The Blackjack Approximator

Author’s Note: This is the second in a series of six articles, each penned by an elite executive at Barona Resort & Casino, which delve into selected cutting-edge business principles and practices that have propelled Barona into being the dominant player in the San Diego gaming market. This article is followed by an in-depth interview with Victor Li conducted by Max Rubin, revealing specific examples of how utilizing “The Blackjack Approximator” will produce measurable results, enhance staff communications and provide for more positive guest experiences.

In today’s rough economic times, everyone is looking for the most value for their buck. This is true of the casino patron as well. All things being equal (which they rarely are), players will frequent the casino that gives them the most comps, the best service and the loosest rules. With the wealth of information available to anyone, in the form of books and movies such as 21, the blackjack IQ of most patrons has increased dramatically over the past decade.

The savvy casino operator can manage to maintain optimal profit levels while offering the best rules on its blackjack games by developing and utilizing a tool that can take the expected values of different guests on different blackjack games and translating those values into easily understood dollar amounts. Then informed decisions can be made to grow and protect the casino’s bottom line. With Barona Resort & Casino’s new Blackjack Approximator, casino executives are able to accurately determine the threat of an advantage player and also calculate the expected value of a below average blackjack player as well.

The concept for the Blackjack Approximator came from the need to deliver more accurate information between the front line staff, such as floor supervisors, who make real-time observations and report their findings to key table game executives so that the ultimate decision-makers can make more confident and informed judgments regarding our guests. After countless hours of trial and error, the aim of translating those visual observations from various evaluators—all subject to different dynamic perspectives—into factually correct and universally understood dollar amounts has finally been achieved.

The Blackjack Approximator is a simple Microsoft Excel-based spreadsheet that takes the observed playing habits of a patron, pulls the data through a series of unseen calculations and outputs two key pieces of information: the expected hourly value of that patron and his or her assessed average bets, as determined by the observed bet spread. This article will highlight how the various components of the Blackjack Approximator work, why its outputs are important to understand, and how it may be utilized to improve both game protection and guest service.

The Blackjack Approximator is composed of two sections: the input/output sheet and the data sheet. Each is further divided into different sections in order to make the program easy to use and even easier to maintain and upgrade. The query-based input/output sheet is meant to be used (and inputted) by the game observer and seen by the end user who is interested only in the final decision-making numbers; the data sheet contains all necessary data to suit the needs of the end user. Now we’ll look at these two sheets and how they work together.

The input/output sheet is the face of the program, and it is the only section that the end user will likely be interested in. The layout is kept clean and minimal. There is an input area for minimum bet and all other inputs, such as game type, bet spread, table conditions and deviations from basic strategy (either in the form of index plays or errors in basic strategy). It is simple and employs the use of drop-down menus that are easy to use and that prevent the user from entering an invalid input. As mentioned earlier, there are only two outputs for the Blackjack Approximator: the theoretical win per hour and average bet. It is interesting to note that theoretical win can be expressed as either a positive or negative number to signify if a patron has a positive expected hourly value or if the casino can expect to profit from that patron. Since the program is used to examine the profitability of a patron, the positive number actually expresses an hourly loss for the casino, whereas as a negative theoretical expresses a win for the casino. The data sheet is the heart of the Blackjack Approximator. It houses all of the data used to arrive at the final outputs. There are four key sections in the data sheet. First and most important is the spread chart. This will generate the base numbers that will be used for the rest of the sections; it is also the only portion that can be reconfigured to suit the user’s needs. There is a different spread chart for each of the blackjack game types available on the casino floor. Each chart has a different spread schedule for different units spread from 1 to 10.

The reason there is a different chart for each game type is because the expected value at each count, and the frequency of each count listed from all negative to counts 0-9 and all counts greater than 9, are different. Therefore, the calculations would not be accurate if they were all treated the same. It is important to point out that all of the game types used for the Blackjack Approximator reflect the games available at Barona Casino.

The spread chart takes the expected value at each count (a negative value denotes a gain for the casino, while a positive value expresses a player edge), and multiplies it through the frequency of each count. This is then multiplied through the spread schedule. While the values for the expected value and frequency cannot be changed, the spread schedule is completely arbitrary (additionally relying upon the correct observations of the floor supervisor to ensure accuracy).

The preset values have been chosen because they present a spread that is both realistic and efficient, with maximum units bet arriving between positive counts of 4 and 5. These values can be reconfigured by the end user to better model a patron who has a different spread. The sum of all the values for each spread schedule, when multiplied by the base unit, will give a baseline expected value in the output box. The next section is the average bet calculator. This is a reworking of the basic spread chart. The EV scale is no longer present, and only the frequency of the count and the spread schedule are multiplied together. The sum of each schedule, when multiplied by the base unit, will give the average bet for the advantage player. Since the average bet data is derived from a portion of the spread chart, any changes made to the spread chart will also affect the calculations for the average bet.

