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Improved Cube Handling in Races

Posted By: Axel Reichert
Date: Monday, 16 June 2014, at 11:40 a.m.

In Response To: Improved Cube Handling in Races (Bob Koca)

Hi Bob,

many thanks for your detailed review, the questions, and comments.

Page 4: Regarding the "optional" pass, you are of course right. That is a clear mistake by me introduced by a last-minute change of the example. Originally the checker was on point 6, I simply forgot to change the description completely.

Page 7: I agree that the motivation for introducing a parameter for crossovers is somewhat lame. Nevertheless, I am of course perfectly free to do so, and the outcome of the optimization process clearly tells that the crossover penalty should be 1 rather than 0 (if integer values are to be used).

Page 14: Measuring the effort is certainly an area for discussion. In your example with a stack penalty of 2 and a stack penalty offset of 2 (for whatever point) a position with 5 checkers on that point gets (5 - 2)*2 = 6 additional pips. If that is the only adjustment, then this position requires an effort of 6. On the other hand, if a method subtracts 2 pips for a smooth distribution of a particular position, the effort is 2. Thus effort is essentially the sum of the absolute values of all adjustments a particular position requires (BOTH players are taken into account). This is why the Thorp count has such a high effort, see table 3 in the article: Every checker on board get a penalty.

Page 16: The short database contains 51502 positions, which amounts to 3*51502 decisions: Is it a double? Is it a redouble? Is it a take? Three opportunities to make a mistake. Hence I divided 1064/154506, resulting in 00688 equity loss per decision (not per position).

Page 17: Higher stack penalty offsets and relative distributional features require less adjustment pips, hence, with my definition of effort, less effort. You are right that mental power is involved in the logical decision ("Do I need to apply a gap penalty?"), but my gut feeling is that this takes less time than actually carrying out the addition. During my investigation I became familiar with several sets of stack penalty offsets (Keith count uses 1, 1, and 3, my method uses 2, 2, and 3). At some point you just see the stack penalty offsets as a geometrical shape kind of hiding the irrelevant checkers on board. But as I wrote above, measuring the effort is certainly a little bit subjective. The key point to understand is that I judged it for every position and did not solely look at the method.

Page 19: I am sorry for not having given Jean-Luc his due credit. In fact I knew his article, but deemed his method for way too complicated for use over the board and hence forgot about it. I reread it now. Jean-Luc does his work for positions with all checkers on points 0 to 6, which is quite limiting in my humble opinion. Second, as you wrote, his method involves many more calculations. However, if we assume his method ALWAYS results in being off the real EPC by at most 0.82, then, in combination with Trice's doubling criterion (more on this later), this would result in a total equity loss of around 680, indeed much better. I will if can easily incorporate his EPC approximation into my testing and, if so, will let you know about the outcome. The question still remains whether I would be willing to do the maths over the board and what to do if you are still bearing in.

Regarding getting a feel for EPC adjustments: Maybe you are right, but I wanted an easy algorithmic solution for the problem.

Regarding Walter's 49/6 with -3: You are right that this is meant for pips-vs-rolls positions, but it was the only doubling criterion for EPCs I could find, hence I (ab)used it as a general criterion. Is there anything out there that can be used for the full range of race cubes?

Page 22: Memorizing a look-up table for the pip value depending on the race length is certainly possible, but I wanted to avoid it for the sake of simplicity.

I did try my EPC approximation with the Kleinman metric. Total equity loss: 4803. Using exact EPCs with Kleinman results in a total equity loss of 4122.

Page 23: You are right that the doubling window moves depending on race lengths. However, I am not aware of any algorithmic solution for this inherent limitation that I would be willing to do over the board.

Thanks again and best regards


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