Let us examine the math of a simple 7 side count
psyduck said:
tthree,
I simulated the effect of surplus 7 using BS and flat betting for the 6deck shoe game I play. The change in advantage when surplus of 7 = 1/deck is shown below. You can see, 15 and 16 vs dealer's 7 and 8 are not the biggest sufferers. Other hands that suffer more than 4% advantage loss are included.
Sure one needs to consider the frequency of each hand. I wonder if you are aiming at the wrong hands using the information of 7s (or your block of cards). Anyway, something for you to think about.
Change in advantage when surplus of 7 = 1/deck (using BS):
Code:
hand change in advantage(%) hand frequency(%)
15 vs 7 -1.3 0.7
15 vs 8 -1.1 0.5
16 vs 7 -1.1 0.6
16 vs 8 -1.1 0.5
10 vs 4 -4.4 0.3
A3 vs 5 -4.0 0.09
A3 vs 6 -4.1 0.09
A4 vs 4 -4.6 0.08
A5 vs 4 -4.4 0.09
A7 vs 4 -5.0 0.1
22 vs 4 -4.2 0.04
66 vs 3 -5.1 0.04
66 vs 4 -4.9 0.04
77 vs 2 -4.3 0.07
77 vs 4 -5.9 0.07
88 vs 3 -4.3 0.04
88 vs 4 -6.7 0.04
99 vs 3 -4.6 0.04
99 vs 4 -5.6 0.04
Interesting topic for me.
The frequencies are off here. Psyduck used 2 card hand frequencies for his first group. The actual frequencies are all .96 and the split frequencies are all .043. The doubling frequencies are a more complicated issue so we will just use these as I have no reason to doubt they are correct.
The overall change in advantage = .96*(-1.3 + 3*(-1.1)) + .3*(-4.4) + .09*(-4 + -4.1 + -4.4) + .08*(-4.6) + .1*(-5) + .043*(-4.2 + -5.1 + -4.9 + -4.3 + -5.9 + -4.3 + -6.7 + -4.6 + -5.6) = .96*(-4.6) - 1.32 - 1.125 - .368 - .5 - 1.9608 = -4.416 - 5.2738 = -9.6898%% = -.096898%
So a side count of sevens increases the players advantage by about .1% for flat betting. The player probably has a 1 to 1.5% advantage using basic counting and his betting ramp. Your percent increase in advantage is about .1/1 = 10% for the low end. And your advantage is increased by .1/1.5 = 6.7% for the high end. So side counting sevens increases your advantage over the casino by 6.7% to 10% of your original advantage.
Now we consider that your optimal bet is determined by your advantage at each true count so you would bet slightly more with a slightly larger advantage. Since Psyduck plays HILO I assumed the .1% increase in advantage he showed was for HILO. I used HILO sweet 16 and fab 4, H17,DAS,Sr,RSA, 6 deck cut off 1 deck. The spread was practical optimal bets, play all, spread 1 to 12.
-NO SIDE COUNT HILO COUNT---HILO WITH SEVEN SIDE COUNT
TC freq advan opbet netproduct|advan opbet netproduct
<-1 .4516 -1.54% 10= -6.95464 | -1.44% 10 = -6.50304
00 .2599 -0.22% 10 = -0.57178 | -0.12% 10 = -0.31188
+1 .1075 +0.42% 25 = 1.12875 | +0.52% 30 = 1.67700
+2 .0749 +1.02% 60 = 4.58388 | +1.12% 65 = 5.4527
+3 .0363 +1.60% 90 = 5.22720 | +1.70% 95 = 5.8625
+4 .0283 +2.28% 120= 7.74228 | +2.38% 120= 8.08248
+5 .0136 +2.84% 120= 4.63448 | +2.94% 120= 4.79808
+6 .0113 +3.46% 120= 4.69176 | +3.56% 120= 4.82736
+7 .0053 +3.99% 120= 2.53764 | +4.09% 120= 2.60124
+8 .0046 +4.54% 120= 2.50608 | +4.64% 120= 2.56128
+9 .0022 +5.05% 120= 1.33320 | +5.15% 120= 1.35960
10 .0018 +5.51% 120= 1.19016 | +5.61% 120= 1.21176
11 .0009 +5.72% 120= 0.61776 | +5.82% 120= 0.62856
12 .0007 +6.37% 120= 0.53508 | +6.47% 120= 0.54348
13 .0004 +6.66% 120= 0.31968 | +6.76% 120= 0.32448
14 .0003 +7.34% 120= 0.26424 | +7.44% 120= 0.26784
15 .0002 +7.34% 120= 0.17616 | +7.44% 120= 0.17856
16 .0001 +8.20% 120= 0.09840 | +8.30% 120= 0.09960
The total for no side count = 30.06033
The total for 7 side counted = 33.6616
The improvement is 33.6616/30.06033 = 1.11980141
THAT IS A 12% IMPROVEMENT OF PROFIT for a side count of sevens with HILO for a 6 deck shoe with 83% penetration. This is a mathematical approximation. The side count will affect different bets more often than others due to the index numbers used for each hand match up. It should be close though.