Zenfighter: ENHC Effects of Removal Table

[Zenfighter]

An unsettled subject for me, has been always to extract an effect of removal table by computer
simulation for the most common games available
in Western Europe under the ENHC rules. Now with
the aid of Karel's SBA and after 20000 millions
of rounds, finaly we have it here folks. The SE
of the figures are only 2 thousands of a percent,
I wanted to be as 'safe' as possible.

ENHC DB9 DAS and RSA

A = -.642
2 = .367
3 = .421
4 = .527
5 = .663
6 = .446
7 = .248
8 = -.037
9 = -.186
10= -.476

Now we the aid of TOB (page 44),we can compare
it with the effects of removal table for Vegas
Strip rules provided by Griffin and watch the
slight differences. I did this comparative study.

SYSTEM.....VEGAS STRIP.....ENHC

Halves......BC = 1.00......BC = 1.00
RPC.........BC = .986......BC = .980
HILO/7s...BC = .983......BC = .980
HI-LO.......BC = .970......BC = .967

RPC seems to work better under Vegas rules,there
isn't any statistical difference among the other
counts IMHO. So what?
"There is nothing new under the sun."

Regards
Z

[Don Schlesinger]

Nice piece of work. I'd like to suggest that it be included in our "Distinguished Posts" section.

Don

[Mr. Lucky]

I don't understand why the ace is more beneficial in a ENHC D9 game than a standard Strip game. Intuitively, I would think not being able to soft double or double 11 and 10 vs. ace after the dealer checks for BJ would make the ace less valuable than in standard DOA hole card games. Does anyone know why this is not the case?

[Cacarulo]

> Now with the aid of Karel's SBA and after 20000
> millions of rounds, finaly we have it here
> folks. The SE
> of the figures are only 2 thousands of a
> percent,
> I wanted to be as 'safe' as possible.

I suppose 20000 million rounds is for each removal, isn't it?

> ENHC DB9 DAS and RSA

RSA means that you can resplit aces. How many times? Sometimes is better to use SPAn. Now, how about the other rules? S17 or H17? SPL3?

> A = -.642
> 2 = .367
> 3 = .421
> 4 = .527
> 5 = .663
> 6 = .446
> 7 = .248
> 8 = -.037
> 9 = -.186
> 10= -.476

> Now we the aid of TOB (page 44),we can
> compare
> it with the effects of removal table for
> Vegas
> Strip rules provided by Griffin and watch
> the
> slight differences. I did this comparative
> study.

> SYSTEM.....VEGAS STRIP.....ENHC

> Halves......BC = 1.00......BC = 1.00
> RPC.........BC = .986......BC = .980
> HILO/7s...BC = .983......BC = .980
> HI-LO.......BC = .970......BC = .967

> RPC seems to work better under Vegas
> rules,there
> isn't any statistical difference among the
> other
> counts IMHO. So what?
> "There is nothing new under the
> sun."

Very nice work!

Sincerely,
Cacarulo

PS: Have you checked TOB EORs prior to this?

[Cacarulo]

> I don't understand why the ace is more
> beneficial in a ENHC D9 game than a standard
> Strip game. Intuitively, I would think not
> being able to soft double or double 11 and
> 10 vs. ace after the dealer checks for BJ
> would make the ace less valuable than in
> standard DOA hole card games. Does anyone
> know why this is not the case?

I think the answer is in the RSA rule.

Sincerely,
Cacarulo

[Zenfighter]

> I think the answer is in the RSA rule.

> Sincerely,
> Cacarulo

I've got the same feeling when I first looked
at the -.642 figure. RSA adds 0.072% for 6 dks
anyway, easy to get by interpolation of the ones in page 117 of TOB.
On the other hand the average effect of removal
of a high card for the European player is

((4*-.476)+ -.642)/5 = -.509

For a Vegas player

((4*-.51) + -.61)/5 = -.530

Or roughly speaking, the Vegas player has more
motives to be disgusted when he watch the face
cards and the tens go 'down the tubes' as his counterpartner from the other side of the Ocean.
But alas! He is more happy also, when the little
cards disappear. For a high low player

.504 (Vegas) vs. .485 (Europe)

I think our friend Mr. Lucky will be also happy
now.

