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Last one, I promise -- 2-away calc.

Posted By: Chuck Bower
Date: Sunday, 30 December 2012, at 4:40 p.m.

In Response To: Introducing Jason's Rule of 2/3 =) (Jason Lee)

Prompted by Neil's and Jason's 2-tier method, I'm going a step further to a 3-tier. (Side note: all of human quantitative backgammon comes down to a combination of memorization and calculation. These are good examples of attempting to optimize the two parts. I.e. a little more weight on the memorization makes the calculation much easier.) This time I'll go an extra decimal place but you can simplify that easily by dropping the last -- still works.

Both Neil and Jason have simple multiplication (and/or division) substeps. I'm mimicking them with divide by 2 (or a power of 2) as the main substep(s), and tossing in the subtraction of a constant as the second substep.

6-away, 2-away 20.06% (from memory)

7-away, 2-away 15.77% (from memory)

8-away, 2-away 12.46% (from memory)

9-away, 2-away 20.06 / 2 = 10.03. Subtract 0.2 --> 9.83 (actual 9.80)

10-away, 2-away 15.77 / 2 = 7.88. Subtract 0.2 --> 7.68 (actual 7.70)

11-away, 2-away 12.46 / 2 = 6.23. Subtract 0.2 --> 6.03 (actual 6.07)

12-away, 2-away 20.06 / 4 (or / 2 twice) = 5.02. Subtract 0.2 --> 4.82 (actual 4.75)

13-away, 2-away 15.77 / 4 = 3.94. Subtract 0.2 --> 3.74 (actual 3.75)

14-away, 2-away 12.46 / 4 = 3.12. Subtract 0.2 --> 2.92 (actual 2.93)

15-away, 2-away 20.06 / 8 = 2.51. Subtract 0.2 --> 2.31 (actual 2.31)

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