Workshop Archive
Posted By: MathProf <MathProf21@aol.com>
Date: Sunday, 12 March 2000, at 7:13 a.m.
Here is some data on the cut card effect at various penetrations. These are from sims of a single deck game, heads-on, with a generic Basic Strategy. The table below shows the average HiLo true count a player sees as a function of the shuffle point.
CC = 13 Ave TC = -0.249 SE = 0.00176 AR = 7.43 Min = 3 Max = 9
CC = 14 Ave TC = -0.241 SE = 0.00171 AR = 7.24 Min = 5 Max = 9
CC = 15 Ave TC = -0.223 SE = 0.00166 AR = 7.07 Min = 3 Max = 9
CC = 16 Ave TC = -0.214 SE = 0.00160 AR = 6.90 Min = 3 Max = 9
CC = 17 Ave TC = -0.227 SE = 0.00155 AR = 6.73 Min = 4 Max = 9
CC = 18 Ave TC = -0.247 SE = 0.00150 AR = 6.54 Min = 2 Max = 8
CC = 19 Ave TC = -0.250 SE = 0.00146 AR = 6.35 Min = 2 Max = 8
CC = 20 Ave TC = -0.230 SE = 0.00142 AR = 6.16 Min = 4 Max = 8
CC = 21 Ave TC = -0.207 SE = 0.00137 AR = 5.99 Min = 3 Max = 8
CC = 22 Ave TC = -0.208 SE = 0.00133 AR = 5.83 Min = 3 Max = 7
CC = 23 Ave TC = -0.234 SE = 0.00128 AR = 5.65 Min = 3 Max = 7
CC = 24 Ave TC = -0.255 SE = 0.00124 AR = 5.46 Min = 3 Max = 7
CC = 25 Ave TC = -0.243 SE = 0.00121 AR = 5.26 Min = 1 Max = 7
CC = 26 Ave TC = -0.208 SE = 0.00118 AR = 5.08 Min = 3 Max = 7
CC = 27 Ave TC = -0.188 SE = 0.00113 AR = 4.93 Min = 2 Max = 7
CC = 28 Ave TC = -0.210 SE = 0.00109 AR = 4.76 Min = 2 Max = 6
CC = 29 Ave TC = -0.252 SE = 0.00105 AR = 4.57 Min = 1 Max = 6
CC = 30 Ave TC = -0.264 SE = 0.00102 AR = 4.36 Min = 2 Max = 6
CC = 31 Ave TC = -0.223 SE = 0.00099 AR = 4.17 Min = 2 Max = 6
CC = 32 Ave TC = -0.172 SE = 0.00095 AR = 4.01 Min = 1 Max = 5
CC = 33 Ave TC = -0.171 SE = 0.00090 AR = 3.87 Min = 1 Max = 5
CC = 34 Ave TC = -0.228 SE = 0.00086 AR = 3.70 Min = 1 Max = 5
CC = 35 Ave TC = -0.282 SE = 0.00083 AR = 3.48 Min = 1 Max = 5
CC = 36 Ave TC = -0.262 SE = 0.00080 AR = 3.26 Min = 1 Max = 4
CC = 37 Ave TC = -0.173 SE = 0.00077 AR = 3.08 Min = 1 Max = 4
CC = 38 Ave TC = -0.117 SE = 0.00072 AR = 2.96 Min = 1 Max = 4
CC = 39 Ave TC = -0.162 SE = 0.00067 AR = 2.84 Min = 1 Max = 4
CC = 40 Ave TC = -0.272 SE = 0.00063 AR = 2.63 Min = 1 Max = 3
CC = 41 Ave TC = -0.321 SE = 0.00059 AR = 2.36 Min = 1 Max = 3
CC = 42 Ave TC = -0.214 SE = 0.00057 AR = 2.13 Min = 1 Max = 3
CC = 43 Ave TC = -0.066 SE = 0.00052 AR = 2.01 Min = 1 Max = 3
CC = 44 Ave TC = -0.052 SE = 0.00047 AR = 1.95 Min = 1 Max = 2
CC = 45 Ave TC = -0.169 SE = 0.00042 AR = 1.83 Min = 1 Max = 2
CC = 46 Ave TC = -0.365 SE = 0.00034 AR = 1.52 Min = 1 Max = 2
CC = 47 Ave TC = -0.325 SE = 0.00029 AR = 1.15 Min = 1 Max = 2CC is the position of the cut card. CC=13 means that 13 cards are behind it. More precisely, it means that I would begin another round only if 14 or more cards remain undealt. SE is the standard Error on the TC Mean. AR is the "average number of rounds". I also listed the minimum number of rounds and the maximum number of rounds. These are probably not very informative, because if we have one anomalous deck, it could change the min and max.
I have also tracked the data on each round for each of the sims above. Below is the data for the "CC=13" run.
******************** Summary ********************
For Num Decks = 1 Dealt to 13 Cards
Rnds Number AveTc SE
1.0 1345804.0 0.0000 0.00000
2.0 1345804.0 -0.0024* 0.00191
3.0 1345804.0 -0.0022* 0.00288
4.0 1345803.0 -0.0000* 0.00380
5.0 1345803.0 -0.0002* 0.00478
6.0 1345726.0 0.0007* 0.00594
7.0 1323461.0 -0.1360 0.00742
8.0 596495.0 -3.7280 0.01208
9.0 5300.0 -15.3643 0.12059
Min Rounds = 3 Max = 9 Ave = 7.43050Ave TC = -0.249 SE = 0.00176
Above finished at Sunday, March 12, 2000 at 00:38:17 Eastern Standard Time
Shuffle Point was 13
This tells you that on each first round, the average TC was -.0024. The Standard Error was .00191. That is,the mean is not statistically distinguishable from 0; I customarily place a * on all such answers. "Number" is the number of ceks on which such a round was observed.
In this game we see no cut card effect until the seventh round. There are fewer seventh rounds, and those that do occur are from slightly depleted decks. There are far fewer eight rounds, and of course they only come from negative decks. Occasionally we get a ninth round, and those are from very depleted decks.
I have table like this for all the runs I did; I will try to post that below as a response to this.