From http://www.bjmath.com (Archive copy)
Effect of Count on Dealer Probs.
From Stanford Wong's BJ21
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Posted by MathProf on 3 Oct 1998, 2:50 pm
In a thread below, I made a statement that the probability of the Dealer breaking would increase with moderate increases in the Count, although would eventually decrease. I had in mind comments that Griffin had made about Dealer breaking as a function of 10s density. Don disagreed with that, and SW added some clarifying comments in support of Don's position. So to further clarify the situation, I prepared some brief calculations. The tables below show final Dealer probabilities. The calculations are with exact methods. The first tables studies the effect of tens density. What I did here was to start with a single deck, and then add (or subtract) a 10 at each level to increase the proportion. The initial pack is a Single Deck minus 6 tens (for 46 cards) and the final pack is Single Deck + 20 tens, and contains 72 cards. Normal composition is noted with a *. As you can see from the table, the Bust probability increases until the density gets to the 42% level before starting to decrease, as Griffin had suggested.
% 10s Bust Under 17 18 19 20 21 BJ Sum
21.7 26.96 0.00 14.54 15.48 14.91 15.16 9.08 3.86 100.00
23.4 27.37 0.00 14.35 15.21 14.70 15.51 8.80 4.07 100.00
25.0 27.72 0.00 14.17 14.94 14.49 15.89 8.53 4.26 100.00
26.5 28.03 0.00 13.99 14.69 14.28 16.32 8.27 4.42 100.00
28.0 28.31 0.00 13.80 14.44 14.07 16.78 8.02 4.57 100.00
29.4 28.54 0.00 13.62 14.20 13.87 17.27 7.79 4.71 100.00
* 30.8 28.75 0.00 13.44 13.97 13.68 17.78 7.56 4.83 100.00
32.1 28.92 0.00 13.27 13.75 13.48 18.31 7.34 4.93 100.00
33.3 29.07 0.00 13.09 13.53 13.29 18.86 7.13 5.03 100.00
34.5 29.19 0.00 12.92 13.32 13.11 19.42 6.92 5.12 100.00
35.7 29.29 0.00 12.75 13.11 12.93 19.99 6.73 5.19 100.00
36.8 29.37 0.00 12.59 12.91 12.75 20.57 6.54 5.26 100.00
37.9 29.43 0.00 12.42 12.72 12.57 21.16 6.36 5.32 100.00
39.0 29.48 0.00 12.26 12.53 12.40 21.76 6.19 5.38 100.00
40.0 29.51 0.00 12.10 12.35 12.24 22.36 6.02 5.42 100.00
41.0 29.52 0.00 11.95 12.17 12.07 22.96 5.86 5.46 100.00
41.9 29.52 0.00 11.80 12.00 11.91 23.57 5.70 5.50 100.00
42.9 29.51 0.00 11.65 11.83 11.76 24.17 5.55 5.53 100.00
43.8 29.49 0.00 11.50 11.67 11.61 24.77 5.41 5.56 100.00
44.6 29.45 0.00 11.36 11.51 11.46 25.38 5.27 5.58 100.00
45.5 29.41 0.00 11.22 11.35 11.31 25.98 5.14 5.59 100.00
46.3 29.36 0.00 11.08 11.20 11.17 26.57 5.01 5.61 100.00
47.1 29.30 0.00 10.95 11.05 11.03 27.17 4.89 5.62 100.00
47.8 29.23 0.00 10.81 10.91 10.89 27.76 4.77 5.63 100.00
48.6 29.16 0.00 10.68 10.77 10.76 28.35 4.65 5.63 100.00
49.3 29.08 0.00 10.56 10.63 10.63 28.93 4.54 5.63 100.00
50.0 29.00 0.00 10.43 10.50 10.50 29.51 4.43 5.63 100.00
Then I went to study the effects of the HiLo Count. Here I started with a 10 deck Pack. At each level I added 4 10s and a Ace, and removed a low card. This produces a "typical" or representative pack with a prescribed HiLo True Count. That True Count is given in the first column of the table below. The table below shows that there is a different pattern for HiLo. The maximum value of dealer breaking is attained at approximately normal deck composition. In particular, Don and SW were correct (and yes, I was incorrect) in stating that there was less total dealer breaking in positive HiLo Shoes.
