Can You Apply Game Theory to Blackjack?

Pile of Scattered Poker Cards, Casino Blackjack Table
You’ve probably at least run across the term “game theory” at some point. It’s shown up in a lot of different places, from articles of optimal hands in Texas Holdem to the 2018 movie Crazy Rich Asians.

You may have wondered what game theory is and if it’s really as powerful as you would be led to believe. Could it have lead Constance Wu’s character to essentially dominate everyone she played poker or mahjong against? Simply put, game theory is very powerful, maybe not as powerful as it has been shown in the movies, but still pretty cool.

Normally, game theory is shown in head-to-head card games, but I started wondering… Could it apply to other games like playing blackjack? The results were somewhat mixed, but ultimately, game theory can help with blackjack if used properly.

Let’s look at how blackjack can help, understand the obstacles blackjack presents when using game theory and, of course, learn what exactly game theory is.

What Is Game Theory?

Game theory is simply the application of math (technically, “mathematical models of strategic interaction” according to Wikipedia) to the decisions you make.

These decisions including whether you fold or raise in Texas Holdem or, potentially, whether you hit or stay in blackjack.

Game theory applies to more than just poker. It finds its way into nearly every human endeavor from stock trading to police work to poker and, over time, it can produce mathematical models that are really good at predicting human behavior.

However, all of the places that get game theory applied to them have a few things in common. First, they all have at least two players in competition. The rules of the game are mostly clear and players gain a better result for some actions than others.

Limitations of Game Theory

Even though Hollywood would have you believe otherwise, game theory isn’t an all-powerful tool for making perfect decisions. In fact, it requires two things to make it work.

First, you need a lot of data. No one just has a eureka moment and invents a mathematical model describing the perfect way to play US poker games or rule the stock market.

Instead, researchers working on the problem build a model and test it. They learn from their tests, then they refine the model, rebuild it, and test again. After a bunch of iterations, they will then produce either a massive failure or model that might work after it has been vetted in the real world.

Guy Sitting Taking Notes in Notebook, Poker Cards Facing Down on Table

Wait, don’t go anywhere. This only sounds like math class. It’s really poker.

The other thing that game theory needs is a small number of variables (in other words, not a lot going on). In fact, the University of Alberta folks who pioneered a lot of this research are pretty quick to point out their models work best when it’s one-on-one because that’s when the fewest number of things might change.

To bring this point home, people are messy, and if you get a lot of them in one game, they can make game theory’s head spin and leave you looking for other ways to dominate the table.

Why Game Theory Isn’t Optimal for Blackjack

Now that you’re ready to don your cap and gown and earn a degree in higher order mathematics (or not), it’s time to look at why game theory is not optimal for blackjack.

At first, it would seem that blackjack and say, Texas Holdem, are similar enough that if game theory applied to one (Holdem) it would apply to the other. However, there’s something fundamentally different between the two activities and that’s the level of interaction.

In Texas Holdem, there is no house and you’re not playing the dealer. Each player is out to beat every other player in the game to win the pot. Player interaction is assured, thus, the essential definition of game theory is met—two more players trying to get a better result.

Player Interaction in Blackjack

This is not true in blackjack. You can play your entire hand of blackjack and have no interaction with another soul except “hit me” or “stay.” What your “opponent” does—in this case, the dealer—is all mandated by a predetermined set of rules, so there really is no other player to play against.

Two People Sitting at Blackjack Table Grabbing Casino Chips

In some ways, the closest you come to any kind of interaction in blackjack is that the players can affect the outcome of your hand by choosing to take cards or not. However, that’s not the kind of decision that game theory can help with since you have no control over what other players do and you will never have enough information before the round is over on how previous plays affect your hand.

Frankly, if you could model that, you’d have to take into account all previous hands because they all take cards from the same set of decks. That’s not mathematical modeling. That’s card counting.

Why Game Theory Works for Blackjack

Because of everything above, the general theory is that game theory (pun intended) isn’t for blackjack. There’s not enough decision making for game theory to accurately model it.

At the end of the day, I’m just not sure that’s the whole story. We’re not going to arrive at a true mathematical model of blackjack by the time this article is over, but there are at least good arguments that such a model should be able to exist.

How do we know a mathematical model can exist?

Basic Strategy – Blackjack’s Mathematical Model

It’s safe to say that your basic strategy blackjack players aren’t going to get much of a boost out of game theory.

There’s already a mathematical model to follow (basic strategy) that has been shown to produce favorable results in a lot of real world scenarios.

By the way, it should be pointed out that the above statement is not an indictment against basic strategy or blackjack players who follow it. I would advise literally everyone to follow basic strategy, especially in the beginning. However, basic strategy can be spruced up.

Adding More Information to Blackjack

Don’t let anyone fool you (including what I said above). Yes, the house in blackjack isn’t as wily an opponent as those you might meet at a poker table, but blackjack has winners and losers. There’s strategy, and there are things you can do to win or at least increase your chances of getting a better result.

In my opinion, that makes them close enough to a game theory opponent that game theory could apply.  What it’s missing, though, are additional sources of information, which is sometimes called counting cards (though neither you nor I will ever call it that).

We’re just going to track aces, twos, threes, and kings. This is a variation on the strategy that the MIT blackjack team used to win a lot of money from the casinos.

Unfortunately, they were MIT kids and we are not. So, we’re just going to add one for each ace and king and subtract one for each two and three. The higher the number, the less likely the deck is going to produce a higher value card.

Colored Casino Chips and Deck of Cards, Blackjack Table

Of course, now we run into our problem.

We’re still a mathematical model short of true game theory. This means that we have to build a model of when to stay, hit, etc. based on the value of our hand and the number in our head. We then have to convert that model into something that live humans can employ during the heat and emotion of a blackjack game.

Like I said above, we’re not going to solve blackjack and game theory today. I’m merely saying that we can, at the end of the day, inject additional sources of information into what most think of as a system that wouldn’t otherwise support it.

In other words, there’s hope that with a little bit of mind tracking, we can develop a true model (not a fly-by-night system) that will let everyone dominate the poker table.

Conclusion

Game theory is a fascinating topic and a practice that is changing how we’re doing everything, including betting our chips at the poker table. It is somewhat unfortunate that there are not already prevalent applications of game theory to the game of blackjack, but part of that could just be basic strategy’s fault. It’s a good system on its own.

Still, there’s likely a time down the road when brilliant game theorists will look at blackjack and realize there is an untapped source of information that can be fed into a model, whether that’s keeping track of a few cards.

I just can’t wait for that day because then I can say, “I told you so.” Until then, I’ll track the high cards and the low cards and build my own way to succeed at blackjack.