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BGonline.org Forums
Keith count doubling window
Posted By: Stein Kulseth
Date: Friday, 24 April 2009, at 11:25 a.m.
I have been looking at the Keith count (http://www.bkgm.com/articles/CubeHandlingInRaces/) and have been surprised by the quite narrow doubling window described. After doing the counts as specified, a difference of 4 indicates an initial double/take, diffs of 3 and 2 ar RD/T and diffs of 1 or less are drops. This does not seem to fit with conventional wisdom that the CPW corresponding to the D/T - RD/T - RD/D points are about 69% - 71% - 78%, and that each pip should be worth around 2%.
I did a little study on the excerpt of Tom's database that he has provided for download, and computed the gains on doubling / taking as a function both of the Keith count difference, and the range of the race length - as measured by the Keith count of the on-roll position.
At least for this database it seems that for short races (< 60 pips) the indicated doubling strategy holds, but each pip seems to be worth more (about 3%). For longer races (> 60 pips) it seems that you can venture an initialø double with a Keith count difference of 5, and a redouble on 4, and here the pip worth is closer to 2%.
Also, note that the DB is dominated by short races so that the overall numbers for the DB as a whole resembles those for short races.
Data for the numerically inclined, ranges indicate the Keith count of the doubler, diff indicates the difference to the opponent's Keith count:
Initial doubling gains:
diff 20-39 40-59 60-79 80- 0 0.130 0.105 0.107 0.102 1 0.136 0.113 0.117 0.117 2 0.125 0.100 0.107 0.107 3 0.079 0.069 0.082 0.084 4 0.017 0.026 0.048 0.056 5 -0.035 -0.022 0.013 0.028 6 -0.091 -0.073 -0.034 -0.001 7 -0.145 -0.125 -0.068 -0.029 8 -0.187 -0.169 -0.111 -0.058 Redoubling gains:
diff 20-39 40-59 60-79 80- 0 0.112 0.090 0.090 0.085 1 0.115 0.093 0.096 0.097 2 0.097 0.073 0.081 0.081 3 0.037 0.033 0.048 0.051 4 -0.039 -0.021 0.006 0.015 5 -0.105 -0.084 -0.038 -0.022 6 -0.178 -0.151 -0.100 -0.061 7 -0.246 -0.220 -0.146 -0.101 8 -0.302 -0.279 -0.204 -0.142 Taking gains:
diff 20-39 40-59 60-79 80- 0 -0.204 -0.168 -0.145 -0.102 1 -0.061 -0.048 -0.044 -0.036 2 0.090 0.060 0.042 0.040 3 0.274 0.193 0.148 0.128 4 0.462 0.332 0.250 0.205 5 0.617 0.484 0.352 0.288 6 0.769 0.636 0.490 0.381 7 0.913 0.793 0.596 0.471 8 1.033 0.920 0.725 0.562 CPWs:
diff 20-39 40-59 60-79 80- 0 0.816 0.815 0.812 0.805 1 0.783 0.788 0.791 0.791 2 0.749 0.765 0.772 0.775 3 0.709 0.736 0.750 0.756 4 0.669 0.706 0.728 0.739 5 0.636 0.673 0.706 0.722 6 0.604 0.641 0.677 0.702 7 0.575 0.608 0.654 0.683 8 0.551 0.581 0.627 0.664 Number of positions in database:
diff 20-39 40-59 60-79 80- 0 1164 847 509 229 1 1014 839 569 252 2 1138 823 603 263 3 1148 900 637 310 4 1015 910 599 336 5 1019 908 661 388 6 781 891 700 433 7 502 885 721 444 8 247 849 688 481
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