1. ## Nora: Playing Efficiency

Hi!

I have a question: how do you calculate the playing efficiency in blackjack?
I would like to find a formula or something that shows me how the PE is calculted, not just what PE a counting system has.

I would really appreciate some help with this!

2. ## ES: Re: Playing Efficiency

The Playing Efficiency of 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 oerfect 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 game is simulated in which playing decisions are made on basis of the Hi-Lo count, 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 finally taking the ratio of the Hi-Lo gain to the latter gain.

> Hi!

> I have a question: how do you calculate the playing
> efficiency in blackjack?
> I would like to find a formula or something that shows
> me how the PE is calculted, not just what PE a
> counting system has.

> I would really appreciate some help with this!

3. ## Don Schlesinger: Nice answer!

Can't add anything. I think what you've written is 100% correct.

Thanks for dropping by. How is everything going?

Don

4. ## David Spence: Re: Playing Efficiency

Though the simulation method described earlier would provide the most accurate values for playing efficiency, I question its practicality. From Griffin, "Reliable simulation estimates of this...are extraordinarily time consuming, so the correlation method proves ideal...."

The Efficiency Calculator in CVData provides PEs instantaneously, indicating that a calculation, rather than a simulation, is used to generate the numbers.

In Chapter 4 of The Theory of Blackjack, 6th ed., the PE and tags of an optimal single-parameter count were determined by calculation. PEs of other counts were determined similarly, though, once the tags and PE of the optimal system are determined, a simpler correlation analysis could be used to provide an estimate of other systems' PEs. I suspect the latter is what's done in CVData (Norm, please correct me if I'm wrong).

If you're really interested in this and don't have The Theory of Blackjack, email me and I can explain how to estimate the PE using the relatively simple correlation analysis.

David

5. ## ES: Thanks for the kind words!

Things are OK, except for the lack of low minimum games or favorable conditions in Atlantic City, the Strip in Vegas becoming more like the AC and my difficulties with my job search. I'm glad to see some more posts on this site. Things have been far to quiet lately. This is because of the lack of good games, not any fault of Viktor or Bettie. David Spence provides more i9nsight into PE below. Good talking to you, Don!

> Can't add anything. I think what you've written is
> 100% correct.

> Thanks for dropping by. How is everything going?

> Don

6. ## Don Schlesinger: Re: Playing Efficiency

> Though the simulation method described earlier would
> provide the most accurate values for playing
> efficiency, I question its practicality. From Griffin,
> "Reliable simulation estimates of this...are
> extraordinarily time consuming, so the correlation
> method proves ideal...."

You forget that was was "extraordinarily time consuming" in Peter's day probably can now be done in five minutes. :-)

> The Efficiency Calculator in CVData provides PEs
> instantaneously, indicating that a calculation, rather
> than a simulation, is used to generate the numbers.

No, not necessarily true. Norm has trillions of canned simulations of hands for every conceivable card-counting system. I'd bet that he simply plugged them in to get the PEs.

> In Chapter 4 of The Theory of Blackjack, 6th ed., the
> PE and tags of an optimal single-parameter count were
> determined by calculation. PEs of other counts were
> determined similarly, though, once the tags and PE of
> the optimal system are determined, a simpler
> correlation analysis could be used to provide an
> estimate of other systems' PEs. I suspect the latter
> is what's done in CVData (Norm, please correct me if
> I'm wrong).

See above. Virtually 100% of Norm's work is done by simulation -- although the ROR and goal calculators use directly the formulas from BJA3.

Don

7. ## David Spence: Re: Playing Efficiency

> You forget that was was "extraordinarily time
> consuming" in Peter's day probably can now be
> done in five minutes. :-)

Very true :-) But doing a correlation analysis is still more practical than simulation, assuming a player doesn't have access to a program that can simulate optimal play based on the exact composition of remaining cards. An example of the calculation (albeit for BC instead of PE) is given on p. 44 of The Theory of Blackjack, 6th ed., and it would be easy to do for virtually any player. You'd just need the optimal tags and PE given in the last row of the table on p. 46.

> No, not necessarily true. Norm has trillions of canned
> simulations of hands for every conceivable
> card-counting system. I'd bet that he simply plugged
> them in to get the PEs.

I'd be curious to hear how the Efficiency Calculator in CVData determines values. Its speed, its use of the word "estimate," and its claim that it calculates PE "as defined by Peter Griffin" still lead me to think that it performs a correlation analysis as opposed to a simulation. Norm?

David

8. ## Norm Wattenberger: Re: Playing Efficiency

It was a long time ago. If I remember correctly, CVData does indeed perform a correlation analysis. Only it uses different coefficients based on the value of the ace.

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