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BGonline.org Forums
Missed doubles and PR
Posted By: Timothy Chow In Response To: Missed doubles and PR (Dmitriy Obukhov)
Date: Friday, 16 September 2016, at 10:50 p.m.
Dmitriy wrote:
@ Tim: obviously, it is very hard, if even possible, to find a real backgammon position that satisfies all criteria I outlined before. But why is it important?
My point was just that you can't lose more equity than is available to you to lose. The danger of inventing imaginary scenarios that "prove" the opposite is that you can end up with a scenario that sounds like it could happen but actually couldn't. And I think it's actually an instructive exercise to try to invent a position where it seems you can keep losing equity via missed doubles, without ever regaining equity through opponent misplays or unlucky rolls.
But anyway, you said you're convinced, so there's no point continuing this "branch" of the discussion.
As for your examination analogy, I think a better analogy might be the following. To test your spelling ability, I give you some words to spell, but instead of picking each word randomly, I pick a random point in the dictionary and start giving you five consecutive words from the chosen point onwards. In particular, I ask you to spell "accommodate", "accommodates", "accommodating", "accommodation", and "accommodations". You get them all wrong, and I declare you to be a terrible speller.
It is possible to take the view that the ultimate purpose of playing backgammon is not to win or to have fun, but to measure your PR. On this view, the rules of backgammon have a flaw: Consecutive cube decisions tend to be correlated, and therefore don't provide independent random samples of your PR. If we take this view, then my suggestion wouldn't be to change the definition of PR, but to change the sampling method. That is, stop playing backgammon and instead devise some other method, such as a proficiency test, that will measure PR more accurately and with lower variance.
I personally do not think that the purpose of playing backgammon is to measure PR; rather, PR is a tool to enhance the backgammon-playing experience. So I get dinged multiple times for correlated reasons. So what? I've obtained the information I want about my game. Once we start going into weird contortions to try to make sure the variance in the measurement of my PR is as low as possible, we are starting to lose our sense of perspective. (Indeed, even the whole business of excluding forced decisions strikes me as a loss of perspective. It doesn't even necessarily lower the variance. But I digress.)
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