Zenfighter: American Ace vs European Ace

[Zenfighter]

Player edge given first card Ace

6dks, S17, DOA, DAS, RS=4, NRSA

A vs 2 = 59.3161088%
A vs 3 = 61.6339049%
A vs 4 = 64.3913026%
A vs 5 = 67.8204449%
A vs 6 = 71.4098707%
A vs 7 = 65.8827197%
A vs 8 = 59.7156369%
A vs 9 = 51.3050514%
A vs T = 35.6727214%
A vs A = 12.0977045%

Average expectation = 50.4818176923%

6dks, S17, DB9, DAS, RSA and ENHC

A vs 2 = 59.9203561119%
A vs 3 = 61.7843869923%
A vs 4 = 63.7320845466%
A vs 5 = 65.9114286945%
A vs 6 = 68.5124451875%
A vs 7 = 66.6872745608%
A vs 8 = 60.4967020726%
A vs 9 = 52.0503552227%
A vs T = 36.3361141020%
A vs A = 11.6781%

Average expectation = 50.4705838302%

I want to thank Mr. Cacarulo for letting me ?steal? him, the EV tables and prob. of
occurrences for the American rules to find the average expectations 2 through 9.
A vs T and A vs A have been modified, due to the danger of the dealer ending with a
Natural. The European expectations are my entire responsability, obviously.
I hope you like this ?soft double vs rsa? fight with an amazing final result.

Regards
Z

[Don Schlesinger]

> I hope you like this ?soft double vs rsa?
> fight with an amazing final result.

I always knew that those European rules hurt us! :-)

Great post! Thanks.

Don

P.S. Viktor: Please archive in the appropriate spot ("Distinguished Posts"). Thanks.

[Zenfighter]

> I always knew that those European rules hurt
> us! :-)

> Great post! Thanks.

> Don

> P.S. Viktor: Please archive in the
> appropriate spot ("Distinguished
> Posts"). Thanks.

Is me, the one who has to thank you, for being
sensitive enough, to see, that even a simple post like the above one, requires a lot of tedious calculations to perform it. In other words, it?s more a matter of transpiration than inspiration. :-)

Regards
Z

[Don Schlesinger]

> Is me, the one who has to thank you, for
> being
> sensitive enough, to see, that even a simple
> post like the above one, requires a lot of
> tedious calculations to perform it. In other
> words, it?s more a matter of transpiration
> than inspiration. :-)

For our non-European friends, understand that "transpiration" is our "perspiration."

Don

[Viktor Nacht]

[Wildcard]

> Player edge given first card Ace

> 6dks, S17, DOA, DAS, RS=4, NRSA

> A vs 2 = 59.3161088%
> A vs 3 = 61.6339049%
> A vs 4 = 64.3913026%
> A vs 5 = 67.8204449%
> A vs 6 = 71.4098707%
> A vs 7 = 65.8827197%
> A vs 8 = 59.7156369%
> A vs 9 = 51.3050514%
> A vs T = 35.6727214%
> A vs A = 12.0977045%

> Average expectation = 50.4818176923%

Let me say at the outset, that I appreciate the effort and calculations involved in deriving the end product. However, I am unable to appreciate the need for 10 decimal places to reach a conclusion related to blackjack.

I recall in school we always used 3.1416 when using the value of pi when needed. I am aware there are those who have calculated pi to the umpteenth decimal...for what purpose I have no clue.

Is there a need to reach 10 decimals to make a point (I've seen posts with up to 15 decimal places) about gaming? If there is a point, what is it? I see no need to go beyond two decimal places and round up at that.

How can I really appreciate 50.4818176923%, vs 50.48% Am I gonna live long enough to have the other decimal places have one scintilla of impact on my game?

Again, I appreciate the effort and math, but are we killing an ant with a bowling ball here?

[Don Schlesinger]

I suppose he does it because ... he can! :-)

Some of our computational analysis is set to super-precision, because, in comparing EVs for BS plays, we sometimes really need quite a few decimal places to determine the superiority of one play over another.

So, the programs churn out the results with all this precision, and when they are transferred to our screens, we simply read what's there. It's easier for the programmer to relay what his screen shows than for him to go and truncate all of his results.

So, put your hand over the screen and cover the decimals you're not interested in! :-)

Don

[Cacarulo]

sometimes the program's output comes with all those decimals and we simply copy & paste it as it.
Of course, we could run the program again with less decimals but we are too lazy to do that

Sincerely,
Cacarulo

[Sun Runner]

> However, I am
> unable to appreciate the need for 10 decimal
> places to reach a conclusion related to
> blackjack.

... has brought to a stop more than one of my posts!

SR

[Zenfighter]

> Let me say at the outset, that I appreciate
> the effort and calculations involved in
> deriving the end product. However, I am
> unable to appreciate the need for 10 decimal
> places to reach a conclusion related to
> blackjack.

> I recall in school we always used 3.1416
> when using the value of pi when needed. I am
> aware there are those who have calculated pi
> to the umpteenth decimal...for what purpose
> I have no clue.

> Is there a need to reach 10 decimals to make
> a point (I've seen posts with up to 15
> decimal places) about gaming? If there is a
> point, what is it? I see no need to go
> beyond two decimal places and round up at
> that.

> How can I really appreciate 50.4818176923%,
> vs 50.48% Am I gonna live long enough to
> have the other decimal places have one
> scintilla of impact on my game?

> Again, I appreciate the effort and math, but
> are we killing an ant with a bowling ball
> here?

Dear Wildcard
The need of these damn decimals when dealing with BJ expectations, probabilities of occurrence, running computer programs and/or doing CA analysis is simple to put
the inevitable inaccuracies, during the computational process as FAR as possible from
the important figures, that are, for we BJ players, and for practical purposes, enough with two decimals of accuracy as you pointed.
As an example, if you round each of the above rounds to two decimal places and find
afterwards the average expectation, this will be then 50.46% and not the figure that?s
been posted in the above article, as you can see. So it will be wrong, hence.
Consider that to produce every row of the article, there are a lot of expectations and
occurrences involved who must be finally weighted to find the particular expectation
for the row in question. Do you really think, it is possible to achieve two decimals of
accuracy if during the process you round up the decimals to simplify the task? I?m
sure you don?t.
What?s matter is 50.48% or if you prefer SW Basic BJ?s figure of 50.5% advantage.

Moral: Never round until the final result is achieved.

Let me end by telling you, that I?m planning for my next life and/or reincarnation :-) to
be as good as Cacarulo with his double precision 15 decimals. No chances for this one,
believe me.

Thanks for your question, hope this clarifies.

Regards
Z