The last two sections of the data sheet are for index plays and mistakes in basic strategy. These two sections are meant for different classes of players—one for the advantage player and the other for the patron who is less than average at blackjack. Since they are not meant to be used in unison, the initial values on the i/o sheet have been set to 0 so they will not interfere with one another. The gain from each play is further correlated with how often the correct count arrives for each game type and how many units should be bet at this count, based on the chosen spread schedule. The gain is also dependent on how consistently each play is used; these have been separated into always, sometimes and never, which translates into a 100 percent, 50 percent and 0 percent gain.

As noted earlier, the initial value is always set at a 0 percent gain. This data will further refine the expected value for the advantage player. The errors in basic strategy section is used to examine the below average blackjack player. I will examine why this is important to the casino executive later. Similar to the indices play section, the errors section lists the top 10 most common errors in basic strategy. These were chosen based both on the frequency in which these hand show up and also historical mistakes that poor blackjack players consistently make.

When using this function, it is important to use a flat bet (1-unit spread), since it would be nearly impossible to accurately predict the playing habits of someone who is not playing with the count. The plays have also been separated into the always, sometimes and never categories, just as in the indices section. These four sections, along with a host of game condition multipliers, such as game speed, make up the data sheet of the Blackjack Approximator.

Having been introduced to the outer shell and the inner workings of the Blackjack Approximator, we will now examine why these numbers are important and how they can be used by the table game executive to protect and grow the bottom line. The two main functions of the program are to better assess the potential damage of an advantage player and also to know a more precise value of a high-end, below-average blackjack player. First, we will look at how the Blackjack Approximator can help protect against advantaged players and aid in being able to distinguish between the truly dangerous ones and those who may be nothing more than nuisances with great advertising value. Second, we will examine how it can aid in making us better able to market to the high-worth patron with less-than-proficient blackjack skills.

As we know so well, card counters are a wide-ranging breed, from the weekend recreational counters who do little damage to the well-banked and well-trained professionals who can really eat away at a casino’s profits. The only way a table games executive can distinguish between the two is to be provided with accurate information as to the players’ theoretical to (or against) the casino. Now, with the aid of the Blackjack Approximator, an executive can assess the potential damage and take appropriate action.

It is important to note at this point that not all counters are bad for a casino. Depending on the size of a casino, the level of action it is willing to take and its underlying operational philosophies, a small-time counter or “grazer” (someone with a theoretical of under $25 per hour) may be viewed as someone doing nothing more than providing free advertisement to the rest of your guests. Others playing on the table with the grazer may view the dealer or table as being lucky and become more frequent visitors, or they might bet more when playing with the particular dealer. The small-time counter may only become a real problem if he begins to teach others his knowledge and skill sets, which diligent observations can detect and curtail if it becomes an issue.

For the more aggressive and better-funded counter, the Blackjack Approximator can provide the table game manager with an accurate number to work from and thus make an educated decision whether to restrict play or to merely stop further comps in attempt to neutralize the threat. Of course, even for a larger more dangerous counter (for example, someone playing at a $500 per hour theoretical), there are many other factors that may affect the final decision of the executive. These factors may include, but are not limited to, the frequency and amount of tokes; relationships with other profitable casino guests; offsetting slot machine play or large amounts of time spent on games such as roulette, baccarat or novelty games; and, perhaps the most difficult to understand and predict, the size of the player’s bankroll … which a wise table game manager should never even attempt to assume.

Card counters notwithstanding, let’s now examine how the Blackjack Approximator can help the table game executive improve marketing abilities by being able the find the players that are worth the most to the casino and comp them accordingly. It might be said that all casino executives love to see a high-worth blackjack player who often varies from basic strategy without rhyme or reason, but until now, all such players were bunched together with a poor rating (at best) and given the same moderate increase in their comp value. With the Blackjack Approximator, the 10 most common basic strategy errors have been calculated into a dollar amount. Since each play has a different value based on the observed playing habits of each patron, over time the casino will have a much more accurate picture of the true worth of that player. With this information, the casino can offer greater up-front comps, promo chips, discounts and other offers to reward that level of play.

The last (and perhaps most important) feature of the Blackjack Approximator is to derive a more accurate average bet for the basic blackjack player. Often, a floor supervisor will see someone betting $100, then glance over and see that same person betting $500. If the process is repeated over and over (which rarely happens), when the rating is finally closed, it would be safe to assume the floor supervisor will enter in a rating between $200 and $300. This figure is often overly generous and can lead to excessive comp value. Using the Blackjack Approximator and choosing the appropriate spread schedule, the casino executive can now arrive at a closer value to the actual average. This number is often significantly less than that of a basic averaged-out bet. For example, someone with a mildly aggressive spread schedule on a double deck game, with a 5-unit spread and $100 base, only has an average bet of $173.51, versus the $250 average that might otherwise have been given. Over time, the difference can lead to significant variance in the comp value earned by the guest and result in your best (meaning most profitable) guests earning the comps they rightly deserve.

