BJ Deterministic adjusted basic strategy algorithm

Hello everyone.

I'm a economics(with a passion for statistic) and I was discussing with my computer science student colleague about this theoretical strategy and I would like see your opinions (Mathematicians, computer scientist and statisticians would be really helpful)

This is the Idea:

The Basic Strategy is calculated based on a brand new shoe, completely shuffled with all cards, right? But as the cards are passing, we can know more about the cards left in the shoe (no, I'm not talking about card counting), right? So what if we run a program to analyze all the possible card combinations and "moves" (hit, stand, double, split), but knowing the cards that already have been dealt and giving us the average expected value of each "move". We would have a slight different "Basic strategy" each round, correct? (Now a question, not rhetorical). Like the same process to calculate the basic strategy but discounting the past cards.

Could this adaptive "Basic strategy" give us a better E.V. than the normal basic strategy? Maybe even given a positive E.V.?
And if I use this algorithm to calculated the E.V. of the next round based on the already dealt cards (like a super complete card counting) and beating using Kelly (based on the E.V. and the variance of the E.V., the bigger the variance the less confident the 'prediction). How big would be my advantage over the dealer?

And using both strategy, how big would my advantage?


And computer technical questions. Although I know this approach would be impractical, how powerful a computer would have to run this algorithm? How much time it would take (In Big O notation, time complexity)? Would a Mont Carlo approach, instead the deterministic (testing all combinations), give a satisfactory result or maybe the error is to big to compensate not using the normal basic chart? Could a branch-and-bound or branch-and-cut optimization be useful?

There are any prior research/study/paper using this approach? If have I thank you if you share. And if you have any comment or idea to this approach, comment.

(Sorry any mistake, non-native english speaker)

Since now, thank you folks.

I'm not sure what you think card counting is, but what you are describing is card counting. There are many, many books about it. I'd start with Theory of Blackjack if I were you.

No, I know what card counting is. What I'm describing is, computer aided, calculate every single combination of cards and "moves", based on my hand and dealer's card and past cards to determinate which of then have the best E.V., exactly like the calculation of the basic strategy chart but adapting according to past cards, a exaggerated example just to show the point, if I know that only have 7s, 8s and 9s left on the shoe and my hand is 12, make no sense to stand doesn't matter the dealers card. I know that a card counting system could aid but not give the precise information.

The second part is more similar to card counting, but at this approach, knowing my exactly E.V. I could bet more precisely, maximizing my return and lowing my variance.

But see, this is a theoretical approach, a mental experiment, not like I would put a NASA computer in my backpack an walk to a casino.

Quote: andrelorenzo

No, I know what card counting is. What I'm describing is, computer aided, calculate every single combination of cards and "moves", based on my hand and dealer's card and past cards to determinate which of then have the best E.V., exactly like the calculation of the basic strategy chart but adapting according to past cards, a exaggerated example just to show the point, if I know that only have 7s, 8s and 9s left on the shoe and my hand is 12, make no sense to stand doesn't matter the dealers card. I know that a card counting system could aid but not give the precise information.

The second part is more similar to card counting, but at this approach, knowing my exactly E.V. I could bet more precisely, maximizing my return and lowing my variance.

But see, this is a theoretical approach, a mental experiment, not like I would put a NASA computer in my backpack an walk to a casino.

You're just describing a very advanced card counting system. You would be surprised what some people are capable of doing in their heads (for single-deck games, anyway)

you insist that you know what card counting is, and that what you are proposing is different from card counting, yet I cannot see the difference.

maybe you can give a brief description of what your idea of card counting is, and then tell us what exactly is the difference.

Kind of, kind of. The pointing here is if the changing on the BS in 8 deck game, based on the knowledge of past cards (100% accurate, not card counting approximations) could lead to lower house edge or even a tie game or a positive E.V., without need of bet spread.

what OP described is ultimate card counting.
In fact, with a not so complicated computer program, it can tell you what your best action is for each and every card,
you don't need to know basic strategy or anything.

Quote: andrelorenzo

Kind of, kind of. The pointing here is if the changing on the BS in 8 deck game, based on the knowledge of past cards (100% accurate, not card counting approximations) could lead to lower house edge or even a tie game or a positive E.V., without need of bet spread.

