Roll Variance in the Bearoff - Part 2

by Douglas Zare
8 October 2014


Douglas Zare

In Part 1, we found that roll variance is a useful addition to the effective pip count for analyzing backgammon races. For a particular position on roll, a linear function of the combination of epc and roll variance could be used to estimate close take/pass decisions with a standard error of 0.022 EMG, compared with typical errors of 0.057 for linear functions of the effective pip count alone.

Each extra pip was worth about 0.127, while each extra unit of roll variance costs 0.317, or about 2.5 pips. What happens if you vary the position of the roller?

Let's do the same analysis for other positions with about the same effective pip count of 52, but different roll variances for the leader.






Position A2: Red's roll variance is 0.542.






Position B2: Red's roll variance is 0.814.






Position C2: Red's roll variance is 1.255.


These positions have epcs of 51.984. 51.943, and 51.952, respectively. These are within a twentieth of a pip, so if you just go by the epcs, you might expect the equities after Double/Take to be extremely close. Because the roll variances differ greatly, the equities in EMG are 1.025, 0.967, and 0.870, respectively, when White takes.

The best linear fit for the equity of Double/Take in position A2 for positions with epcs between 54 and 58 is -5.978 + 0.132 epc - 0.378 rv. In other words, a position with an effective pip count of 56 with a roll variance of 1 would have an equity estimated at 1.054. Each extra pip for the taker is worth 0.132, and each unit of roll variance is worth 2.857 pips.
 
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Article text Copyright © 1999-2018 Douglas Zare and GammonVillage Inc.

 
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