Zenfighter: Spring already? TOB, March

[Zenfighter]

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

[bfbagain]

and comment on the practical issue of ace side counts for SD.

But first, some kudos. Once upon a time higher mathematics was not only a calling, but a love for me. Life however, has many twists and turns, and so you can only devote so much time to the issues that provide one to making a living, and higher math skills and it's subsequent interest had waned and deteriorated over the years. However, that being said, I never question the math, and like many I'm sure, are deeply indebted to those like you Z, and DonS, and Cacarulo, et al for doing all the "heavy lifting" in the field of BJ Math. It saves me time and I appreciate it, and if someone makes an error, there are those in the community who will take the time to double check it and all of us benefit from it.

Again, thanks to all who's love and committment to this higher calling enrich us all

Now, to the practical side.

Or, can a single deck player survive without the necessity of the added extra work?

Yes and no. Yes, if insurance and 11 vs 10 double downs after the first round dealt isn't an issue to the player. No, if the player is able to employ a greater than 1-2 spread and the above is important.

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.

When I first learned Omega II, (as I have a somewhat obsessive nature), I spent hours and hours - literally months - perfecting this strategy, and that included 6 deck play. So the time spent side counting aces, for 6 decks as well as SD/DD, was just part of my program. We know today, that the ace side count, with the rare exception, has little to no value in a 6 deck game today. Unfortunately for me, (and fortunately as well) side counting aces in 6 deck games is rote. It takes really no effort to do it, even though the benefits are almost non-existent. Would I take the time to learn it today for multiple deck games? No, of course not.

Single deck, however, is a different animal, as to knowing whether the proper distibution of aces has been played or not is extremely valuable for not only betting, but for insurance, and the ever-present 11 vs. 10 double down.

Those are the main reasons that ace side counting for SD games (for me) are worth the price.

cheers
bfb

[Zenfighter]

I?d add only, that your choice of selecting Omega is a wise one. I once did a comparative study regarding EoR?s for different rules, only to watch with amazement how well American rules EoR ?s correlated with Omega tags. If you can handle the ?beast ?, more motives to be proud.

Nice reply, thanks.

Sincerely

Z