No way you could overcome the house edge in an 8-deck game. Strategy variations are not worth much in 8-deck.

In single-deck, with really good rules, and good enough penetration (like, Ro6) maybe it would be close.

Ok, call this card counting. That is not important.
As I said, the question is, what E.V. of the use of precisely best action given past cards, without bet spread, is?

Although is not a complex program, 200 lines or less may be enough, given the characteristic of probabilities's counts (Factorial, exponential etc), in a 8 deck game will give a giant amount of calculations.

Quote: andrelorenzo

Ok, call this card counting. That is not important.
As I said, the question is, what E.V. of the use of precisely best action given past cards, without bet spread, is?

Although is not a complex program, 200 lines or less may be enough, given the characteristic of probabilities's counts (Factorial, exponential etc), in a 8 deck game will give a giant amount of calculations.

So, calculate it.

I do see what the OP is saying, theoretically after every hand of an 8 deck shoe is dealt, the "perfect" strategy card changes being as the remaining composition of the shoe is different. So instead of just counting cards like normal and playing a certain way when the counts in your favor and a certain way when it's not... You actually figure out what would the perfect hit,stand,double , split , insurance strategy look like going into each individual hand.

I'm assuming this would only work in an online shoe game since there's no way to scan the cards played and produce a perfect strategy in seconds and without the casino seeing whatever device you're using to do it.

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Quote: michael99000

I do see what the OP is saying, theoretically after every hand of an 8 deck shoe is dealt, the "perfect" strategy card changes being as the remaining composition of the shoe is different. So instead of just counting cards like normal and playing a certain way when the counts in your favor and a certain way when it's not... You actually figure out what would the perfect hit,stand,double , split , insurance strategy look like going into each individual hand.

I'm assuming this would only work in an online shoe game since there's no way to scan the cards played and produce a perfect strategy in seconds and without the casino seeing whatever device you're using to do it.

Yes, but, as the number of cards increases, the gains from this get smaller and smaller. By the time you are at 8 decks it is worth very little. That is why I suggested looking at single deck instead.

Index plays... without bet spread... -EV in almost every case.

You're describing card counting w/o bet spreads.

Quote: michael99000

I do see what the OP is saying, theoretically after every hand of an 8 deck shoe is dealt, the "perfect" strategy card changes being as the remaining composition of the shoe is different. So instead of just counting cards like normal and playing a certain way when the counts in your favor and a certain way when it's not... You actually figure out what would the perfect hit,stand,double , split , insurance strategy look like going into each individual hand.

I'm assuming this would only work in an online shoe game since there's no way to scan the cards played and produce a perfect strategy in seconds and without the casino seeing whatever device you're using to do it.

Yeah, that is it.

My intention is not try to do this actually, is more a academic question.

Quote: AxiomOfChoice

Yes, but, as the number of cards increases, the gains from this get smaller and smaller. By the time you are at 8 decks it is worth very little. That is why I suggested looking at single deck instead.

This make sense.




Well, I think I gonna write this program and a "computer dealer", to test this with and without bet spread. When finished I post here in the forum to you guys take look in the results and in the program (considering my free time, it's gonna take a loooong time. kkkk).

Is the Thorp's original program or Julian Braun's one available? To me have a starting point?

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Quote: Ibeatyouraces

Look up Keith Taft.

Interesting, very interesting...

Quote: andrelorenzo

Although is not a complex program, 200 lines or less may be enough, given the characteristic of probabilities's counts (Factorial, exponential etc), in a 8 deck game will give a giant amount of calculations.

I think you're underestimating the problem. Good, optimized blackjack code is going to be more than 200 lines. I'd probably start with Eric Farmer's code.

Quote: andrelorenzo

The Basic Strategy is calculated based on a brand new shoe, completely shuffled with all cards, right?

Yes. And Basic strategy makes the additional simplification that the strategy will not change with cards observed during dealing the same hand (i.e. for split hands, but also for additional cards after a hit)

Quote:

But as the cards are passing, we can know more about the cards left in the shoe (no, I'm not talking about card counting), right?

