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BGonline.org Forums
A comment about the takepoint formula
Posted By: Timothy Chow In Response To: A comment about the takepoint formula (Matt Cohn-Geier)
Date: Wednesday, 14 April 2010, at 3:04 p.m.
MCG wrotE:
E.g. if we know exactly how often we win a single/G/BG on a 2-, 4-, 8-, 16-, etc. cube then everything else becomes very easy. The problem is that these things are not known before a rollout.
Yes, absolutely true. It's also true that, before a rollout, I don't know where along the live/dead cube spectrum I should place my estimate of the recube vig.
The question therefore is, what characteristics of the position can we hope to learn by studying it, and that will be helpful when we are faced with a similar but different position over the board next time?
The traditional approach, as I understand it, is this: By means of a rollout, I learn that I should have chosen 17% (if I recall your figures correctly), which is close to the live-cube end of the spectrum. So now I know that this position has relatively high recube vig. Fine. But now suppose I change the position slightly, or change the score slightly. How do I adjust my calculations? Maybe I intuitively feel that the alteration reduced the recube vig. But by how much? Over time, by studying enough positions, I can get some feeling for this, but my sense is that this is a difficult task because "recube vig" (in this sense) is a rather nebulous concept. It doesn't relate in any simple way to concrete features of the position or to the gammon prices at this score.
The alternative approach that I'm suggesting is this: By means of a rollout, I ascertain that (say) I get in a recube 30% of the time; 11% of the time my opponent takes, and in almost half of those cases I win. Again, fine. Now suppose I change the position or the score slightly. How do I adjust? Well, I need new estimates of those numbers (30%, 11%, 5%). My point is that these are concrete concepts that relate directly to my backgammon experience. Everyone understands immediately and intuitively what it means that "I get in a recube 30% of the time and about a third of those are takes." My guess, therefore, is that our intuitions will have an easier time trying to adjust these figures than trying to adjust that nebulous recube vig figure directly. It seems more plausible to me that I'll be able to make an estimate like "Well, here I think I'll be able to recube only 25% of the time and the majority of those (say 20%) will be drops; the takes will probably split 50-50" than "Well, here I think the recube vig will be 5% less than in the other position." For example, suppose I play out the position against the bot a few dozen times. I will be able to get a direct sense of how often the cube gets turned, and why, just by watching what happens. But I don't get a direct sense that the recube vig puts my takepoint at 17%.
This is why I'm suggesting it's better to think in terms of effective gammons. I think it is closer to what our brains naturally learn when we study positions.
Now some of the other comments you've made make me suspect that you have another objection lurking in the background. This (hypothetical) objection runs something like this, "O.K., let's say I grant for the sake of argument that I am able to estimate OTB how often I get a recube, how often I get a take, etc. How does that help me figure out the recube vig? I still need to interpolate between the live-cube and dead-cube bounds, and I don't see how those percentages you're telling me to estimate let me figure out where I should interpolate." I don't know if you have this objection or not, but I'll answer it anyway. The answer is that once you have the percentages I listed (i.e., recubes, effective gammons), you don't need to bother with the live-cube and dead-cube takepoints any more. As you point out, now that you know how many games end with 1, 2, 4 points, everything is easy. In fact it's maybe even easier than you think, because the effective-gammon formula is exactly the same as the formula you already know, just with different numbers plugged in. It's true that effective gammons don't necessarily help you figure out recube vig in the traditional sense, but the point is that you don't need to know the recube vig in the traditional sense. Recube vig is just a means towards an end (a take decision), and if you can attain that end without estimating recube vig, then so much the worse for recube vig.
Finally, let me repeat one of my caveats: the effective gammons approach really works only when the cube is likely to be turned only once more, and gammons after a redouble/take are negligible. If these assumptions are not true then I have nothing better to offer than the traditional approach of muddling along with the nebulous recube-vig concept. However, in cases like the present position, I believe that the effective-gammon approach tracks our intuitions more closely, once you get used to the concept.
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