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BGonline.org Forums
Have you noticed this before?
Posted By: Chris Yep In Response To: Have you noticed this before? (Alireza Saatchi)
Date: Tuesday, 8 March 2016, at 1:33 p.m.
I commend you on discovering your own simplifying formulas for backgammon.
Here's a comparison of your O/(P+O) approximation to the Kazaross XG2 MET:
O/(P+O) approximation 1 2 3 4 5 1 50.00% 66.67% 75.00% 80.00% 83.33% 2 33.33% 50.00% 60.00% 66.67% 71.43% 3 25.00% 40.00% 50.00% 57.14% 62.50% 4 20.00% 33.33% 42.86% 50.00% 55.56% 5 16.67% 28.57% 37.50% 44.44% 50.00% Kazaross XG2 MET 1C 2 3 4 5 1C 50.00% 67.74% 75.08% 81.44% 84.18% 2 32.26% 50.00% 59.95% 66.87% 74.36% 3 24.92% 40.05% 50.00% 57.15% 64.79% 4 18.56% 33.13% 42.85% 50.00% 57.73% 5 15.82% 25.64% 35.21% 42.27% 50.00% Difference (Kazaross XG2 MET – O/(P+O)) 1 2 3 4 5 1 0.00% 1.07% 0.08% 1.44% 0.85% 2 -1.07% 0.00% -0.05% 0.20% 2.93% 3 -0.08% 0.05% 0.00% 0.01% 2.29% 4 -1.44% -0.20% -0.01% 0.00% 2.17% 5 -0.85% -2.93% -2.29% -2.17% 0.00% Looking at the above tables, my recommendation is that if you're going to use the O/(P+O) approximation, only use it for scores less than or equal to 4-away/4-away (and don't use it at all for 1-away scores). In my opinion, the errors are too large for 5-away/2-away (2-away/5-away), 5-away/3-away (3-away/5-away), and 5-away/4-away (4-away/5-away).
So, my recommendation is to just use your approximation for 4a/2a, 4a/3a, and 3a/2a. (Of course your approximation also works for 4a/4a, 3a/3a, and 2a/2a, though you don't need an approximation for those scores.)
If you're not already familiar with them, I also suggest looking at Rick Janowski's MET approximation formulas and "Neil's Numbers" (invented by Neil Kazaross). You can find these MET approximations by searching this forum or looking through bkgm.com. These shortcuts (plus your O/(P+O) approximation) may save you some time over the board.
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