If you knew all the cards played...

[Daggers]

i asked this question when i first joined. let's say you are playing a 2 deck game and there are 3 10's, 4 9's, 5 8's, 2 6&5's, no 3's, 5 2's, and 2 aces left unseen. And you have a 16 v 10. there are 14 out of 23 cards left that can bust your hand. 61% your hand will bust. that is what you can do with the information. but how to decide whether or not to hit with the percentage of busting or not would be up to a variety of factors i think. im not sure if this logic is right or if someone has the capability to this that it will be more profitable than an existing count.

 

[London Colin]

Yes, right LC, I assume we're dealing with such huge #'s that its not realisitic to pre-compute everything.

Lets say if this was pre-computed (tracking the 13 cards), in a 6 deck shoe, would have to account for approximately:

24 ^ 13 permutations ~ 900 quadrillion permutations

24 being the 0-24 remaining cards of each rank, 13 being each different rank.

I think that would actually be 25^10. (25 because 0-24 is 25 different possibilities, and 10 because there is no need to distinguish between T,J,Q,K.) A smaller number, but still pretty big.

I assume its a huge non-feasible amount of computing time for a CA of each permutation. And is this such a big number that it can't be stored on a computer)?

Maybe its possible a grouping of similar hand results and culling out non-realistic situations (for example less than 1/2 deck cut) might significantly reduce the #'s of calculations needed to be made and stored. Have no concrete idea how to do this, but somebody smarter might

I know it's an academic discussion, but I would think there isn't much to be gained with six decks in any case, so limiting things to the smaller numbers involved with 1 or 2 decks would be the first place to make a saving.

And, as I think you are saying, there is no need to examine subsets that are smaller than the cutoff size.

I actually wrote some code a while ago to enumerate every possible subset at a given depth (i.e. when precisely n cards have been seen).

Also, wondering how real time you can get with CA, as you mentioned "more or less", and I think your right. There would be situations where you can't really do it in real time in a real life situation, like lets say at a 8 deck game, you hit, and get a card, and have to make another decision, a computer would not be fast enough to do the CA of this new situation in real time?

We are talking about a few seconds, prior to the deal, in which the CA computes the overall advantage and thus tells you how much to bet. This calculation incorporates all the playing decisions you might subsequently make; so if you are playing heads-up there are no further calculations to make until the next round is due to be dealt. (Except that if you split, you might want to take account of all the cards drawn to your first split hand.) And if there are other players then you want to take account of their cards.

But these calculations can be done much, much quicker than the pre-deal calculation because you know the dealer's up card and your own starting hand. You don't have to calculate the whole tree of possible hands, just a small branch of it. The tricky part would probably be keeping up with the dealer while entering the cards into the system using your toes or whatever.:grin:

 

[Gamblor]

LC, right, it would be 25 considering 0-24 counts - I'm pretty sure, meh don't care much for values off by 1 which gets me into a lot of trouble often . But it would also be 25 ^ 9 * 97 in a 6 deck game (or 0- 96 possible count values for ten value cards) if you were to consider all 10 value cards the same (which is another good simplification w/o losing any accuracy).

Yeah was thinking you can cull out a lot of calculations, for example lets say you have a deck with 4 ten value cards immediately taken out, you probably don't have to bother calculating the CA for 5 or more 10 value cards missing.

He he don't always have to update values with our toes :grin:

 

[London Colin]

LC, right, it would be 25 considering 0-24 counts - I'm pretty sure, meh don't care much for values off by 1 which gets me into a lot of trouble often . But it would also be 25 ^ 9 * 97 in a 6 deck game (or 0- 96 possible count values for ten value cards) if you were to consider all 10 value cards the same (which is another good simplification w/o losing any accuracy).

Glad you spotted my deliberate mistake!

Yeah was thinking you can cull out a lot of calculations, for example lets say you have a deck with 4 ten value cards immediately taken out, you probably don't have to bother calculating the CA for 5 or more 10 value cards missing.

He he don't always have to update values with our toes :grin:

I'm pretty sure real-time would be feasible, so it's not really an issue. But I'm not sure it makes sense to filter out the rarest of deck compositions; these will be the ones which offer the greatest rewards for perfect play.