Yes. But observe that this is the precise angle card counting uses. Card counting has not the same efficiency as exact combinatorial analysis, but is much easier to perform.

Quote:

So what if we run a program to analyze all the possible card combinations and "moves" (hit, stand, double, split), but knowing the cards that already have been dealt and giving us the average expected value of each "move". We would have a slight different "Basic strategy" each round, correct?

Yes and No. All moves will have different expected values for each round, based on the cards already observed. However, the variations in EV are usually much smaller than their difference, leading to only a few strategy variations in any practical scenario.

Quote:

Like the same process to calculate the basic strategy but discounting the past cards.

Yes.

Quote:

Could this adaptive "Basic strategy" give us a better E.V. than the normal basic strategy?

Of course, the EV will be higher. The question is, by how much.

Quote:

Maybe even given a positive E.V.?

Maybe. That depends on the details of the game. On a single deck game, each observed card not in the current round gives the player about 0.02% in EV.
On multiple deck games, this value is much much less.

Quote:

And if I use this algorithm to calculated the E.V. of the next round based on the already dealt cards (like a super complete card counting) and beating using Kelly (based on the E.V. and the variance of the E.V., the bigger the variance the less confident the 'prediction). How big would be my advantage over the dealer?

This would be a quantity which would depend on the details of game rules, especially the number of decks used and how many cards you are going to see before the deck is shuffled again.

Quote:

And using both strategy, how big would my advantage?

What "both" strategy ?

Quote:

And computer technical questions. Although I know this approach would be impractical, how powerful a computer would have to run this algorithm? How much time it would take (In Big O notation, time complexity)? Would a Mont Carlo approach, instead the deterministic (testing all combinations), give a satisfactory result or maybe the error is to big to compensate not using the normal basic chart? Could a branch-and-bound or branch-and-cut optimization be useful?

The math is easy. My laptop can calculate compositional EV for thousands of games in a split second. Even your mobile phone could do it for any specific game in a reasonable time.
Monte Carlo is no good use here, as you are looking for very tiny EV variations, that means you need a large number of samples to get significant results.

Quote:

There are any prior research/study/paper using this approach? If have I thank you if you share. And if you have any comment or idea to this approach, comment.

Of course there are.

This is nothing new it has all been done before in casinos I don't remember the guys name, but he was a music teacher or something I think this was one major factor in the NV device laws. This guy probably invented the first micro computer and computer networking.

There used to be a few online casinos that had countable Blackjack the name was something like global world casino. A similar program was used.

There also used to be a online casino, I use the word casino lightly because they only had Blackjack and it was very archaic. It was a totally player banked BJ game (great concept), the player payed a commission. You would sit down in the dealers seat and just wait for people to come play. The problem was that there were very few people.
you could sit for hours at a time and no one would come. When they did play they were usually small bettors.

Quote: andrelorenzo

Hello everyone.

I'm a economics(with a passion for statistic) and I was discussing with my computer science student colleague about this theoretical strategy and I would like see your opinions (Mathematicians, computer scientist and statisticians would be really helpful)

This is the Idea:

The Basic Strategy is calculated based on a brand new shoe, completely shuffled with all cards, right? But as the cards are passing, we can know more about the cards left in the shoe (no, I'm not talking about card counting), right? So what if we run a program to analyze all the possible card combinations and "moves" (hit, stand, double, split), but knowing the cards that already have been dealt and giving us the average expected value of each "move". We would have a slight different "Basic strategy" each round, correct? (Now a question, not rhetorical). Like the same process to calculate the basic strategy but discounting the past cards.

Could this adaptive "Basic strategy" give us a better E.V. than the normal basic strategy? Maybe even given a positive E.V.?
And if I use this algorithm to calculated the E.V. of the next round based on the already dealt cards (like a super complete card counting) and beating using Kelly (based on the E.V. and the variance of the E.V., the bigger the variance the less confident the 'prediction). How big would be my advantage over the dealer?

And using both strategy, how big would my advantage?


