Blackjack Calculator: Optimal and Personalized Strategies

[lucas]

Dear community,
We are Alejandro, Javier, and Lucas, and after a long journey of research and development, we are proud to present a set of completely new betting strategies for the game—designed to adapt precisely to each player's personal preferences. Our strategies match or exceed the performance of well-known systems, and here’s how they work:

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DECISION METHOD (DM)

The first component of a complete strategy is the Decision Method (DM). This refers to the mechanism used to make decisions during each round (hit, stand, double, etc.). The DM determines how your returns are distributed per round.
So far, our strategies incorporate two possible DMs:

• Composition-Dependent Decision (CDD): Chooses the decision that yields the highest expected return at every moment, based on the exact composition of the deck and the hands of both the player and the dealer.
  
  
  
• Basic Strategy: Follows the classical basic strategy rules to make decisions.

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BETTING METHOD (BM)

The second component is the Betting Method (BM). This method is based on a card counting system, which generates a “count” based on the cards that have been dealt and is used to extract information about the state of the deck. The idea is that the player can then use this count to calculate the optimal bet size.
Our strategies currently support two types of BMs:

• Composition-Dependent Bet (CDB): Calculates bet size based on the exact composition of the deck before each round.
  
  
  
• True-Count-Dependent Bet (TCDB): Calculates bet size based on the True Count, derived from the Hi-Lo counting system.

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ADJUSTABLE STRATEGY

Once a DM and BM are selected, we can proceed to formulate a personalized betting strategy. As we’ve seen, the DM and the deck composition determine the return distribution per round, while the BM yields a "count" tied to that composition. Combining both, we can calculate the following:

• EV(count, DM): The expected return of the upcoming round, given the current count and the chosen decision method.
  
  
  
• STD(count, DM): The standard deviation of the return for the upcoming round, based on the count and decision method.
  
  

Using EV and STD, we developed a new formula for generating optimized betting strategies. This formula incorporates three user-defined parameters, allowing the strategy to reflect each player’s risk profile and personal objectives:

• ARI (0–20): The Absolute Risk Inclination, based on the initial bankroll.
  
• RRI (0–20): The Relative Risk Inclination, based on the current bankroll.
  
• TR (25%, 50%,…200%, etc.): The Target Return the player is aiming to achieve in a single session. Once this return is approached, the strategy will scale down bets and ultimately stop once the target is hit.
  
  

The optimal bet per round is calculated as:


Wager(ari, rri, tr) = MIN[0.5 * current_bankroll, (EV / STD) * (ari * initial_bankroll + rri * current_bankroll), 0.5 * (1 + tr - current_bankroll)]


This is the most efficient way to reach a target return TR during a betting session, based on the risk tolerance defined by ARI and RRI, and the chosen DM and BM.

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TESTING

All of our 25,000+ strategies have been tested in millions of simulations across the most common Blackjack variants (currently configurable: ENHC, soft 17, double options, penetration, number of decks, etc.).In the SIMULATIONS section of our site, you can visualize both the density distribution and cumulative distribution of outcomes across up to 10,000 rounds per strategy. These graphs are complemented by tables, performance indicators (EV, median, ROR, etc.), and a real-time simulator that lets you track bankroll evolution under any given strategy.


We’re extremely excited to share this with the community, and we’re here to answer any questions, feedback, or contributions you may have.


BJTHEOREM – https://bjtheorem.com/

[DSchles]

"Without realizing it, months went by, and our codes became more complex, always improving our models but still with room for improvement. Until one day, after almost 2 years of hard work and many challenges, we achieved it: WE BEAT THE DEALER!"

Congratulations on accomplishing something that the rest of the world has been doing for almost 65 years!

Don

[Freightman]

"Without realizing it, months went by, and our codes became more complex, always improving our models but still with room for improvement. Until one day, after almost 2 years of hard work and many challenges, we achieved it: WE BEAT THE DEALER!"

Congratulations on accomplishing something that the rest of the world has been doing for almost 65 years!

Don

I also perused the bullshit. OP would have been far better off incorporating the advanced concepts of the vaunted FBM ASC.