I doubt shoe games with typical levels of pen would yield any meaningful extra advantage, but 1D and 2D with decent pen could throw up enough extreme deck compositions (whose EV's from perfect play differ markedly from what simple, linear, EOR-based calculations would suggest) to make a significant difference.

 

[iCountNTrack]

Well this has been known since Thorp days, that the fewer the cards we have and the more cards we deal the greater is the gain we expect from playing strategies adjustments.
KC and I worked on sims of perfect play using composition dependent CA as implemented by his program. Running the sims is computationally expensive and i had to use up 4 different computers with high end CPUs (each computer would run a sim of 5 million rounds, sum up and average the results). The results are not published yet. But i can give two illustrative examples.

For 1 deck S17 DAS 75% flat betting (to ensure that all the gain is from playing)
Using High Opt II (full indices) ev is 0.882%
Using Perfect Play (quasi-perfect) ev is nearly doubled standing at 1.531%

On the other hand for a 6 deck S17 DAS 75% flat betting
Using High Opt II (full indices) ev is -0.276%
Using perfect play ev is -0.163%

 

[aslan]

I think you all are thinking linearly because you use linear counts. What would be employed here is a straight 10 dimensional EOR counting system. I doubt anyone could actually do it even if they could remember all the cards but you would gain a lot if you could. Especially with few cards left to be played.

In order to actually make it within the limits of what anyone but a superhuman freak there would need to be compromises made. The compromises would give back some of the theoretical but I think you would still be amazed at the gain.

Shades of Rainman. Imagine a 10-dimensional count? To know the moving EOR count at all times would be a really super system. A computer could do it, but one would have to have it implanted under their skin to avoid detection. Even then ECM might catch them. Move over, Big Bubba!

 

[London Colin]

Well this has been known since Thorp days, that the fewer the cards we have and the more cards we deal the greater is the gain we expect from playing strategies adjustments.
KC and I worked on sims of perfect play using composition dependent CA as implemented by his program. Running the sims is computationally expensive and i had to use up 4 different computers with high end CPUs (each computer would run a sim of 5 million rounds, sum up and average the results). The results are not published yet. But i can give two illustrative examples.

For 1 deck S17 DAS 75% flat betting (to ensure that all the gain is from playing)
Using High Opt II (full indices) ev is 0.882%
Using Perfect Play (quasi-perfect) ev is nearly doubled standing at 1.531%

On the other hand for a 6 deck S17 DAS 75% flat betting
Using High Opt II (full indices) ev is -0.276%
Using perfect play ev is -0.163%

The flat-betting comparison is certainly interesting, but this doesn't show to what extent quasi-perfect assessment of the pre-deal EV would cause you to make larger (or indeed smaller) bets, and thus make bigger overall gains compared to simple counting.

I don't know; maybe it doesn't actually make all that much difference unless you get down to very deep levels of pen?

 

[FLASH1296]

iCountNTrack ,

Thanx muchly for the very interesting data. It is much appreciated.

I do not wish to be a nit-picker, but why not use a more realistic

H17 Single Deck game or S17 NDAS or S17 NDAS D9?

 

[aslan]

This use of an EOR device is interesting as a hypothetical, but IMO there is no device that is beyond detection.

Yet in NJ, the possession of a gambling device is considered a disorderly persons offense (I think that's a misdemeanor), but is punishable by up to $25,000 fine and/or 18 months in jail. That's a lot to risk for me personally.

However, the NJ Constitution refers to "gambling devices" and the Casino Control Act refers to "cheating devices." Are they one and the same? In what way is using a calculator or computer program cheating? We even use them legally in some school exams nowadays, unless the test is designed to rely on your head knowledge alone.

If the rules of the casino clearly specify no computer/calculator aids, that's one thing, but if they fail to specify, I see no moral wrong with using tools to aid one's ability to make mental calculations.

Is it even legal for them to deny the use of calculators/computers? That's another question.

 

[iCountNTrack]

The flat-betting comparison is certainly interesting, but this doesn't show to what extent quasi-perfect assessment of the pre-deal EV would cause you to make larger (or indeed smaller) bets, and thus make bigger overall gains compared to simple counting.

I don't know; maybe it doesn't actually make all that much difference unless you get down to very deep levels of pen?