And computer technical questions. Although I know this approach would be impractical, how powerful a computer would have to run this algorithm? How much time it would take (In Big O notation, time complexity)? Would a Mont Carlo approach, instead the deterministic (testing all combinations), give a satisfactory result or maybe the error is to big to compensate not using the normal basic chart? Could a branch-and-bound or branch-and-cut optimization be useful?

There are any prior research/study/paper using this approach? If have I thank you if you share. And if you have any comment or idea to this approach, comment.

(Sorry any mistake, non-native english speaker)

Since now, thank you folks.

You are talking about using indices for card counting. Since you are not card counting, your idea is nonsense.

I think what andrelorenzo talking about is the following using the following example:
Lets take a Marginal Hand 16 v 10.
BS is Hit
Composition dependent BS (I think 16 with 4 cards +) is stand

If you were to calculate Perfect BS for every 16 (2 cards, 3 cards etc) for every single composition of the deck at every single depth in the shoe, then sometimes the BS will be Hit and sometimes it will be Stand and you calculate the Average Weighted EV of Hit v Stand and then maybe these will differ sufficiently for the Of the top Evs so as to make the EV for Stand a better overall strategy. Things like cut card effect could contribute to such differences.

This would only apply to a few marginal hands like 16 v 10, 12 v 4 etc (probably less than 10 different hands). For all the rest of the hands the correct BS would be the Off the Top Ev. And in the ones that strategy should change (if there are any) the change in EV would be very small.
I doubt that anything more than 0.05% would be gained in multi-deck if any.

Quote: AceTwo

I think what andrelorenzo talking about is the following using the following example:
Lets take a Marginal Hand 16 v 10.
BS is Hit
Composition dependent BS (I think 16 with 4 cards +) is stand

If you were to calculate Perfect BS for every 16 (2 cards, 3 cards etc) for every single composition of the deck at every single depth in the shoe, then sometimes the BS will be Hit and sometimes it will be Stand and you calculate the Average Weighted EV of Hit v Stand and then maybe these will differ sufficiently for the Of the top Evs so as to make the EV for Stand a better overall strategy. Things like cut card effect could contribute to such differences.

This would only apply to a few marginal hands like 16 v 10, 12 v 4 etc (probably less than 10 different hands). For all the rest of the hands the correct BS would be the Off the Top Ev. And in the ones that strategy should change (if there are any) the change in EV would be very small.
I doubt that anything more than 0.05% would be gained in multi-deck if any.

I see no difference between his suggestion and card counting indices and composition dependent strategy that is worth commenting on or worth distinction. But I will comment that composition dependent strategy is useless, and his suggestion is infinitely more useless.

Quote: Sonuvabish

I see no difference between his suggestion and card counting indices and composition dependent strategy that is worth commenting on or worth distinction. But I will comment that composition dependent strategy is useless, and his suggestion is infinitely more useless.

I think what he is saying, is that because BS is calculated based on Off the Top deck compositions, then maybe for some marginal hands this BS is 'wrong'. Wrong in the sense that if you were to use the alternate strategy, then over the whole shoe maybe it will produce better results. This might be true for some very marginal hands like say 12 v 4 (I think that is the most marginal hand in 6d S17). Cut card effects also come into play which means that some end of shoe compositions of deck are more/less likely also.
For very marginal hands (and only for them) this MIGHT make a difference changing the correct BS and making a very small difference in EV.

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Quote: Ibeatyouraces

He's talking about tracking every rank and betting optimally based on exact composition of the remaining cards, ala George the computer.

That's card counting. And cheating.

Quote: AceTwo

I think what he is saying, is that because BS is calculated based on Off the Top deck compositions, then maybe for some marginal hands this BS is 'wrong'. Wrong in the sense that if you were to use the alternate strategy, then over the whole shoe maybe it will produce better results. This might be true for some very marginal hands like say 12 v 4 (I think that is the most marginal hand in 6d S17). Cut card effects also come into play which means that some end of shoe compositions of deck are more/less likely also.
For very marginal hands (and only for them) this MIGHT make a difference changing the correct BS and making a very small difference in EV.

