## Sep 19 Using Game Theory in Brazilian Jiu Jitsu.

### Game Theory Basics

Game theory is an incredibly complex field. It’s used in sports, economics, and of course, games. I love games of all kinds. I enjoy thinking about how to play the game in the most efficient, or optimal, way.

Basically, Game Theory (often called GTO or “Game Theory Optimal”) is the science of how humans compete with each other. It’s equal parts probability and psychology. In game theory, you are playing against people. But you also play against the game itself, to exploit flaws in design.

A simple example is Rock, Paper, Scissors (RPS). In theory, it’s an almost completely random game. Each player has three options, each option has a one in three chance of winning. Since each player can choose anything, your best strategy is simply to pick randomly and hope for the best. . .right?

As it turns out, researchers in China got 360 students to play 300 rounds each of RPS. They found that humans did not choose randomly. Players tended to repeat hands they won with, and change the hands they lost with. Thus, a GTO emerged: assume a player will repeat the hand they beat you with and play accordingly. If you are beaten with rock, you should play paper the next turn (there were other GTOs, but you get the point).

Simple, right?

This strategy far from guarantees that you will win best out of three. But the more rounds of RPS you play, the more a narrow advantage will turn into a big statistical gap.

### GTO works best in long, complex games

Simple games, like Connect Four, can be “solved”. That is, people have figured out mathematical solutions. GTO isn’t needed when there are solutions or exploits. Complex games, like Monopoly, cannot. So they need a GTO approach. In Monopoly, for example, you can maximize your chances of winning by buying orange and red properties.

Doing this doesn’t guarantee you win a game, but the more games you play, the more you will be rewarded for playing optimally.

### BJJ is perfect for GTO.

At High Percentage, we already think of BJJ as a game. It has rules, players, resources, and elements of randomness. It’s complex, and in your career you will play the game thousands of times, either training or competing. Just like investing early in your life, training even slightly more optimally early in your BJJ career will snowball into huge advantages later.

### Isn’t BJJ too complex?

No, and I would argue that BJJ is much easier to play optimally than other games at this stage of the sport. BJJ is certainly complex, but so are card games like poker, which people use game theory to exploit all the time. But unlike poker or chess, the game of BJJ has some key differences that open it up for GTO:

### 1) No one has done enough research to find the optimal way to play.

Compare BJJ to a game like, Baseball. Baseball is over 100 years old. It has matured enough that, at a pro level and even an amateur level, organizations know the GTO way to approach the game. Baseball scouts have formulas for determining the value of each player. Unlike BJJ, games are played in a best-of-seven series. This reduces randomness even more. When we watch baseball, we are essentially watching a well calculated battle of math and probabilities play out.

BJJ as a sport is still young. There is not widespread agreement of the GTO approach. Some people feel it’s all about the control game, others favor a singular focus on things like leglocks. We use limited sample sizes and overvalue our own experiences to support our biases.

In fairness, people are starting to develop game theory in BJJ. The most obvious example is John Danaher’s systematized leg lock and back take system, which he has recently made available to the public via his DVDs.

### 2) Players are ignoring optimal play. . .for now.

In any game, there will always be players who are not interested in GTO. When you go to Vegas, for example, the vast majority of players are there to have fun, not use complex strategies to maximize value.

Imagine if you were first baseball GM to incorporate “moneyball theoryyears before your competitors did. You would have a serious advantage for a limited time, until your competitors learned to adopt your approach.

For the time being, BJJ is a game whose players have deeply ingrained biases about correct play. They are very reluctant to change their approach, even in the face of compelling evidence. They will eventually be replaced by a new generation that will embrace new techniques. If you want evidence of this, look no further than the first few UFC events. Royce Gracie had an optimal way to play the game of fighting, so optimal is was practically an exploit. He experienced incredible early success, but new players quickly studied his approach. Twenty five years later, nearly every UFC fighter is playing optimally, with similar skills and techniques.

### 3) Game theory will benefit lower level players the most

At the black belt level, competitors are already playing the game near optimally. We know this because matches are incredibly close. Simple mistakes can blow a game wide open. But the white and blue belt levels are rife with competitors that are playing sub-optimally. Not just in the moment, but where they choose to spend their precious training time, which is where GTO comes in the most. They can beaten, consistently, by players who have a better understanding of the game.

### Where do we start?

High Percentage has a mission: to use science and data to create the game theory behind BJJ. We want new students to have a razor sharp focus on what is proven to be high percentage. We’ll be writing articles periodically about game theory concepts and how we can apply them to BJJ. But most importantly, we will keep gathering data in BJJ matches of all levels to continually refine what we know about the game.