A short answer to your questions below, at the
risk of my wife filling a divorce order, (it's
5.30 a.m., I just returned from my local casino)

1)S17 resplitting any pair and aces unlimited
2)I've checked TOB prior, in the middle and
after, in fact I sleep with the book under my
pillow. I will understand this "bastard" one day!

Thanks to you and Don for being so nice.

Regards
Z

[Zenfighter]

[Cacarulo]

> An unsettled subject for me, has been always
> to extract an effect of removal table by
> computer
> simulation for the most common games
> available
> in Western Europe under the ENHC rules. Now
> with
> the aid of Karel's SBA and after 20000
> millions
> of rounds, finaly we have it here folks. The
> SE
> of the figures are only 2 thousands of a
> percent,
> I wanted to be as 'safe' as possible.

> ENHC DB9 DAS and RSA

> A = -.642
> 2 = .367
> 3 = .421
> 4 = .527
> 5 = .663
> 6 = .446
> 7 = .248
> 8 = -.037
> 9 = -.186
> 10= -.476

> Now we the aid of TOB (page 44),we can
> compare
> it with the effects of removal table for
> Vegas
> Strip rules provided by Griffin and watch
> the
> slight differences. I did this comparative
> study.

> SYSTEM.....VEGAS STRIP.....ENHC

> Halves......BC = 1.00......BC = 1.00
> RPC.........BC = .986......BC = .980
> HILO/7s...BC = .983......BC = .980
> HI-LO.......BC = .970......BC = .967

> RPC seems to work better under Vegas
> rules,there
> isn't any statistical difference among the
> other
> counts IMHO. So what?
> "There is nothing new under the
> sun."

It seems to me that you've calculated the EORs for single deck (as in TOB). Now, if you want an exact representation of your game you should have to calculate the EORs for the correct number of decks which is probably six.
Now, maybe I'm wrong and you did calculate the EORs for 6 decks.

Sincerely,
Cacarulo

[Zenfighter]

> It seems to me that you've calculated the
> EORs for single deck (as in TOB). Now, if
> you want an exact representation of your
> game you should have to calculate the EORs
> for the correct number of decks which is
> probably six.
> Now, maybe I'm wrong and you did calculate
> the EORs for 6 decks.

> Sincerely,
> Cacarulo

Practical effects of removal tables are ALWAYS
normalized to one deck values for technical
purpouses, so you don't have to worry the simulation was done running through 6dks.
In other words, if you want to know exactly how
much is your gain under ENHC rules having watched
a 5 out of the packet the answer is easy:

.663/6 = .1105 and not the whole figure of course! I thought that was clear. Simple, the whole 6kd shoe contains only 18s fives, which is
assuming every single packet is one five poor.

On page 127 of TOB Griffin says:
"The effects of removing a single card of each
denomination appear in the next table:even though AC games are all multiple deck the removals are
from a single deck so comparisions can be made
with other similar tables and methods presented
in the book."
If you turn the page and watch the table for
efrem on Early Surrender (gone with the wind
unfortunately),don't dream with a .92 advantage
by watching a 5 is only a .92/6 = .1533 one.

How can a reader of this tables be sure the figures are accurately extracted?
Theory states:
The effect of removal times the probability of
drawing the card sums to zero.
"Someone" knowledgeable told me, that to cluster
the final result around zero in the range of
+/- [0.05] was enough indication of the fairness
of the table.
So, for Griffin's table on page 44 we have:

(.38*4/52)+(.44*4/52)+(.55*4/52)+(.69*4/52)
+(.46*4/52)+(.28*4/52)+(-.18*4/52)+(-.51*16/52)
+(-.61*4/52) = -0.0023

So, Griffin's table clusters within +/-[0.01].

Let's all take a beer to honour our BJ hero!

Regards
Z

[MathProf]

Like others here, I was surprised at your numbers, particularly your number for the Ace. I decided to do a Combinatorial Analysis to determine the EoRs.

