Author: Ratko V Tomic
Date: 11:09:57 11/04/99
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> But IMHO there are two errors in your calculations that > compensate each other! Interesting and correct observation. After typing in the initial part of the message, I took a calculator to recheck the calculations from the input numbers as appearing on the screen and found I somehow had an extra factor of 4 for the optimized case (i.e. optimized case now needed 0.05 more bits than the unoptimizeded one, even though on a scratch paper where partial calculations were scattered, the encircled final result was 1.95 bits gain). So, looking at the screen, I somehow convinced myself, after the few seconds of glancing at the numbers, that I was missing a divisor 2!*2! from the NBP instead of the NR factor (where they were actually dropped). So I typed in /4 after all those numbers making up the NBP factor, retyped the divided results and now the final result agreed exactly with the one on paper, shortcircuiting thus any need for a final common-sense check. Thanks for pointing this problem out. (I could have lived the rest of my life with the wrong bishop placement divisor in my head :) > F = (N/2)^2 * (N/2-1)^2 / (N * (N-1) * (N-2) * (N-3) / 4) Yes, that (the "factorial effect") is the source of the main part of the correction. > Now: 3812256 / 984064 = 3.874 ==> 1.954 bits > > The correct calculation must keep into account pawns and therefore it is > necessary to follow your procedure, but the result is only a little different. It's interesting how little the pawn effect (+p) changes the result (reduces the gain): Gain (+p) = 1.9521 Gain (-p) = 1.9538 So the pawn effect gain reduction is 0.0017 bits, while the gain reduction due to the factorial effect alone is 0.05 bits (from the 2 bits), i.e. the pawn effect reduces the gain by only about 3.4% of the factorial effect (which itself was only 2.5% gain reduction of the 2 bits bishop gain, which in turn were only 1.5% reduction of the initial 134 bit code size). Oddly, for me it was the pawn effect which made your initial 2 bit bishop gain suggestion look overly optimistic.
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