A side count of aces for the Hi Opt I.

We will work all this thoroughly, with the aid of our new EoR?s tables from BJA3 Appendix D.
We?ll assume here the following rules: s17, das, spl3 and spa1.

Average absolute effect of the Hi Opt I monitored cards: 3,4,5,6 and Ts

Looking at Table D17 (betting correlations) for the above-mentioned rules we have:

Avg. eff. = (.4339 + .5680 + .7274 + .4118 + (4 * .5121))/ 8

Avg. eff. = 0.5237

Enter Griffin: just a bit less than that of the ace, [. 5794] the most important uncounted cards. It therefore seems reasonable to regard an excess ace in the deck as meriting a temporary readjusting of the running count (for betting purposes only) by plus one point

With roughly calculations we can make a quick inference:

(.5794/.5237)* 100 ? 100 = 10.64% more for the ace than the average effect we got above. That is:

Adjusted index (Ai) = -1.1064 approximately.

Striving for accuracy with the aid of Griffin.

Ai = [(13* Ei * Sum Ci^2)/(12 * I) where

Ei = EoR for the ace

Ci = tag values for the Hi Opt I

I = inner product (tag values times EoR?s)

So we have then:

Ei = -0.5794

Sum Ci = 1^2 + 1^2 + 1^2 + 1^2 + 4 * [(-1) ^2] = 8

I = 1* .4339 + 1*. 5680 + 1* .7274 + 1* .4118 + 4 * (-1) * (-.5121) = 4.1895

Finally plugging all the figures inside we get:

Ai = (13 *(-.5794) * 8) /(12 * 4.1895) and solving we get:

Ai = -1.1986 as the correct adjusted index, so

Ai = -1.2


Adjusting our running count with the side count of Aces. Theory.

1) Find the excess or deficiency of Aces at the selected card level. E.g. ? deck remains
and you have seen two aces gone, thus your pack is one Ace deficient.

2) For each card deficient that our pack has we add the value of Ai to the RC.

3) For each card in excess that our pack has we subtract the value of Ai from the RC.

4) Finally we divide by the number of decks remaining to find the TC and place our bet.


An example

26 cards already gone, RC = 2 and 3 Aces played.

Here the pack is one Ace poor, therefore our Ai = -1.2

RC = 2 - 1.2 = 0.8 and our

TC = 0.8 / (1/2) = 1.6

Lets say you?re spreading $25 to $100 with TC 1 = $50, TC2= $75 and TC=>3 $100

How much you would bet here? Answer: $50 ($200 for a black chip player)

Same example with the traditional Ai = -1

RC = 2-1 = 1

TC = 1/(1/2) = 2

How much you bet here? Answer $ 75 ($300 for a black chip player)

One form of avoiding the worries here, is to think, that using the traditional index (-1), the times the player is over betting any given TC will compensate those times he is under betting it, and so, in the long run the expectation will remain the same. Go ahead and do what you want, but side counting aces is not for everybody, or at least not everybody can do it exactly as it is.


Side count adjusted indices for different ace-neutralized counts 

 

 

System	       Adj.index	Rounded	     Common 

 

						 

Hi Opt I	-1.1986		-1.2		-1 

						 

Gordon		-1.2075		-1.2		-1 

						 

Hi Opt II	-2.1859		-2.2		-2 

						 

Omega		-2.2873		-2.3		-2 

						 

UAPC		-3.2740		-3.3		-3



To be continued. :-)

Zenfighter