HiLo Bust Under 17 18 19 20 21 BJ Sum
-10.0 27.85 0.00 14.53 15.55 14.60 15.79 9.01 2.67 100.00
-9.0 28.00 0.00 14.40 15.40 14.50 15.98 8.87 2.85 100.00
-8.0 28.13 0.00 14.27 15.25 14.40 16.19 8.73 3.04 100.00
-7.0 28.24 0.00 14.14 15.11 14.29 16.40 8.58 3.23 100.00
-6.0 28.34 0.00 14.02 14.96 14.19 16.62 8.43 3.43 100.00
-5.0 28.43 0.00 13.90 14.82 14.08 16.86 8.28 3.63 100.00
-4.0 28.49 0.00 13.78 14.68 13.98 17.10 8.13 3.84 100.00
-3.0 28.54 0.00 13.67 14.54 13.87 17.35 7.97 4.06 100.00
-2.0 28.56 0.00 13.56 14.40 13.77 17.62 7.81 4.28 100.00
-1.0 28.57 0.00 13.45 14.27 13.66 17.90 7.65 4.51 100.00
0.0 28.56 0.00 13.34 14.13 13.56 18.18 7.48 4.74 100.00
1.0 28.53 0.00 13.23 14.00 13.46 18.48 7.32 4.98 100.00
2.0 28.48 0.00 13.13 13.87 13.36 18.79 7.15 5.23 100.00
3.0 28.41 0.00 13.03 13.74 13.25 19.11 6.98 5.48 100.00
4.0 28.31 0.00 12.93 13.62 13.16 19.45 6.80 5.74 100.00
5.0 28.19 0.00 12.83 13.50 13.06 19.79 6.63 6.00 100.00
6.0 28.05 0.00 12.73 13.38 12.96 20.15 6.45 6.27 100.00
7.0 27.89 0.00 12.64 13.26 12.87 20.52 6.28 6.55 100.00
8.0 27.70 0.00 12.55 13.15 12.77 20.90 6.10 6.83 100.00
9.0 27.49 0.00 12.46 13.04 12.68 21.29 5.92 7.12 100.00
10.0 27.25 0.00 12.37 12.93 12.60 21.70 5.74 7.41 100.00
PS: Both tables were done using S17.
I have one question to make.
4 tens and an Ace minus a low card in a ten pack simulation should give +0.6 True point count per level not +1.
Did I miss something here?
I would appreciate any feedback on this
Effect of Count on Dealer Probs.
From Stanford Wong's BJ21
--------------------------------------------------------------------------------
Posted by MathProf on 3 Oct 1998, 2:50 pm
In a thread below, I made a statement that the probability of the Dealer breaking would increase with moderate increases in the Count, although would eventually decrease. I had in mind comments that Griffin had made about Dealer breaking as a function of 10s density. Don disagreed with that, and SW added some clarifying comments in support of Don's position. So to further clarify the situation, I prepared some brief calculations. The tables below show final Dealer probabilities. The calculations are with exact methods. The first tables studies the effect of tens density. What I did here was to start with a single deck, and then add (or subtract) a 10 at each level to increase the proportion. The initial pack is a Single Deck minus 6 tens (for 46 cards) and the final pack is Single Deck + 20 tens, and contains 72 cards. Normal composition is noted with a *. As you can see from the table, the Bust probability increases until the density gets to the 42% level before starting to decrease, as Griffin had suggested.
