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Two concrete examples of using "View Statistics"
Posted By: Timothy Chow
Date: Wednesday, 20 January 2010, at 4:41 p.m.
In Response To: Two concrete examples of using "View Statistics" (Matt Ryder)
Yes, I've seen Doug's article. It's not clear to me, however, that the simplicity of his formula makes it "more practical." Over the board, let's say you have a good feeling for the cubeless equity of your current position. You know that, per Zare, you have to add your recube vig to get the cubeful equity. But how are you going to estimate the recube vig?
With either Doug's approach or my suggested approach, of course, one has to study lots of examples. However, the question is, what are you trying to learn from the examples? Recube vig varies from position to position and is influenced by several factors; how do you sort them out? My answer, which seems ridiculously simple once I state it, but which I didn't fully appreciate before diving into this subject, is that the key to understanding recube vig is the following principle:
Winning a single game after getting your opponent to take your double is equivalent to winning a gammon. Losing a single game after taking your opponent's double is equivalent to losing a gammon.
If you are an experienced player then you are already used to making (say) checkerplay decisions by considering things like, "I think Play A wins more games than Play B but loses too many extra gammons, so I'll choose Play B." The additional piece of advice I have now is, when you're estimating gammon wins and losses, you should factor in effective gammon wins and losses, i.e., single wins and losses with an extra cube turn. To an excellent first approximation, that's what recube vig is all about.
Let's look at the Phil Simborg position again. Forget all the math for the moment. When you're weighing 8/5* against 4/2 3/2 over the board, what are you considering? You might correctly assess that 4/2 3/2 wins more games and loses fewer gammons than 8/5*. If you stopped here, you would decide in favor of 4/2 3/2. But wait! I'm pointing out that you haven't thought about effective gammon losses. How often is your opponent going to be able to offer you a cube you can't refuse and then beat you? It's clear that this is an important factor to consider. It turns out that the answer is, "often enough to make 8/5* the better play." The player who stops to think about effective gammon losses and who has a better feeling for how often they will happen will clearly play better than the player who doesn't. Therefore:
1. "View Statistics" is valuable, because it will give you quantitative information about your effective gammon wins and losses. Even if you can't memorize all this information, I believe you can get a sense for it over time from exposing yourself to a lot of examples. And surely you have little hope of getting a sense for effective gammon wins and losses if you don't look at that information.
2. Even if the math in my two examples seems beyond you, you can improve your play just by learning to think in terms of effective gammons instead of just actual gammons. Perhaps you got the impression from my two concrete examples that only those backgammon gods who have all their gammon prices and takepoints memorized and who can do complex calculations instantly in their head can benefit from "View Statistics." This is not the case. Just training yourself to think in terms of effective gammons instead of actual gammons will increase the sophistication of your approach to the game by a notch.

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