[DSchles]

I've completed reading the whole site, especially the references. No mention, of course, of Peter Griffin. You wonder if they know who he is. In a way, I feel sorry for these people because they obviously have done an extraordinary amount of research and expended a great deal of time and effort ... reinventing the wheel! There is a great irony in the fact that the last person with whom I exchanged several acrimonious emails on this kind of topic was Richard Werthamer, who did exactly the same thing, and seemed incredulous to learn that, well, others had actually dared to think of all of this decades before him. It was if he had crawled out from under a rock somewhere. So, imagine my surprise when, of all the possible experts they could have cited, Werthamer somehow appears on their list. Has anyone else here ever heard of him or, more importantly, give a shit about him?

My dear friend Karel Janecek started out somewhat like this, as well, but was much more humble when I contacted him. He seemed genuinely fascinated by the fact that others had come before him! I wonder what these people would think of the long thread begun here by Eric Farmer in which Cacarulo, k_c, ICountandTrack, and other luminaries have participated.

Don

[Archvaldor]

This looks like AI slop, written in a style which borrows the jargon of existing sources but does not actually mean anything.

[OnlineAP]

Ralph Waldo Emerson said “All my best thoughts were stolen by the ancients.” It is hard to have an original thought about any well-known problem where the solution of that problem yields profits. In science, you might get some credit for publishing work that was done simultaneously with another group that beat you into publication. If you reproduce work from another group after it has become publicly available (even if not formally published), then you generally cannot even get your copycat work published. You are expected to be familiar with all prior work.

It is hard to feign ignorance about a subject that is featured in several blockbuster Hollywood movies.

By the way, 'personally maximizing my winnings' involves largely avoiding the game of blackjack. I doubt this is the kind of advice I would get from a subscription.

[JohnGalt007]

I've also read through the paper and the references (no Griffin? really?), and I'm afraid I have to agree with Don, Freightman, and Archvaldor. Besides a few syntactical idiosyncrasies in the introduction and conclusion that are characteristic of AI-generated essays, there is nothing new presented here. The marketing language and hype in the website is off-putting at best and intentionally misleading at worst. The mathematical models and code are interesting (to me) in and of themselves, but it might not be so to others, and I already know these tools besides.

It's wrong to repackage the old and sell it online as if it was new, especially since a huge body of knowledge is already widely available. It feels like an adamantium-titanium surgical scalpel was crafted and used just to take a slice of butter and slather it on bread, when a simple steel butter knife would do just fine, and then telling the masses that this is the superior way to butter bread. If they had been very clear that that's what they were doing, then I can understand and have a little more sympathy; e.g. "here's a new proof of this theorem we already know is true, and to the best of our knowledge this particular approach is new", or "here's a review of this available literature". But that doesn't seem to be the case here.

[lucas]

"Without realizing it, months went by, and our codes became more complex, always improving our models but still with room for improvement. Until one day, after almost 2 years of hard work and many challenges, we achieved it: WE BEAT THE DEALER!"

Congratulations on accomplishing something that the rest of the world has been doing for almost 65 years!

Don

Hi. That's literally the least important part of the whole site, it was just meant to be a lively introduction. In fact, we forgot to update that section, thanks for pointing it out.

[lucas]

I've completed reading the whole site, especially the references. No mention, of course, of Peter Griffin. You wonder if they know who he is. In a way, I feel sorry for these people because they obviously have done an extraordinary amount of research and expended a great deal of time and effort ... reinventing the wheel! There is a great irony in the fact that the last person with whom I exchanged several acrimonious emails on this kind of topic was Richard Werthamer, who did exactly the same thing, and seemed incredulous to learn that, well, others had actually dared to think of all of this decades before him. It was if he had crawled out from under a rock somewhere. So, imagine my surprise when, of all the possible experts they could have cited, Werthamer somehow appears on their list. Has anyone else here ever heard of him or, more importantly, give a shit about him?