% 10s Bust Under 17 18 19 20 21 BJ Sum
21.7 26.96 0.00 14.54 15.48 14.91 15.16 9.08 3.86 100.00
23.4 27.37 0.00 14.35 15.21 14.70 15.51 8.80 4.07 100.00
25.0 27.72 0.00 14.17 14.94 14.49 15.89 8.53 4.26 100.00
26.5 28.03 0.00 13.99 14.69 14.28 16.32 8.27 4.42 100.00
28.0 28.31 0.00 13.80 14.44 14.07 16.78 8.02 4.57 100.00
29.4 28.54 0.00 13.62 14.20 13.87 17.27 7.79 4.71 100.00
* 30.8 28.75 0.00 13.44 13.97 13.68 17.78 7.56 4.83 100.00
32.1 28.92 0.00 13.27 13.75 13.48 18.31 7.34 4.93 100.00
33.3 29.07 0.00 13.09 13.53 13.29 18.86 7.13 5.03 100.00
34.5 29.19 0.00 12.92 13.32 13.11 19.42 6.92 5.12 100.00
35.7 29.29 0.00 12.75 13.11 12.93 19.99 6.73 5.19 100.00
36.8 29.37 0.00 12.59 12.91 12.75 20.57 6.54 5.26 100.00
37.9 29.43 0.00 12.42 12.72 12.57 21.16 6.36 5.32 100.00
39.0 29.48 0.00 12.26 12.53 12.40 21.76 6.19 5.38 100.00
40.0 29.51 0.00 12.10 12.35 12.24 22.36 6.02 5.42 100.00
41.0 29.52 0.00 11.95 12.17 12.07 22.96 5.86 5.46 100.00
41.9 29.52 0.00 11.80 12.00 11.91 23.57 5.70 5.50 100.00
42.9 29.51 0.00 11.65 11.83 11.76 24.17 5.55 5.53 100.00
43.8 29.49 0.00 11.50 11.67 11.61 24.77 5.41 5.56 100.00
44.6 29.45 0.00 11.36 11.51 11.46 25.38 5.27 5.58 100.00
45.5 29.41 0.00 11.22 11.35 11.31 25.98 5.14 5.59 100.00
46.3 29.36 0.00 11.08 11.20 11.17 26.57 5.01 5.61 100.00
47.1 29.30 0.00 10.95 11.05 11.03 27.17 4.89 5.62 100.00
47.8 29.23 0.00 10.81 10.91 10.89 27.76 4.77 5.63 100.00
48.6 29.16 0.00 10.68 10.77 10.76 28.35 4.65 5.63 100.00
49.3 29.08 0.00 10.56 10.63 10.63 28.93 4.54 5.63 100.00
50.0 29.00 0.00 10.43 10.50 10.50 29.51 4.43 5.63 100.00
Then I went to study the effects of the HiLo Count. Here I started with a 10 deck Pack. At each level I added 4 10s and a Ace, and removed a low card. This produces a "typical" or representative pack with a prescribed HiLo True Count. That True Count is given in the first column of the table below. The table below shows that there is a different pattern for HiLo. The maximum value of dealer breaking is attained at approximately normal deck composition. In particular, Don and SW were correct (and yes, I was incorrect) in stating that there was less total dealer breaking in positive HiLo Shoes.
HiLo Bust Under 17 18 19 20 21 BJ Sum
-10.0 27.85 0.00 14.53 15.55 14.60 15.79 9.01 2.67 100.00
-9.0 28.00 0.00 14.40 15.40 14.50 15.98 8.87 2.85 100.00
-8.0 28.13 0.00 14.27 15.25 14.40 16.19 8.73 3.04 100.00
-7.0 28.24 0.00 14.14 15.11 14.29 16.40 8.58 3.23 100.00
-6.0 28.34 0.00 14.02 14.96 14.19 16.62 8.43 3.43 100.00
-5.0 28.43 0.00 13.90 14.82 14.08 16.86 8.28 3.63 100.00
-4.0 28.49 0.00 13.78 14.68 13.98 17.10 8.13 3.84 100.00
-3.0 28.54 0.00 13.67 14.54 13.87 17.35 7.97 4.06 100.00
-2.0 28.56 0.00 13.56 14.40 13.77 17.62 7.81 4.28 100.00
-1.0 28.57 0.00 13.45 14.27 13.66 17.90 7.65 4.51 100.00
0.0 28.56 0.00 13.34 14.13 13.56 18.18 7.48 4.74 100.00
1.0 28.53 0.00 13.23 14.00 13.46 18.48 7.32 4.98 100.00
2.0 28.48 0.00 13.13 13.87 13.36 18.79 7.15 5.23 100.00
3.0 28.41 0.00 13.03 13.74 13.25 19.11 6.98 5.48 100.00
4.0 28.31 0.00 12.93 13.62 13.16 19.45 6.80 5.74 100.00
5.0 28.19 0.00 12.83 13.50 13.06 19.79 6.63 6.00 100.00
6.0 28.05 0.00 12.73 13.38 12.96 20.15 6.45 6.27 100.00
7.0 27.89 0.00 12.64 13.26 12.87 20.52 6.28 6.55 100.00
8.0 27.70 0.00 12.55 13.15 12.77 20.90 6.10 6.83 100.00
9.0 27.49 0.00 12.46 13.04 12.68 21.29 5.92 7.12 100.00
10.0 27.25 0.00 12.37 12.93 12.60 21.70 5.74 7.41 100.00
PS: Both tables were done using S17.
I have one question to make.
4 tens and an Ace minus a low card in a ten pack simulation should give +0.6 True point count per level not +1.
Did I miss something here?
I would appreciate any feedback on this
