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Revised 21 Ats Opening Roll Heuristic
Posted By: AdamStocks
Date: Saturday, 10 May 2014, at 4:44 a.m.
My previous attempt at a heuristic for an opening 21 roll ATS was messed up because I found out later that I had inadvertently used some wrong data. I've now revised it using the correct XG2.1 opening book figures. The new heuristic follows the same basic form but with tweaked constants. The result is a bit more 'slotty'  in line with the general feeling of the forum about my previous attempt (see: http://www.bgonline.org/forums/webbbs_config.pl?, but please bear in mind that it is bad due to the aforementioned cockup). The new version (choosing between splitting or slotting) is:
For a score of Aaway,Baway (works for both NonCrawford and Crawford scores);
If (EvenAaway,1away,PostCrawford) Or (0.7*A+3.5 is less than B) Then SPLIT Else SLOT
A less formal form which is slightly easier to remember is:
If (Opponent has a 'free drop score') Or (7A+35)/10 is less than B) Then SPLIT Else SLOT
Out of the 253 possible scores of a 15point match (225 NonCrawford and 28 Crawford), it is correct in 237 scores and wrong in 16 scores (most of which are at scores outside 9away,9away). The total error across all 253 scores is about 0.393% MWC, or about 0.0486 EMG. Average error is about (0.0486/253)= just under 0.0002 EMG for a randomly chosen score. As a comparison, the average error from a pure guess (tossing a coin to split or slot) is about 0.0064 EMG, which is incidentally almost exactly the same average error from either always splitting or always slotting.
Across the 16 incorrect results, the heuristic's average error is about 0.0030 EMG, but over half of that comes from 3 main exceptions:
1away,5away,Crawford) error 0.0094 EMG (incorrectly splitting) 1away,7away,Crawford) error 0.0081 EMG (incorrectly splitting) 1away,9away,Crawford) error 0.0085 EMG (incorrectly splitting)
Maximum error of any other incorrect result other than these three exceptions is about 0.0030 EMG,
Average error of any other incorrect result other than these three exceptions is about 0.001438 EMG
If anyone has a more accurate/more practical 21 Opener heuristic, please let me know and I'll buy us both a stiff drink :)

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