Position # 51

[PersianLord]

Position information:

Pip-Count: Red 89-124 White
Score:   Red 2-0 White
Match:      5-pointer

Red is on roll. Cube action?

Spoiler

Note: Consider the following analysis as thoughts of an intermediate fibsroid.

This is a really strange position. First let us see how GNUBG evaluates probabilities of each outcome in this position:

84.7% 50.3% 1.5% - 15.3% 2.2% 0.0%

( Red's winning chances are posted first )

As can be seen, if red redoubles to 4 and white accepts and put the whole match on line (of course after the mandatory re-double to 8 ), white will have 15.3% GWC which equals his MWC. Consulting K.Woolsey's match equity table, we realize that trailing 5-away,1-away gives the trailer a MWC of 15%. So white is better off putting whole match on line NOW, because his GWC is now higher than 15%. So it's a take, if red throws the cube.

But what about red? He has decent chances to win this game with lots of room for winning the match by winning a gammon. So he should play on, because if he doubles, his decent gammon chances will be rendered void.

Thus it's a Too good to double position for red because of his decent gammon chances and yet a Take for white because of profitibality in terms of equity. Here is GNUBG's analysis:

Cube analysis

2-ply cubeless equity  +1.104 (Money:  +1.191)

   84.7%  50.3%   1.5% -  15.3%   2.2%   0.0%

Cubeful equities:

1. No double            +1.056
2. Double, pass         +1.000  ( -0.056)
3. Double, take         +1.000  ( -0.056)

Proper cube action: Too good to redouble, take

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[sixty_something]

i understand your frustration, PersianLord .. i fixed the   problem in your original post .. i also inserted an image in the question portion of your poll .. i cannot understand why your PNG image at blogspot.com would not display properly, but will advise our admins, stog and webrunner

i have suggestions on how to check for and fix   problems and how to post an image check the links below:

nbsp; issues

i'm working on a sticky post for posting images, but will have to return to it later

[stiefnu]

Spoiler

I guess I understand the difference between Too Good to Double/Take and Too Good to Double/Pass but, in practice, what difference would it make?  If Red has decided it's too good to double, White won't get the chance to either take or pass, as Red will still have the cube.   

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[PersianLord]

Spoiler

I guess I understand the difference between Too Good to Double/Take and Too Good to Double/Pass but, in practice, what difference would it make?  If Red has decided it's too good to double, White won't get the chance to either take or pass, as Red will still have the cube.   

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Spoiler

Hi. By your logic, we shouldn't have also No double/Take as well 

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[stiefnu]

Spoiler

Yes, that too!

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[sixty_something]

Spoiler

how about Too dumb to cube/But wish I had .. i had one such moment ahead 2-0 in a TL match with johnwayne today .. he scolded me mercilessly for not doubling and spanked me later for the match

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[playBunny]

Spoiler

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[playBunny]

Spoiler

Why are we all whisperi-, I mean spoilering?

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[dorbel]

Gnu 2-ply analysis shows that White does minutely better to take than to pass, increasing his theoretical MWC by 0.01%! This may be an error caused by rounding up as Gnu assembles the various theoretical outcomes and compares them to the match equity table. In practice passing and taking are effectively equal here. However, as we have observed on numerous occasions in the past, Gnu 2-ply analysis isn't the be-all and end-all. Both Gnu and Snowie rollouts show that this position is clearly too good to double and equally clearly a pass. In round numbers they give Red 87% match wins if he doesn't double, 86% if he doubles and gets a take, 85% if he doubles and White passes. These are cubeless rollouts, during which Red never doubles. Clearly by holding on to the cube he can improve these figures during those games where the gammon threat shrinks and he can use the cube correctly later on.
The noted mathematician Doug Zare thinks that a "too good to double/take" position exists and I believe has even published a mathematical proof of this. I wouldn't argue with that, indeed I can't as I am incapable of understanding his proofs! In practice, I don't think that it has any practical value, not least because no human player can evaluate this type of position with sufficient accuracy.
I would say looking at this that players who double the Red side would be very rare, simply because you can't  produce an accurate estimate of wins, losses and gammons to feed into the match equity table that we all carry in our heads (!!). Over the board, I would play on until White anchors, then think again. Usually when that happens, Red is suddenly not good enough to double and White has an easy take. If, for example, Red rolls 6-4 and plays 22/16, 14/10 and White then rolls a 4, Red won't have a double.

[zare]

The noted mathematician Doug Zare thinks that a "too good to double/take" position exists and I believe has even published a mathematical proof of this. I wouldn't argue with that, indeed I can't as I am incapable of understanding his proofs! In practice, I don't think that it has any practical value, not least because no human player can evaluate this type of position with sufficient accuracy.

Too Good/Take positions are common for the leader in match play, and they occasionally occur at even match scores. They have been discussed by people like Kit Woolsey before I even started studying backgammon. When a double or redouble kills your gammon threat, a gammonish position might be TG but still a take.

With some slight modifications, you could turn this position into a clear TG/Take position. Imagine changing the match score to 3-away 16-away. Even with 2 checkers up on a 5 point board, the trailer should be eager to take and make the automatic recube to 8, hoping for a freak match-winning gammon.

You might be thinking of a proof I gave that TG/Take can't happen in theory in money play (with ordinary assumptions). Holding the cube can't be worth that much in money play. Redoubling doesn't kill your gammons in money play.

To address the actual position:

Spoiler

I agree with the rollouts which say that this is TG/Pass, but let's look beyond the rollouts. In this type of position, Snowie 4 rollouts typically overvalue the trailer's chances because Snowie trades some wins to go for the gammon during the rollout. At DMP, after the redouble to 8, Red will be content to win the game, and will not give White as many chances.

Red's decisions will be more difficult than White's. Rollouts will underestimate Red's equity, but individuals should honestly assess how well they know how to bring Red's position home. If it were only slightly too good in theory (rather than a lot), many players would do better by cashing. E.g., if it were worth 1.030 to play on, ask whether your errors will exceed your opponent's by 0.030. If so, strongly consider cashing.

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