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Keith count doubling window

Posted By: Stein Kulseth
Date: Friday, 24 April 2009, at 12:25 p.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 initialÝ 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-
00.1300.1050.1070.102
10.1360.1130.1170.117
20.1250.1000.1070.107
30.0790.0690.0820.084
40.0170.0260.0480.056
5-0.035-0.0220.0130.028
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-
00.1120.0900.0900.085
10.1150.0930.0960.097
20.0970.0730.0810.081
30.0370.0330.0480.051
4-0.039-0.0210.0060.015
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
20.0900.0600.0420.040
30.2740.1930.1480.128
40.4620.3320.2500.205
50.6170.4840.3520.288
60.7690.6360.4900.381
70.9130.7930.5960.471
81.0330.9200.7250.562

CPWs:

diff 20-39 40-59 60-79 80-
00.8160.8150.8120.805
10.7830.7880.7910.791
20.7490.7650.7720.775
30.7090.7360.7500.756
40.6690.7060.7280.739
50.6360.6730.7060.722
60.6040.6410.6770.702
70.5750.6080.6540.683
80.5510.5810.6270.664

Number of positions in database:

diff 20-39 40-59 60-79 80-
01164847509229
11014839569252
21138823603263
31148900637310
41015910599336
51019908661388
6781891700433
7502885721444
8247849688481

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