Indexes

[Cacarulo]

The formulae to extract algebraic derived indices appeared first, as you surely know, in a paper called “An Algebraic Approximation to Optimal Blackjack Strategy.”
To approximate and being flawed at the same time looks like a contradictio in terrminis, because experience has taught us, that they tend to approach the Monte Carlo derived ones, quite fairly.

Question: Why this paper is not for sale anymore?
Answer: Because a few RNG’s computer wizards appeared on the scene,
Karel and Norm among the best of them. End of the story.

“If you find something you dislike inside these indices, then go with the
Simulated ones.”

That’s not me Don, that`s “Stanford Wong” ????

Zenfighter

Hi ZF,
Just for the good old times why don't you try your "algebraic formula" with the following EORs?
I'd like to see what you get.

ENHC EORs (6D,S17)

16vT  -0,0737666321  -0,0477254379   -0,1251217054  -0,2711696129  -0,3909196569  0,2640094486   -0,1002494499  -0,0047231158   0,0840144477  0,1663488952  -0,0214987953
15vT  -0,0140108193   0,0257341659   -0,0509031578  -0,1215662326  -0,2659897844  -0,3209474681  -0,0764802365   0,0145664519   0,0991357124  0,1776031800   3,2453799009

USA EORs (6D,S17)

16vT  -0,0795828086  -0,0517226577   -0,1355910869  -0,2938520598  -0,4236160449   0,2860806513  -0,1086389216  -0,0051243226  0,0910338037  0,1802533618  -0,0232903616
15vT  -0,0264376828   0,0288284805   -0,0542175392  -0,1307897213  -0,2872905040  -0,3468439521  -0,0819334677   0,0167268811  0,1083681355  0,1933973425   3,5158282260

Note that the EORs were derived from a 312-card shoe.
Sincerely,
Cac

[Gronbog]

Cac, try using

 ...

around the text you want to be aligned. You can find the button under "Go Advanced"

[Cacarulo]

Cac, try using

 ...

around the text you want to be aligned. You can find the button under "Go Advanced"

Thanks GB! Anyway, it doesn't look the way I want. Too complicated.

Cac

[Zenfighter]

Hi ZF,
Just for the good old times why don't you try your "algebraic formula" with the following EORs?
I'd like to see what you get.

ENHC EORs (6D,S17)

16vT  -0,0737666321  -0,0477254379   -0,1251217054  -0,2711696129  -0,3909196569  0,2640094486   -0,1002494499  -0,0047231158   0,0840144477  0,1663488952  -0,0214987953
15vT  -0,0140108193   0,0257341659   -0,0509031578  -0,1215662326  -0,2659897844  -0,3209474681  -0,0764802365   0,0145664519   0,0991357124  0,1776031800   3,2453799009

USA EORs (6D,S17)

16vT  -0,0795828086  -0,0517226577   -0,1355910869  -0,2938520598  -0,4236160449   0,2860806513  -0,1086389216  -0,0051243226  0,0910338037  0,1802533618  -0,0232903616
15vT  -0,0264376828   0,0288284805   -0,0542175392  -0,1307897213  -0,2872905040  -0,3468439521  -0,0819334677   0,0167268811  0,1083681355  0,1933973425   3,5158282260

Note that the EORs were derived from a 312-card shoe.
Sincerely,
Cac

OMG. Can’t believe my eyes! Do you think Cac, that I’m “39” like Norm?

Let’s go slowly with all of this. Just a few inferences from their numbers.
Full-deck favorability figures, for carry on the action, are the most important
ones. An example.

Hand T,5 v T

US (m) =3.515833 ENHC (m) = 3.245380
Difference= 0.270453, roughly a 0,3% more in EV for the American player by hitting his hand. Nothing to write home, anyway, because the negative expectation of this hand is atrocious.

By brute force:

Hand Hitting Standing Difference
T,5 v T -0.503907 -0.540055 0.036148 US
T,5 v T -0.542438 -0.575876 0.033438 ENHC

0.036148 - 0.033438 = 0.00271 or 0.3%

Have a look again at Cac’s indices posted above and enjoy.

