Cacarulo: Answer to Zenfighter

[Cacarulo]

(The original question was posted on bjmath.)

For this game I have the following EV?s

hitting = -.51176
splitting = -.461818 (or yours refined -.4617)

Table 3 yields an almost perfect M (mean) because:

-.51176 + .0499378 = -.461822 a fantastic approach to the true figure.

This is not an approach. By the definition of EOR the mean (m) is calculated as follows:

mean (m) = EV(split) - EV(hit)

so,

EV(split) = mean + EV(hit) which is what you're doing.

A bit of EOR's Theory

If instead of using a 52-card deck you used a 49-card deck (with 8,8 and T removed) then "mean" would be the exact difference between EV(split) and EV(hit). According to the EV tables in bjmath (88vT,1D,S17,DOA,NDAS,SPL1):

EV(split) = -46.1726% 

EV(hit)   = -51.1755% 

mean      =   5.0029%

Depending on the cards removed you can have different means. For example:

1) 52-card deck (no cards removed)

mean = 5.0692%

2) 51-card deck (upcard removed)

mean = 5.5999%

3) 49-card deck (T,8,8 removed)

mean = 5.0029%

All these calculations assume that we are using conditional expectations but what if we used total expectations (before the dealer has checked for bj)?

1) 52-card deck

mean = 4.6793%

2) 51-card deck

mean = 5.1607%

3) 49-card deck

EV(split) = -50.5667% 

EV(hit)   = -55.1612% 

mean      =   4.5945%

An important thing you should note is that the EORs must sum to zero. This won't happen (against a dealer Ten or Ace) if we use conditional expectations so my advice is to use total expectations.
If you use the same strategy that you used for calculating the mean then your EORs will sum to zero!

Hope this helps.

Sincerely,
Cacarulo

[Zenfighter]

[Zenfighter]

EoR?s for 8-8 vs T, SD, S17, RSP = 4

 

Card		NDAS		DAS 

 

A		-1.27104	-0.949164		 

2		-1.2636	        -1.09609 

3		-1.15219	-1.30972 

4		 2.02959	 2.18893 

5		 2.76094	 2.9767 

6		-1.43213	-1.26653 

7		-2.30582	-2.01812 

8		-1.52645	-1.39225 

9		 1.22329	 1.15226 

T		 0.733376	 0.428107 

 

M		5.35143	         6.45157 

 

m    		7.76563	         8.90414		 

 

ss	       29.62745         27.14592		 

 

Checksum       -0.003906        -0.001556 

 

 

From the above tables we can presume that the expectations for resplitting are:

NDAS = -.511755 + 5.35143 = -.458241

DAS = -.511755 + 6.45157 = -.447239

The checksum of the EoR?s is telling us to trust only 3 digits, therefore we have with
the aid of these tables computed finally:

NDAS = -.458

DAS = -.447

I think we are approaching slowly to produce better EoR?s tables. The intention behind
all this, is to help the average player to extract data with them, without the need to be
a computer programmer and/or to handle combinatorial analyzers very sensitive to the
slightest mistake.

As Griffin?s said, these methods are only approximate. Nothing can substitute a perfect
CA test when striving for the utmost accuracy extracting EV?s.

Needless to say, your comments are priceless for me. Looking forward for any improvement.

Sincerely
Z

(P.S. Cac, please double check the exact EV?s for RSPL = 4, DAS and NDAS, thanks)