I wasn't sure if this was H17 or S17. I did both; obviously the S17 will have the higher Ace EoR. Here are the results for that

 

  1    -0.638%     

  2     0.368%     

  3     0.425%     

  4     0.539%     

  5     0.680%     

  6     0.448%     

  7     0.247%     

  8    -0.037%     

  9    -0.186%     

 10    -0.461%     

Here the size of the Ace EoR a bit lower than yours. I was surprised to see it come out that high. You and Cac are right that RSA does bump it up. Here are the results without RSA:

 

  1    -0.596%     

  2     0.362%     

  3     0.419%     

  4     0.534%     

  5     0.674%     

  6     0.443%     

  7     0.243%     

  8    -0.040%     

  9    -0.188%     

 10    -0.462%     

There is always the possibility of a subtle bug in a program, so I wouldn't stake my reputation on these numbers. But I have a fair amount of confidence in the results. In the absence of additional data, I am inclined to favor these numbers over yours. For one thing, the methodology of using CA is better for computing EoRs.

I would happy to discuss the issue further, in attempt to account for the discrepancy.

BTW, I computed that the Basic Strategy EV for the game was -0.5416% with as SD of 1.113




> An unsettled subject for me, has been always
> to extract an effect of removal table by
> computer
> simulation for the most common games
> available
> in Western Europe under the ENHC rules. Now
> with
> the aid of Karel's SBA and after 20000
> millions
> of rounds, finaly we have it here folks. The
> SE
> of the figures are only 2 thousands of a
> percent,
> I wanted to be as 'safe' as possible.

> ENHC DB9 DAS and RSA

> A = -.642
> 2 = .367
> 3 = .421
> 4 = .527
> 5 = .663
> 6 = .446
> 7 = .248
> 8 = -.037
> 9 = -.186
> 10= -.476

> Now we the aid of TOB (page 44),we can
> compare
> it with the effects of removal table for
> Vegas
> Strip rules provided by Griffin and watch
> the
> slight differences. I did this comparative
> study.

> SYSTEM.....VEGAS STRIP.....ENHC

> Halves......BC = 1.00......BC = 1.00
> RPC.........BC = .986......BC = .980
> HILO/7s...BC = .983......BC = .980
> HI-LO.......BC = .970......BC = .967

> RPC seems to work better under Vegas
> rules,there
> isn't any statistical difference among the
> other
> counts IMHO. So what?
> "There is nothing new under the
> sun."

> Regards
> Z

[Zenfighter]

> Like others here, I was surprised at your
> numbers, particularly your number for the
> Ace. I decided to do a Combinatorial
> Analysis to determine the EoRs.
> I wasn't sure if this was H17 or S17. I did
> both; obviously the S17 will have the higher
> Ace EoR. Here are the results for that
> 1 -0.638%
> 2 0.368%
> 3 0.425%
> 4 0.539%
> 5 0.680%
> 6 0.448%
> 7 0.247%
> 8 -0.037%
> 9 -0.186%
> 10 -0.461%
> Here the size of the Ace EoR a bit lower
> than yours. I was surprised to see it come
> out that high. You and Cac are right that
> RSA does bump it up. Here are the results
> without RSA:
> 1 -0.596%
> 2 0.362%
> 3 0.419%
> 4 0.534%
> 5 0.674%
> 6 0.443%
> 7 0.243%
> 8 -0.040%
> 9 -0.188%
> 10 -0.462%
>
> There is always the possibility of a subtle
> bug in a program, so I wouldn't stake my
> reputation on these numbers. But I have a
> fair amount of confidence in the results.
> In the absence of additional data, I am
> inclined to favor these numbers over yours.
> For one thing, the methodology of using CA
> is better for computing EoRs.
> I would happy to discuss the issue further,
> in attempt to account for the discrepancy.
> BTW, I computed that the Basic Strategy EV
> for the game was -0.5416% with as SD of
> 1.113

We all know that programmers use algorithms that
generate pseudo random numbers, hence the secuences of numbers are not really random.
Despite the fact that Karel may be,is touched by an angel, what's sure is the fact that he is not
God, the only one by the moment who can generate
a random one. In other words, with the Monte Carlo
Simulation, what I used here to produce the data,
one can never be quite sure of the "accuracy" of
the final result.
Being said that, let's compare the data.

