear in?  I recall that 8 checkers off + one closed out on the bar == about a 50% chance of winning.  What about with 12 checkers off?  It must be something like 95%.  Since we will only hit about 1/3 of the time, this makes our winning chances something like 1.5%.

Seems to me that the chance of winning is less than the chance of our runner getting caught in rkb's homeboard.  I see several scenarios that catch the runner : one is rkb rolls doubles, followed by a lame roll on our part  That's 1/6 (doubles) times 1/4 (9 rolls that fail to clear his homeboard) for a total of 1/24 or 4% for that possibility alone. There are other possible scenarios which increase the backgammon rate.

Maybe I overestimate his winning chances after being hit, but that's my back-of-the-envelope calculation.

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[ah_clem]

Spoiler

Maybe I overestimate his winning chances after being hit...

Upon doing some research, it appears that I do overestimate it.
See http://www.bkgm.com/rgb/rgb.cgi?view+946

The Spleischft formula says that if O has n checkers borne off and one checker on the bar with X's home board closed out, O's winning  chances are 6*(n+1) out of 100 games.  (here n must be > 8, there's another foumula for 8 and less).  Assuming rkb bears off two checkers next roll and we hit right away and we obtain a closeout, the forumla gives rkb winning chances of 6*(12 +1) == 84%. 

Assuming a 1/3 chance to hit, that gives us about a 5% winning chance. Furthermore, since we haven't made our ace point yet, we might be able to send a second checker back by recirculating.  So our chances are probably better than 5%.

I'm going to stick with my vote, since looking up formulae is borderline cheating, and also because it seems to be close to the 4% backgammon rate above. 

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[Zorba]

Spoiler

Good approach there ah_clem, but there's an extra thing to consider here. Bascially the two things you're looking at here (hitting and running off the gammon) are not independent events but related.

If rkb rolls doubles (1-1 doesn't work, so it's 5/36 not 1/6), he leaves a blot but is also in a good position to backgammon us: The lowest pips rolls of 1-1 2-1 3-1 4-1 and 3-2 would not run out. But... nearly all of these would hit! This is common when it comes to "run off the backgammon" problems like this one: it's usually the ones or twos that hit one the few remaining checkers, and rolls with ones (or twos) are obviously those that wouldn't escape the backgammon.

So without doing an exact calculation, after rkb taking 4 checkers off it's more like we either hit the remaining one, or run off the backgammon. The chance of losing a backgammon is therefore still very small. Our winning chances after staying back are quite small, but clearly higher than that.

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[NIHILIST]

Spoiler

Maybe the liggest downside to staying is we're forced to close our board, making it nearly impossible to hit a second checker and become the favorite. In many cases the best we can hope for is to hit, save the gammon, and gain a little extra vig with the free drop. Still, I'm for staying.

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Bob

[dorbel]

Spoiler

Because dorbel says so isn´t any help as you say. It just seemed so obvious to me to stay that I didn´t bother to supply the reasoning. If we hit a shot White will have between 11 and 14 checkers off. We never get to pick up a second checker. If he has 14 checkers off I think that we still win about 5% of the time, somebody somewhere has an exact figure, but it is about right. I also think that this winning chance jumps by about 5% with every extra checker, so that if White held the cube for example, he could double us out with 12 checkers off and with 11 off we would have a marginal take/pass, indicating that we would be around 22% to win cubeless. These estimates may be off by a little, but it  doesn´t matter, even if they are a lot worse than this they still provide us with a clear guide to what we should be doing here, which is staying. The risk of being backgammoned is too small compared to our winning chances to run. Note that hitting always saves us a gammon as well, which is the difference between having a free drop and not, worth about 1.5% of match equity.

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[socksey]

oopsy daisy....

I did exactly the same thing originally.  Must be a brain fluke!   

I'm with the majority on the move, so far.   

socksey



The only consistent feature of all your dissatisfying relationships is you. - Lithograph from Despair.com

[ah_clem]

rollout

Spoiler

Staying and trying to win is the correct play.  But running is not "an enormous blunder", especially if you actually pay attention to how you run.

We win about 5% of games if we stay.  That's pretty much what the Spleischft formula predicted.  We only lose backgammon 2.5% of the time, so hanging back and trying to win is the way to go.  Thanks to Zorba for pointing out the erroneous part of my analysis - moves that fail to clear rkb's homeboard also hit.

Of the running plays, there's a huge difference in the gammon rate.  My mental shortcut of "gammons don't count" oversimplifies things. Gammons don't count much, but having a free drop is worth something.  That explains why 24/6 16/10  is only a  .03 error while the other running plays are .05 to .06.

Good discussion on this move.  I definitely learned something.




    1. Rollout          16/4 7/1(2)                  Eq.:  -0.984
       0.052 0.000 0.000 - 0.948 0.545 0.026 CL  -0.984 CF  -0.984
      [0.001 0.000 0.000 - 0.001 0.001 0.001 CL   0.002 CF   0.002]
     
    2. Rollout          24/6 16/10                   Eq.:  -1.015 ( -0.031)
       0.000 0.000 0.000 - 1.000 0.245 0.000 CL  -1.015 CF  -1.015
      [0.000 0.000 0.000 - 0.000 0.002 0.000 CL   0.000 CF   0.000]
       
    3. Rollout          24/12 16/4                   Eq.:  -1.030 ( -0.046)
       0.000 0.000 0.000 - 1.000 0.478 0.000 CL  -1.030 CF  -1.030
      [0.000 0.000 0.000 - 0.000 0.001 0.000 CL   0.000 CF   0.000]
       
    4. Rollout          24/6 7/1                     Eq.:  -1.030 ( -0.046)
       0.000 0.000 0.000 - 1.000 0.487 0.000 CL  -1.030 CF  -1.030
      [0.000 0.000 0.000 - 0.000 0.001 0.000 CL   0.000 CF   0.000]
       
    5. Rollout          24/12 16/10 7/1              Eq.:  -1.033 ( -0.049)
       0.000 0.000 0.000 - 1.000 0.529 0.000 CL  -1.033 CF  -1.033
      [0.000 0.000 0.000 - 0.000 0.001 0.000 CL   0.000 CF   0.000]
       
    6. Rollout          24/18 16/4 7/1               Eq.:  -1.044 ( -0.060)
       0.000 0.000 0.000 - 1.000 0.715 0.000 CL  -1.044 CF  -1.044
      [0.000 0.000 0.000 - 0.000 0.001 0.000 CL   0.000 CF   0.000]
       
    7. Rollout          24/12 7/1(2)                 Eq.:  -1.048 ( -0.064)
       0.000 0.000 0.000 - 1.000 0.773 0.000 CL  -1.048 CF  -1.048
      [0.000 0.000 0.000 - 0.000 0.001 0.000 CL   0.000 CF   0.000]
       
    8. Rollout          24/18 16/10 7/1(2)           Eq.:  -1.048 ( -0.064)
       0.000 0.000 0.000 - 1.000 0.782 0.000 CL  -1.048 CF  -1.048
      [0.000 0.000 0.000 - 0.000 0.001 0.000 CL   0.000 CF   0.000]
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