Playing Efficiency

Normally this is a linear estimate (not realistic for small subsets of cards) of the ratio of profit by using a card counting system, to the total profit one could gain over basic strategy, if one could track every card and perfectly determine the change in outcome. For us, mere mortals who use a single parameter card counting system to locate favourable opportunities, so as to bet extra units and deviate also from basic strategy if we presume a gain of any sort, a certain portion of the "cake" is the maximum we can strive for, while using it.

Optimal systems for variations of strategy

{TOB}:A noteworthy observation is that, if the ace is to be counted zero, improvement in the second decimal cannot be achieved beyond level three.

So for all practical purposes his third raw of the table (TOB, page 46) is the champion, for maximum efficiency with a single parameter count.

A 2 3 4 5 6 7 8 9 T Efficiency

0 1 2 2 3 2 2 1 -1 -3 0.690

Ken (Kenneth S. Uston) quickly picked-up the count and with the aid of his friend Stanley Roberts (Gambling Times Incorporated) his book MDBJ went

to the presses in the year 1981. The famous UAPC went public. A "Rolls-Royce" for strategic departures. Dynamite for hand-held games!

Curiously, when striving for maximizing overall strategic efficiency, the ace is not to be neutralized. TOB absolute single parameter champion is this one:

A 2 3 4 5 6 7 8 9 T Efficiency

51 60 85 125 169 122 117 43 -52 -180 0.703

If we divide by 200 we get:

Table 1

A 2 3 4 5 6 7 8 9 T

0.255 0.300 0.425 0.625 0.845 0.610 0.585 0.215 -0.260 -0.900

A sort of EoR`s table, isn`tit? Believe it or not, researchers and publishers have used this one to evaluate the playing correlations of their own systems.

Learning by example: The Uston Advanced Count

A short formula and a pocket calculator enough to extract playing correlation and efficiencies for your selected point count.

1) Find first the correlation coefficient for the above playing EoR`s that correspond to your counting system. E.g. UAPC

Corr = (inner product)/ (sqr (ss eors * ss point tags))

Inner product = (1 * .300) + (2 *.425) + (2 *.625) + (3 *.845) + (2 *.610) + (2 * .585) + (1 * .215) + (-1 * -.260) + (4 * -3 *-.900) = 18.600

EoR`s sum of squares = 5.50845

Tags sum of squares = 64

Solving

cc = 18.600/ (sqr (5.50845 * 64)) = 18.600/18.7761 = .9906

UAPC playing correlation = .9906

In other words almost as good as the reference from above.

Another question is the efficiency as outlined in the first paragraph of the article. So despite the fact that efficiency tends to increase as a function of the deck being depleted (penetration), its approximation to the cc only occurs as a limit.

Playing efficiency formula:

PE = (1.405 -(1-cc)) * (cc/2)

UAPC tested:

PE = (1.405 -(1 -.9906))*(.9906/2) = .691

UAPC Playing efficiency = .691

Don`t be timid and find the PC and PE from the Hi-Lo count for yourself!

For the selected playing counts from BJA3, Table D18, page 522, we get the following PE results with the same procedure outlined above:

Hi-Lo Hi-Opt I RPC AOII Halves

0.511 0.609 0.554 0.671 0.565

Carlson`s Omega emerges as a winner here? No surprise at all. Just put the AOII tags, ace through ten (0, 1, 1, 2, 2, 2, 1, 0-1,-2) below Table I,

and the reason for it will appear in front of your eyes.

Can we put some competition to UAPC with another three-level count?

Approximating the EoR`s from Table I, we can build three groups here.

1) Aces, deuces, threes, eights and nines

2) Fours, sixes and sevens

3) Fives and tens

So putting equivalent tags below we get

1, 1, 1, 2, 3, 2, 2, 1,-1,-3

A heretic three-level count (aces = + 1, huh!) but with the following numbers:

PC = .997

PE = .699

Make no mistakes here. Once any betting spread is involved this count won`t beat UAPC with a side count of aces.

The reason for this is its meagre betting correlation.

Betting correlation = .8393 Our dreams reduced to ashes!

While the saying,There is Nothing New Under the Sun, seems to be often the case, it doesn`t hurt to look at old things with new eyes, anyway.

Finally, let`s check both playing correlations.

IL18 multi-deck playing correlations

Heretic UAPC

16 v T 0.706246 * 0.704785

16 v 9 0.498523 0.503510 *

15 v T 0.900817 * 0.892171

13 v 3 0.943059 * 0.924748

13 v 2 0.933367 * 0.912163

12 v 6 0.876600 * 0.843130

12 v 5 0.902709 0.904753 *

12 v 4 0.909761 0.912085 *

12 v 3 0.895447 * 0.878108

12 v 2 0.827060 * 0.807781

11 v A 0.980394 * 0.968034

10 v A 0.908509 0.949819 *

10 v T 0.741422 0.813861 *

9 v 7 0.785766 0.825422 *

9 v 2 0.896061 0.905951 *

T,T v 6 0.855622 0.897604 *

T,T v 5 0.849197 0.900497 *

Insurance 0.915811 * 0.901388

A tough fight among both, with UAPC leading the double downs and the splits, but Don`s multi-deck Super-Illustrious are: Insurance, 16 v T, 15 v T

and 12 v 3, plays for what the first count shows some superiority.

After watching delighted Norm`s new site (with beautiful colours, yes), the card-eater fantasy is crossing my mind, but instead of having seated at the table our garden-variety Hi-Lo`s counter, with one of the above two guys. They could "handle" our hand, too. A pristine colour-fantasy, but for High-Stakes and rich card counters, I am afraid. These guys look expensive, damn! :-)

Zf

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