On computing Playing Efficiency ...

[ZenMaster_Flash]

The Playing Efficiency of a card counting system is the ratio of the gain produced by making playing decisions based on the count using that system to the maximum gain possible from knowledge of exactly what cards remain to be played and perfect use of this knowledge.
I do not know of any formula to compute the PE of a counting system.
No such formula appears in the books by Thorp, Schlesinger, Griffin, Snyder, Wong, Grosjean, etc.
I suppose that it is obtained by simulation, e.g. to get the PE for Hi-Lo.

A) A game is simulated in which playing decisions are made on basis of the Hi-Lo count,

B) then the game is simulated in which playing decisions are made on basis calculating
the gain or loss from hitting, standing, doubling, splitting or surrendering taking into
account how many of each card remains to be played and

C) finally taking the ratio of the Hi-Lo gain to the latter gain.

[lij45o6]

Flash,

PE has always been something that has bothered me. PE is not "mathematically quantifiable", in that, there is a method/algorithm that can quantify the solution to any question/system. For example: BC. Betting Correlation is something that is quantifiable. Here is why it is:

You have a system called "X" with an array of u ("mu") values. You have a game "Y" with an Effect of Removal array of v values.

u = <u_1, u_2, ...u_(n-1), u_n>
v = <v_1, v_2, ...v_(n-1), v_n>

Now you take the sum of the squares of the values from u and v:

f(x)=Sigma(from n=1, lim->x_n) of x^2;

where the sum (Sigma) is the sum of all values from the first iteration to the limit of the last value in either u or v, and square the values.

Next, you find the correlation value by finding :

Sigma(u*v)/(ROOT(F(u)*(F(v)))); where Sigma(u*v) is the sum of all scalar values u*v.

This algo should give one the correlation of a counting system with respect to the games effect of removal.


There is no such algo for PE that I know of.