I get it but it is useless. As mentioned above, without cheating and in isolation, this is about as effective as composition dependent strategy, and monumentally less effective than card counting. Card counting makes composition dependent strategy pointless by canceling its gain (unless you use CD indices) AND anyone who even knows what that is probably knows how to count. There are more card counters than perfect strategy players. A perfect CD player who doesn't count probably doesn't exist. For the basic strategist, the only CD hand worth knowing is the 3+ card 16 v 10 stand because it becomes basic strategy in a surrender game. Since 10,2 v. 4 is so popularly noted, and possibly the most important as you mentioned, I have that one involuntarily memorized--which really is only useful on video blackjack that I shouldn't even play, or when the count is exactly zero, and I would otherwise consider standing to appease the ploppies, I won't.

His post shows he clearly does not understand how card counting works, unless I misread it. His method appears to be entirely dependent on counting cards, yet he claims not to want to count them. Not understanding the game also makes this a doomed proposition.

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Quote: Ibeatyouraces

If you are good enough to know the exact composition of the remaining deck, it certainly is not cheating. I used the George computer as an example. And yes, there are people good enough doing this on SD games.

If you are the rare type of person doing anything close to what he is suggesting, it only applies to SD. And it is using a multi-parameter count with indices, not reinventing the wheel. See first response. ;)

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Quote: Ibeatyouraces

The guy wants to learn something. No need to jump down his throat.

Not my intention, apologies to the OP if it came off like that. Hopefully, he believes that his approach does not appear viable to me, and at best, others seem to state that its possible benefits are minimal. My true intentions are to save the OP time and hassle.

Your title does not convey the meaning of your intent. What you are opining is more closely titled a "Shoe-Composition-Dependent Basic Strategy" which is neither Basic or simple. For this to succeed, one MUST count the remaining ranks, and evaluate the strength of the remaining deck (shoe). Then alter Top-of-Shoe Basic for the revised composition. Google Glasses and an app handy?

Quote: socks

I think you're underestimating the problem. Good, optimized blackjack code is going to be more than 200 lines. I'd probably start with Eric Farmer's code.

Yah, thats a good start. Blackjack 5.0 (DOS version) resides on my ancient desktop. Very good for ES10 decisions on hard 13, A7 vs. Ace decissions, etc.

Quote: Ibeatyouraces

The guy wants to learn something. No need to jump down his throat.

Agreed. It's an academic question. He's not hoping to get rich doing it.

There will be a lot of bs changes, but they will not provide much of an EV difference. They also won't occur frequently. Not my idea of fun, but to each his/her own.

I don't even know where to begin. There are perhaps a few misconceptions on gains in EV due to increased playing efficiency. The gains in EV are significant if you have detailed side counts or information that goes beyond density of Tens. Most counting methods have a high BC but lousy PE, since they use the TC not only for betting purposes but for playing purposes also. A single integer moving up and down a single number line based on density of Ten value cards is all you have to work with leaving you with a PE as low as .51 for Hi-Lo and a little better than that for HiOpt2 and a few other stronger counts.

The concept of "floating advantage" as it is called by blackjack great Don Schlesinger was touched on by the OP in which the index for a given hand is altered based on penetration/no. of cards remaining, meaning the index for deviating from basic strategy can be different at one deck remaining than it is for 3 decks remaining in the shoe, for instance, if I have A,2vs3 my index to double with three decks remaining is TC+6 but with one deck remaining my index to double is TC+8. Number of decks remaining alters the indices in some (but not all) instances but this pales in comparison to the effect that surplus or deficit keycards have on your playing decisions. Keycard effect has little relevance if your system has no means of gathering or utilizing this information though. The bottom line is that the OP is trying to think up things that have already long since been thought up and can save himself a lot of research and hassle simply by looking up the findings of other people's work on the topic rather than trying to reinvent the exact same wheel.

It is in fact possible to increase PE and by doing so increase overall EV dramatically. To do this you must regard TC for betting purposes only and playing decisions are based on deck composition, with the two treated as two entirely separate evolutions. I use Gordon/DHME groupings to be nearly as accurate as having "George" or a CDCA program with you at the table without the legality issue with an estimated PE of .92 or more. Keep in mind that you can diddle your computer program all day long but you sure as hell can't (legally) bring it to the table with you!









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