Calculating pre-deal evs would make things even much slower , because that would require calculating prior to each round. I did however write a code that enumerates all the possible deck compositions for a given penetration and calculate the pre-deal ev for each possible composition. I think you have seen that in one of my posts a while ago.
http://www.blackjackinfo.com/bb/showpost.php?p=175883&postcount=14

But you do raise an important point, people sometimes mistakingly separate betting and playing while the two are very related. You bet according to your pre-deal EVs because that is your advantage. The pre-deal evs is a collection of perfect plays for all possible player cards/dealer up card combination.
Card counting systems make things easier but they create "fudge" factors called tags :grin:, which on average do work but not for all cases.

Let's take a look at a simple example,

a deck with 4 7s, 4 8s, 4 9s, 2 10s (S17, DAS) pre-deal ev is 25.83%
removing one ten INCREASES the pre-deal EV to 35.92%, and removing the other ten also INCREASES the pre-deal EV to 53.40%.

In this case the tag for ten should have been positive because the EV increases after it is removal.
Also we notice that a supposedly "neutral" (Hi-Lo) or "negative" composition (Hi-Opt II) has an EV of 53%.

All these discussions are purely theoretical since you need a time machine to play these games :laugh:

 

[London Colin]

Calculating pre-deal evs would make things even much slower , because that would require calculating prior to each round. I did however write a code that enumerates all the possible deck compositions for a given penetration and calculate the pre-deal ev for each possible composition. I think you have seen that in one of my posts a while ago.
http://www.blackjackinfo.com/bb/showpost.php?p=175883&postcount=14

Yeah, I did some haphazzard experiments of my own a while ago, along similar lines, and hit upon the same performance issues.

A couple of thoughts I had at the time -


Rather than run a sim of game-play, perhaps the EVs of a large, random set of compositions of different sizes could be averaged. (i.e. do what you did in the example you mention, but not for a fixed depth, for every depth up to the pen. defined for the game.)

I managed to confuse myself about what would be a valid way of sampling the shoes. The simplest appoach would be to perform a shuffle and then deal cards one at a time, re-computing the EV after each, until the max pen is reached, and then repeat the process. However, that would yield compositions with impossible sizes (e.g., the first round can never consist of a single card).

So an alternative might be to consume the cards by playing either basic strategy or the CA-calculated strategy (but might even this cause subtle inconsistencies when the 'results' being logged relate to every possible way the round could be played out, rather than one specific way?)

Or maybe a random number of cards could simply be consumed to simulate each round; done in such a way that the average number of cards per round matches what you would expect.



It also occurred to me that it might be possible to use some techniques to compute an estimate for the pre-deal EV that is much better than the simple, linear approach, but a lot faster than a full CA.

I did some work on C++ code to implement the methods described in chapter 15 of TOBJ (Interactive Approximations to Facilitate Rapid Blackjack Computations). I think the chapter only appears in the 6th edition. I had some trouble understanding it, in part due to an error that seems to have got into the book. But Eric Farmer very kindly helped me out and clarified things.

As ever I left things about 80% completed, so this is one of the many projects I ought to go back to and finish off.

All that being said, I don't know how well the 'interactive approximation' technique would perform with the extreme deck compositions.

But you do raise an important point, people sometimes mistakingly separate betting and playing while the two are very related. You bet according to your pre-deal EVs because that is your advantage. The pre-deal evs is a collection of perfect plays for all possible player cards/dealer up card combination.
Card counting systems make things easier but they create "fudge" factors called tags :grin:, which on average do work but not for all cases.

Let's take a look at a simple example,

a deck with 4 7s, 4 8s, 4 9s, 2 10s (S17, DAS) pre-deal ev is 25.83%
removing one ten INCREASES the pre-deal EV to 35.92%, and removing the other ten also INCREASES the pre-deal EV to 53.40%.

In this case the tag for ten should have been positive because the EV increases after it is removal.
Also we notice that a supposedly "neutral" (Hi-Lo) or "negative" composition (Hi-Opt II) has an EV of 53%.

All these discussions are purely theoretical since you need a time machine to play these games :laugh:

That goes back to the question I posed at the end of my previous post. We may not get deep enough penetration to see very extreme cases, but do we know to what extent typical penetrations would yield cases where the bet sizes indicated by the count and by the CA are different?