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Quantifying recube vig, take 2

Posted By: Timothy Chow
Date: Wednesday, 13 January 2010, at 5:01 p.m.

Here are a couple of simple follow-up observations about recube vig in positions like the C-note position where there are no gammons and where the cube is going to be turned at most one more time.

We can summarize the statistics of the C-note position as follows:

White wins 18% of the time; 72% of these wins are with the cube on 4.

Blue wins 72% of the time; 29% of these wins are with the cube on 4.

I am going to call White's wins with the cube on 4 effective gammon wins and Blue's wins with the cube on 4 effective gammon losses. The reason is that 4 points is 4 points regardless of how we got them. So if we pretend that the cube is dead but that somehow White wins a gammon 72% * 18% of the time and White loses a gammon 29% * 72% of the time, and then do the corresponding take calculation, we will get the right answer for the C-note position. Most of us are more familiar with factoring in gammon wins and losses than with factoring in recube vig, so I think that calling the 4 points "effective gammon wins/losses" is psychologically helpful.

In other words, here is how I imagine one might do the take calculation over the board. First, let's say we know that at DMP, White wins 16.6% of the time, because of some reference positions we have learned. We add a little to get 18% wins AtS because we know that some DMP losses will actually be cashed in as wins. Now we need to estimate what percentage of those 18% wins will involve a double/take along the way. This is something that will have to be learned by experience, but it is not implausible that we could get a feeling for this if we set our minds to it. Similarly, we need to estimate what fraction of Blue's 72% wins start off by going poorly enough that White doubles and Blue takes. Again we have to hope to learn this by experience. But once we have these estimates, we just pretend that White wins a gammon 72% * 18% of the time and loses a gammon 29% * 72% of the time, and compute the take decision on that basis.

So for gammon-free positions with at most one additional cube turn, we have a strategy for training ourselves to estimate recube vig in take decisions. Namely, for various reference positions, we "View Statistics" and compute our effective gammon wins and effective gammon losses. Over time, we hopefully acquire a sense for the size of these numbers.

Note that the "cube efficiency" as reported by GNU does not enter directly into these calculations. It's possible that the cube efficiency number will help us make sense of the effective gammon wins and losses; I don't know. In any case, I am arguing that we pay more attention to the "View Statistics" numbers, if not the "cube efficiency" number itself.

When gammons and recube vig are both in the picture, then the situation gets more complicated. Single wins with the cube turned an extra time are still mathematically the same as gammons, but now we also have to factor in the cases when we win or lose 8 points. I'm not sure yet how to handle this complication in a way that we could imagine doing OTB.