My dear friend Karel Janecek started out somewhat like this, as well, but was much more humble when I contacted him. He seemed genuinely fascinated by the fact that others had come before him! I wonder what these people would think of the long thread begun here by Eric Farmer in which Cacarulo, k_c, ICountandTrack, and other luminaries have participated.

Don

Hi. Your reception of our work does not seem very humble. We are super familiar with the great contributions of others in the field, specifically the contributions of eric farmer and k_c, as they are better aligned with our work. The approach we took was to calculate optimal betting strategies according to the exact composition of the deck prior to the start of each round. For this, it was necessary to compute the return distribution of a round as a function of the policy followed during the round in real time (EV and VAR). Then, based on the distribution for each round, we derived a mechanism to compute optimal bets according to that distribution. With all due respect, your “criticism” literally does not point to anything we have done, and only tries to discredit us by mentioning other names. If you are as interested in the study of the game as we are, we would be happy to discuss our work at a technical level.

[lucas]

This looks like AI slop, written in a style which borrows the jargon of existing sources but does not actually mean anything.

Hello my friend. English is not our native language, and although we speak it, we do rely on AI to translate. Sorry if the text is formatted strangely.

[lucas]

I've also read through the paper and the references (no Griffin? really?), and I'm afraid I have to agree with Don, Freightman, and Archvaldor. Besides a few syntactical idiosyncrasies in the introduction and conclusion that are characteristic of AI-generated essays, there is nothing new presented here. The marketing language and hype in the website is off-putting at best and intentionally misleading at worst. The mathematical models and code are interesting (to me) in and of themselves, but it might not be so to others, and I already know these tools besides.

It's wrong to repackage the old and sell it online as if it was new, especially since a huge body of knowledge is already widely available. It feels like an adamantium-titanium surgical scalpel was crafted and used just to take a slice of butter and slather it on bread, when a simple steel butter knife would do just fine, and then telling the masses that this is the superior way to butter bread. If they had been very clear that that's what they were doing, then I can understand and have a little more sympathy; e.g. "here's a new proof of this theorem we already know is true, and to the best of our knowledge this particular approach is new", or "here's a review of this available literature". But that doesn't seem to be the case here.

Hello friend, first of all thank you for your time. The paper is not AI-generated, but its translation was AI-assisted. However, the paper does not capture the totality of our work, in that we prioritize generating a good product over further iteration of the paper. Regarding your criticism, I think it is not entirely accurate. Our work is new and generates strategies that are superior to the known ones. In particular, we deduce optimal bets according to the exact composition of the deck, which has not been developed by anyone before. For this it was necessary to generate a program that computes the return distribution of each round according to the decision policy (hit stand double split) followed during the round in real time. Each round has an associated distribution. From this distribution and the value of the player's bankroll, the optimal amount to bet prior to the start of each round is then calculated. If you are really interested I will be happy to answer all your questions.

[lucas]

Ralph Waldo Emerson said “All my best thoughts were stolen by the ancients.” It is hard to have an original thought about any well-known problem where the solution of that problem yields profits. In science, you might get some credit for publishing work that was done simultaneously with another group that beat you into publication. If you reproduce work from another group after it has become publicly available (even if not formally published), then you generally cannot even get your copycat work published. You are expected to be familiar with all prior work.

It is hard to feign ignorance about a subject that is featured in several blockbuster Hollywood movies.

By the way, 'personally maximizing my winnings' involves largely avoiding the game of blackjack. I doubt this is the kind of advice I would get from a subscription.

Hello my friend. Indeed there is no point in generating an investigation that has already been done. That is why we have gone further in our research. We calculate the return distribution prior to each round according to the policy used during the round in real time, and bases on the exact composition of the deck. Then according to this distribution and the value of your bankroll we deduce betting strategies optimized for the development of your bankroll over time. Not participating in the BJ is your personal stance haha. All our strategies have positive EV, some even positive MEDIAN.

[Norm]

So, imagine my surprise when, of all the possible experts they could have cited, Werthamer somehow appears on their list. Has anyone else here ever heard of him or, more importantly, give a shit about him?

I'm embarrassed to say Werthamer mentions me in his book's preface.