Zenfighter

[DSchles]

I know it may be blasphemy to disagree with my dear friends, but I'm not comfortable with the above discussion. Consider the following two cases:

I'm in the US, and I get 15 vs. T. The dealer checks his hole card, has a natural, and I lose the hand. The point--although I really don't think it's all that relevant--is that none of the statistics of the game catalog that I had 15 vs. T because, well, we only study PLAYABLE hands, and, as it turned out, this one wasn't playable.

Cross the pond to Europe. Same hand, but now NHC. So, I get sucked into playing my hand, foolishly thinking that I have a chance to win, only to see the dealer flip the same Ten as before, only a bit later this time. Same hand, same result! But, because I played my hand out, you now include the statistics and conclude that it is a different (poorer) result from before and yippee for the American!

To me, smoke and mirrors! Same hand, same result. No difference. One hand isn't "better" than the other. Standing or hitting isn't better for one variety; rather, we're being tricked into thinking that, because one time we recognize that we had 15 vs. T and the other time, we conveniently forget that the hand ever existed in the first place.

Or, so it seems to me.

Don

[Cacarulo]

OMG. Can’t believe my eyes! Do you think Cac, that I’m “39” like Norm?

Let’s go slowly with all of this. Just a few inferences from their numbers.
Full-deck favorability figures, for carry on the action, are the most important
ones. An example.

Hand T,5 v T

US (m) =3.515833 ENHC (m) = 3.245380
Difference= 0.270453, roughly a 0,3% more in EV for the American player by hitting his hand. Nothing to write home, anyway, because the negative expectation of this hand is atrocious.

By brute force:

Hand Hitting Standing Difference
T,5 v T -0.503907 -0.540055 0.036148 US
T,5 v T -0.542438 -0.575876 0.033438 ENHC

0.036148 - 0.033438 = 0.00271 or 0.3%

Have a look again at Cac’s indices posted above and enjoy.

Zenfighter

6D, ENHC/USA

16vT = 0.04 / 0.04 (Generic)
T6vT = 0.66 / 0.66
97vT = 0.02 / 0.02
88vT = 0.03 / 0.03

15vT = 3.84 / 3.87(Generic)
T5vT = 3.75 / 3.79
96vT = 3.77 / 3.80
87vT = 3.77 / 3.80

Hi ZF,

Our numbers differ as I expected. I guess the difference is in the algebraic formula used. From what I read you are using Snyder's formula and as far as I remember that formula had some flaws. That is why the differences between the US rules and the ENHC rules are more pronounced.
I'd like to see what indices do you get with 16vT. In my case there are no differences.

Sincerely,
Cac

[k_c]

As Don points out common sense is that there should be no difference between USA and ENHC for the hit/stand index versus dealer up card of 10.

Zenfighter has quoted hit-stand differential from 6 decks:
T,6 v T -0.570817 -0.576608 0.005791 ENHC
T,6 v T -0.534676 -0.540954 0.006278 USA

It looks like there is more of a gain in hit-stand differential for USA, but is there really? If dealer has blackjack, the hit-stand differential is 0. If dealer doesn't have blackjack the hit-stand differential is 0.006278.

So USA hit-stand differential = pDBJ*0 + (1-pDBJ)*0.006278 where pDBJ is prob dealer BJ,
which turns out to equal ENHC hit-stand differential.

The extra complication can be avoided by simply using unconditional EV where player non-BJ loses and player BJ pushes if dealer has blackjack rather than computing EV on the condition that dealer has checked for blackjack and doesn't have it, but either way common sense seems to be validated for hit/stand for USA/ENHC versus up card of 10.

Hopefully helpful,
k_c

[Freightman]

First, to clarify an error in this thread. There is a difference between NHC and ENHC. Second, you are not sucked into playing an ENHC (or NHC) 15 or 16 v A - you’re forced to do it by the rule set.

EV (per hand) is higher v 10 or A in a hole card game (though still negative) v ENHC or NHC. Reason is obvious. Hole card v A or 10, dealer peeks for bj, gets bj and scoops all cards. No need to resolve anything. Higher probability of dealer BJ in higher true counts in Hole Card games preserves more high cards thus elevating player EV when measured against ENHC or NHC.

Regardless, the gain is minimal. Further, the minuscule gain in EV in hole card game is more than offset by faster game speed of the NHC no peek game - especially heads up with a good dealer. Back to hibernation.