The Blackjack Approximator was born out of necessity for an improved level of communication from the front lines of a table games department reaching to the executive suites. The concept of the Blackjack Approximator is very simple: using information that is accessible to any student of blackjack and limiting the users to merely observing and inputting data. It delivers answers that are both accurate and unbiased. It is a program that can be perpetually added to as needed. The information derived from this program will help table game managers make more informed decisions that will ultimately both grow and protect the bottom line and provide better service (and complimentaries) to most of your valued guests.

MR: How long has Barona had the Approximator?
VL: About four months.

MR: How often do you use it?
VL: After a couple of months of beta testing and constantly improving the efficiency, we’re just now introducing version 1.0 to the floor.

MR: How many people know how to use it?
VL: Most of our assistant pit managers, floor managers and some floor supervisors who watch our high-end games know how to use it, and they understand how the numbers are derived.

MR: Are you going to train all of the front line supervisors how to use this?
VL: We only plan on using those floor supervisors who have a clear understanding on how to run down a player.

MR: How many of your floor supervisors can do that?
VL: Virtually all of our floor supervisors who observe our single- and double-deck games.

MR: That’s pretty impressive. What sort of count is built into this thing?
VL: That’s a secret.

 How many floor supervisors at Barona know how to count down a deck?
VL: All of them who watch single or double-deck games—and many who don’t—have the ability to count down a game, and virtually all of our floor supervisors know basic strategy and the concepts behind card counting. Our select floor supervisors know all of the index plays, too. We’re constantly training our floor to improve their effectiveness watching games and being able to evaluate suspected advantage players.

MR: How many APs do you get at Barona?
VL: A lot of our guests understand the concept of high-low cards, but very few know how to use the information and even fewer understand indices. We have a wide range of advantage players, some with very large bankrolls and some who are just grinding. But we’ve been very good at picking off those we feel are a true threat. And, of course, anyone in the Blackjack Hall of Fame or their teammates, and your friends, have agreed not to play here anyway.

MR: Good point. Can all of the pit managers run down a deck in 20 seconds or less?
VL: Yes. They all have that ability.

MR: How do you communicate what you’ve found with the Blackjack Approximator?
VL: The Blackjack Approximator takes words and turns them into solid dollar amounts and allows key execs to make decisions on whether to restrict players. In the past, all they had was a paragraph or two, and now the information is presented in real numbers—and I think numbers speak a lot louder than words.

MR: Spoken like a true engineering major, which I’m told you were. Do some of the results surprise you when looking at the Blackjack Approximator?
VL: Yes, they do, and that comes in two parts. From looking at single to double- to six-deck shoes, both in the hourly EV and what the real average bet is—for example, a one to three spread on a single deck might be profitable for the player, but on our double deck, the player will lose money over time. And that’s easy to see in real numbers. And the real average bets of our recreational players still surprise me.

MR: Why?
VL: Because they’re almost always lower that what I thought they’d be.

So the Approximator works with single, double and six-deck games?
VL: Yes. It works for all the games we offer at Barona.

MR: How?
VL: The numbers work because the data sets have been programmed for all of the game types. And the data includes our penetration for each game, so it perfectly approximates down to the last play a guest might make just before a shuffle.

MR: Did you build this yourself?
VL: Yes, I did.

MR: How long did it take?
VL: Roughly two months. And it’s an ever-evolving product. It’s an ongoing process. But once the skeleton of the Blackjack Approximator is there, it makes it very easy for the end user to modify the data to suit their needs.

MR: Did you get paid extra for building it?
VL: No.

MR: Then why do it?
VL: It’s something that’s beneficial for Barona. It’s an academic tool for me to understand the efficiencies of players and improve the effectiveness of evaluating the worth of potential advantage players or other players earning comps.

MR: How would someone else go about building their own Blackjack Approximator?
VL: They would first have to gather the necessary data, and second they would need a core understanding of how those number have to be put together … (a highly, highly technical explanation follows here).

MR: Whoa! Hold up there. What about normal humans who didn’t go to engineering school? How do we get a Blackjack Approximator?
VL: They can just come to my Blackjack Approximator presentation at CasinoFest in August.

MR: I’m sure a lot of interested folks are going to be at your presentation. Let me know how it goes.
VL: I will.

MR: See you at CasinoFest!

To attend CasinoFest and see Victor Li’s presentation of the Blackjack Approximator, or for more information on the event, visit

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