CA Analysis..........Simulation

BSE = -.5416......BSE = -.5664 SE=.0025
SDH = 1.113.......SDH = 1.11328

Since the simulations have an average SE of
0.0025%, let's round to the cents of percent
an we get this.

CA Analysis..........Simulation

A=-0.64% ............ -0.64%
2= 0.37%...............0.37%
3= 0.43%...............0.42%
4= 0.54%...............0.53%
5= 0.68%...............0.66%
6= 0.45%...............0.45%
7= 0.25%...............0.25%
8=-0.04%..............-0.04%
9=-0.19%..............-0.19%
10=-0.46%.............-0.48%

Thanks again Mathprof for your time. Further investigation must be done. Don't you think so?

Regards
Z

>
>
>
>
>
>

[MathProf]

I guess that these number are really closer than I realized! For some reason, I got the idea in the back of my mind that you Ace number was larger. I thought you posted .68. I don't know where I got that idea from, maybe too much speed reading. So when I only got .638, I thought we are still far apart.

When you posted your numbers next to mine, it is clear that are very similar. So much so that each can be considered a confirmation of the others.

I am not sure that it is worth a lot of effort to try to account for the little difference that we have. However, aside from possible sampling error, there are a couple of possible things to look at.

One is a possible cut card effect. When you ran your sims, did you do a fixed number of rounds, or did you use a cut card. EoRs are based on Basic Strategy play, which is what the CA does. For this, a cut card should not be sued.

A second possibility is the Basic Strategy itself. I have the computer first do a CA to determine the optimal strategy for that particular game. With SBA you have to put in a strategy manually? Differences in strategy can make a difference in the resulting EoRs.

> We all know that programmers use algorithms
> that
> generate pseudo random numbers, hence the
> secuences of numbers are not really random.
> Despite the fact that Karel may be,is
> touched by an angel, what's sure is the fact
> that he is not
> God, the only one by the moment who can
> generate
> a random one. In other words, with the Monte
> Carlo
> Simulation, what I used here to produce the
> data,
> one can never be quite sure of the
> "accuracy" of
> the final result.
> Being said that, let's compare the data.

> CA Analysis..........Simulation

> BSE = -.5416......BSE = -.5664 SE=.0025
> SDH = 1.113.......SDH = 1.11328

> Since the simulations have an average SE of
> 0.0025%, let's round to the cents of percent
> an we get this.

> CA Analysis..........Simulation

> A=-0.64% ............ -0.64%
> 2= 0.37%...............0.37%
> 3= 0.43%...............0.42%
> 4= 0.54%...............0.53%
> 5= 0.68%...............0.66%
> 6= 0.45%...............0.45%
> 7= 0.25%...............0.25%
> 8=-0.04%..............-0.04%
> 9=-0.19%..............-0.19%
> 10=-0.46%.............-0.48%

> Thanks again Mathprof for your time. Further
> investigation must be done. Don't you think
> so?

> Regards
> Z

[Cacarulo]

> One is a possible cut card effect. When you
> ran your sims, did you do a fixed number of
> rounds, or did you use a cut card. EoRs are
> based on Basic Strategy play, which is what
> the CA does. For this, a cut card should not
> be sued.

I agree that this could be part of the difference. ZenGrifter: As MP said you should use a fixed # of rounds (not 1). I think 90 rounds per shoe would be okay.

> A second possibility is the Basic Strategy
> itself. I have the computer first do a CA to
> determine the optimal strategy for that
> particular game. With SBA you have to put in
> a strategy manually? Differences in strategy
> can make a difference in the resulting EoRs.

Probably he used a generic BS strategy for ENHC. My guess is that splitting decisions are not exactly the same.

Sincerely,
Cacarulo