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Improved Cube Handling in Races
Posted By: Todd Kennedy
Date: Wednesday, 18 June 2014, at 2:52 a.m.
In Response To: Improved Cube Handling in Races (Axel Reichert)
Axel, this is a great contribution, thanks. I have a couple comments/suggestions.
1) I do appreciate that you measured error of the formula by any equity lost in an incorrect doubling decision, since this is nearly always the purpose of the calculation. As a matchplayer, however, I am more interested in a count that can lead me to a good CPW, so that I can adjust to the doubling windows at various match scores. As your table on page 26 shows, the average error in calculating CPW is over 4%. As a match player I only need a good CPW estimate if my CPW is between around 65% (for 2a2a) and 80% (for 5a3a). Could you calculate the average CPW error only for those positions inside a window like this  perhaps this will lead to a better parameterization? Your Figure 5 is a good example of what I'm trying to get at, as it counts as a 0 error for cube decisions, but as an 8.6% error for CPW  this is a position that I don't care whether I'm correct or not, so I'd rather this count as a 0% CPW error on a practical basis.
2) I also fully appreciate the value of a practical formula. I remember my head spinning when I saw Lamford's formula (p10 of his "improve" book). But I would suggest a more qualitative approach to determining which formulas have more effort. For example, I favor your formula on page 40 rather than your preferred formula, even though it has 3 additional parameters, simply because I can divide by 5 (by multiplying by 2 and dividing by 10) much more easily than I can divide by 3. Personally I've developed my own formula to convert Keithcount adjusted pips to a CPW rather accurately and it uses what I believe you'd consider to be 8 parameters, but it is easy to memorize and involves only addition and subtraction. (I haven't found it to work well under around 40 pips though, which led me to recently consider EPC based approaches to these like Matussek and Trice, so your paper is very timely for me). So, perhaps considering formulas with more parameters (while keeping the math simple) might lead to a solution with less error.
Todd

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