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Very nice, but just a tad conservative for raw pip counts

Posted By: Timothy Chow
Date: Wednesday, 3 February 2010, at 9:31 p.m.

In Response To: Very nice, but just a tad conservative for raw pip counts (neilkaz)

neilkaz wrote:

Here's some evdence to support that I think "Nack 57" is just a wee bit conservative.

I take it you mean that you think the "gold standard" is a wee bit conservative.

I haven't heard the term "gold standard" before. How was the gold standard derived? In Trice's book he talks about the "one-checker model," meaning that to analyze a race with, say, 67 pips versus 75 pips, one imagines a single Black checker that is 67 pips away from home and a single White checker that is 75 pips from home, and figure out what the doubling points and take points would be in this imaginary race. I'm guessing that the gold standard came from analyzing the one-checker model.

The advantage of the one-checker model is that one can analyze it precisely. The disadvantage, of course, is that real 67-pip/75-pip positions don't behave quite like the one-checker model, even if we restrict our attention to "low-wastage" positions. Neil seems to be suggesting that the distinction might actually make a difference to the doubling window by a pip or so in some cases.

An alternative approach to the one-checker model is to generate a large number of actual 67-pip/75-pip low-wastage positions (either randomly, or taken from actual games), roll them out, and take an average. Provided one has enough computational power, this approach should be more accurate than the one-checker model. But it does require a lot of computer time. The selection of positions also requires some thought. How many positions do we roll out and which ones? Presumably we don't want to choose bizarre positions that would not come up in practice and/or that would take a lot more rolls (or a lot fewer rolls) than average to bring home. At the same time, we want a variety of positions to make sure we're sampling the space of possibilities adequately.

The table of non-contact races that one can download from Backgammon Galore is apparently taken from some larger table. That table would seem like a good starting point. Is anyone interested in rolling out all the positions in that database, or at least all the positions that are close to the doubling window boundaries?

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