References
Exploiting the Spectrum - Single Parameter Card Counting Systems. Chapter 4. TOB
Griffin's formula to balance BC and PE strength.
If K units are bet on all decks diagnosed as favorable and one unit is bet otherwise, the average improvement due to card counting is approximately
[8(K - 1)*BC + 5(K + 1)*PE] /1000 units per hand.
Given that the typical spread in a single deck is a 1 to 4 one, we see clearly that:
24(BC) ~ 25(PE)
in agreement with his statement that the two efficiencies are almost equally important
Let's imagine the following hypothetical scenario:
At single deck games, if you keep your spread to a minimum, that's a 1 to 2 one, they will let you play forever. More than that and you'll be banned from further play. With these limitations, what shall you do?
Let's look again at Griffin's formula, for K=2, this time.
8(BC)<>15(PE)
therefore under these circumstances, the best we can do, seems to be, to pick up a system with a high playing efficiency. For example we can look at those listed on page 46.
The respective champions of their categories are listed there. So let's elaborate the table a little bit
and use his formula also, to obtain the figures from the last row.
OPTIMAL SYSTEMS FOR VARIATION OF STRATEGY
Tags BC PE Units per hand
000111100-1 .8416749 .6364524 0.016280
w/aces .9174248 .6364524 0.016886
01122210-1-2 .9170488 .6714408 0.017408
w/aces .9887936 .6714408 0.017982
01223221-1-3 .9038347 .6912677 0.017600
w/aces .9772912 .6912677 0.018187
01234331-1-4 .9001801 .6932113 0.017600
w/aces .9738382 .6932113 0.018189
02245431-1-5 .908388 .6912826 0.017636
w/aces .9816451 .6912826 0.018222
0 67 93 132 177 131 122 46 -48 -180 .9071413 .6947588 0.017679
41 60 85 125 169 122 117 43 -52 -180 .8577432 .7025000 0.017399
Here the statements:
improvement in the second decimal cannot achieved beyond level three. and
Also bigger is not necessarily better ;or at least not much better, can be derived from the above tables by the keen observer.
The last "point counts" are of academically interest only, and despite the fact of the maximization of the strategic efficiency, their final gains are disappointing.
So our practical counter has two realistic options:
Omega or UAPC? A personal choice. I can't help you here.
With a side count of aces or without it? This is a good question.
Side count tips
1) For each ace deficient we shall add the value of the ace to the RC before dividing by the number of decks (half decks, quarters, etc) remaining, to get the TC for betting purposes.
2) For each ace in excess we subtract the value of the ace from the RC and same as above.
Example: Omega counter
RC = 4 three aces already gone with 26 cards remaining. TC=?
TC = (4 - 2)/(1/2) = 4 without the aces side count the TC = 8!
What a danger if you don't side count! But here, being restricted to a 1 to 2 spread doesn't look like bad news, after all. See what I mean?
3) Side count adjustment index for the first three counts of the main table.
Common use Combinatorial
Level 1 1 1.3 (1.31509)
Omega 2 2.4 (2.414)
UAPC 3 3.5 (3.46383)
Here the more "sophisticated? Omega player will compute the following:
TC = (4 - 2.4)/(1/2) = 3.2 while looking at the conventional side counter with an air of superiority, for his "amateurish" evaluation of the real TC.
Peter again:
Blackjack gurus seem unanimous in the opinion that the ace should be valued as zero since it behaves like a small card for strategic variations.....
For the same reason we can conclude that the BJ gurus are encouraging the average counter to side count aces as a complimentary present, which is far from being an easy stuff when the main goal is playing accurately. I'll be mistaken naturally.
Or, can a single deck player survive without the necessity of the added extra work?
A good question again. Experienced single deck players may know the correct answer. Being a shoe player myself, I won't venture here any further.
To be continued..... TOB, I mean.
Spring is coming. Definitely good news!
Sincerely
Z
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