[Cacarulo]

As Don points out common sense is that there should be no difference between USA and ENHC for the hit/stand index versus dealer up card of 10.

Zenfighter has quoted hit-stand differential from 6 decks:
T,6 v T -0.570817 -0.576608 0.005791 ENHC
T,6 v T -0.534676 -0.540954 0.006278 USA

It looks like there is more of a gain in hit-stand differential for USA, but is there really? If dealer has blackjack, the hit-stand differential is 0. If dealer doesn't have blackjack the hit-stand differential is 0.006278.

So USA hit-stand differential = pDBJ*0 + (1-pDBJ)*0.006278 where pDBJ is prob dealer BJ,
which turns out to equal ENHC hit-stand differential.

The extra complication can be avoided by simply using unconditional EV where player non-BJ loses and player BJ pushes if dealer has blackjack rather than computing EV on the condition that dealer has checked for blackjack and doesn't have it, but either way common sense seems to be validated for hit/stand for USA/ENHC versus up card of 10.

Hopefully helpful,
k_c

I think the difference ZF is seeing has to do with the algorithm used. In the formula that I use, the difference is not significant (15vT). We should not forget that we are talking about an algebraic "approximation" formula that aims to minimize the sum of squared prediction errors across all indices, and then use that general solution to solve for the zero.

Sincerely,
Cac

[Zenfighter]

[QUOTE=DSchles;303774]I know it may be blasphemy to disagree with my dear friends, but I'm not comfortable with the above discussion. Consider the following two cases:

I'm in the US, and I get 15 vs. T. The dealer checks his hole card, has a natural, and I lose the hand. The point--although I really don't think it's all that relevant--is that none of the statistics of the game catalog that I had 15 vs. T because, well, we only study PLAYABLE hands, and, as it turned out, this one wasn't playable.

Cross the pond to Europe. Same hand, but now NHC. So, I get sucked into playing my hand, foolishly thinking that I have a chance to win, only to see the dealer flip the same Ten as before, only a bit later this time. Same hand, same result! But, because I played my hand out, you now include the statistics and conclude that it is a different (poorer) result from before and yippee for the American!

To me, smoke and mirrors! Same hand, same result. No difference. One hand isn't "better" than the other. Standing or hitting isn't better for one variety; rather, we're being tricked into thinking that, because one time we recognize that we had 15 vs. T and the other time, we conveniently forget that the hand ever existed in the first place.

Or, so it seems to me.



I know it may be blasphemy to disagree with my dear friends,

C´mon Don! No blasphemy at all. I remind you that this website
is in America. In other words: The land of Liberty and Freedom of Speech.

“If liberty means anything at all it means the right to tell people what they
do not want to hear.” George Orwell

What you’re trying to say here, is that there is natural tendency of the human mind to forget quickly unpleasant results, and try to concentrate on the nice ones, only.

“These American dealers look like pieces of cake.” Zf.

During the first days playing in USA, I was suffering from amnesia, obviously. Pretty soon, I waked up to reality.

Zenfighter

[Gramazeka]

Unless you are using parallel computing more threads doesn't do anything really. Also what you really want is more physical cores and not threads. Some results show that hyper threading slows down High Performance Computing and people usually turn it off.

Test processors for poker solver

[Gramazeka]

I have updated the post. There is a fine line in the matter of these two processors in particular.

https://cpu.userbenchmark.com/Compar...00X/4043vs4084

The question remains open - which processor is better for computing and for online poker?

The results are impressive.

Ryzen 5600x- 2650 sec vs Ryzen 3700x - 2154 sec. That's what more cores mean for computing.

[Norm]

It's difficult to divine the performance of a chip merely by looking at the specs. As an example, I just "upgraded" from Win10 to Win11. I have an Alder Lake CPU which has asymmetric cores -- some high performance mutli-thread and some efficient single thread. Win11 has thread director support that understands the new chips and guides threads to the correct cores. The results are interesting. CVData ran about 5% slower under Win11. BUT, the PC was much more responsive during the sim and I could interact with CVData while it was simming much better. This allowed me to increase the number of threads used by CVData. Having done that, the sims were faster under Win11 and I still had better response time when examining the sim results during simulation.

Incidentally, the thread director was my only reason to move to Win11. First thing I did was install StartAllBack which reverts the awful user interface to Windows 7, the last decent interface.