Backgammon Theory

Theory

Inconsistencies in how EMG equity is calculated

From:   Jeremy Bagai
Date:   26 November 2007
Subject:   Paper on EMG inconsistencies
Forum:   GammOnLine

http://www.fortuitouspress.com/emg.html I've written a paper that explores what I consider to be a troubling inconsistency within EMG (Equivalent to Money Game) numbers. Here's the basic idea: A. 3-away is doubled to 2 by 2-away. B. 3-away is doubled to 4 by 3-away. C. 3-away is doubled to 8 by 5-away. In each case 3-away must choose between taking for the match or passing and trailing 3-away 1-away for 25% MWC. Suppose in each case she makes a bad take with only 20% CPW, giving up 5% MWC. That 5% error gets transformed into very different EMG errors at the different scores: Case A: Case B: Case C: MWC and EMG lost 3-away, 2-away 3-away, 3-away 3-away, 5-away by taking Position 1: Doubled to 2 Doubled to 4 Doubled to 8 --------------- --------------- --------------- MWC EMG MWC EMG MWC EMG ------ ------ ------ ------ ------ ------ Snowie 4.5 -5.26% -.425 -5.26% -.212 -5.26% -.141 gnubg 0.14 -5.10% -.407 -5.10% -.203 -5.10% -.136 I find it distressing that the same error (taking a 20% CPW for the match rather than passing to 3-away 1-away) is sometimes reported as a .425 error and sometimes reported as a .141 error. I am having a crisis of faith wondering if our "whoppers" and "double whoppers" mean anything at all. The paper goes over this in detail, considers the history of the EMG transformation, and considers some possible alternatives. I don't have a solution, so the paper feels unfinished and unsatisfactory. I'd love your thoughts and comments. (Note that while case A involves an automatic redouble, neither case B nor case C does and they have different EMG errors, so the effect is not based on automatic double weirdness.) Thanks, Jeremy

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