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Understanding Objectives in BJJ (Brazilian Jiu Jitsu Game Theory)

Updated: Nov 15, 2023

The BJJ Game

Brazilian Jiu-Jitsu (BJJ) is a contact sport where two players compete against each other in a manner that is like the game of chess. Although it is a contact sport, there is no striking involved, and winning a match relies on factors that are parallel to the factors in chess. Applying wedges, leverage, and weight distribution using parts of the human body in BJJ is akin to applying the same concepts using chess pieces on the chessboard.


At the novice level of the BJJ game, a player often wins by having more athleticism, more knowledge of techniques, and better instincts in exploiting mistakes. Similarly, in novice levels of chess, a player wins by having more knowledge of techniques and better instincts for exploiting mistakes.


However, at advanced levels in BJJ, the ways of winning at the novice levels are harder to come by because the players are approximately equal in athleticism and technical knowledge, and they tend to make very few mistakes. Thus, like in chess at advanced levels, winning in BJJ at advanced levels requires well-played strategies in the opening game, middle game, and end game.


It's recommended that you have this article on the glossary of jiu jitsu terms open while you are reading this article.


teen applying bow and arrow choke in bjj competition
Bow and Arrow Choke

Primary and Secondary Goals

The primary goal of each BJJ player is to get the opponent to declare a submission, just as a chess player aims to put his opponent into “checkmate”. The most prevalent way for a BJJ player to indicate his defeat is to do something called tap out. When a player cannot continue the match because he becomes unconscious due to the application of a submission, the referee will declare a submission on behalf of that player. Once a submission is declared, the match ceases and the winning player must immediately let go of any submission hold.


As a secondary goal, each BJJ player aims to earn more points than his opponent in case the match timer runs out and the match ends without an early defeat (by submission or disqualification). Throughout the match, the referee awards points to a player for specific actions that progress the game in his favor. The player with the most points wins if the match ends with no submission. If both players are tied in points at the end of the match, then either the referee decides the winner, or the match goes into overtime, depending on the rule set used for the match.


Importance of Positions in BJJ Game Theory


woman applying bjj paper cutter choke from side control top position
Paper Cutter Choke from Side Control

Establishing Top and Bottom Positions

A BJJ match can progress once both players’ positions are established. There are two main positions in a BJJ match, top position and bottom position. A player can assume only one of these positions at a time. Only one player can have top position, and only one player can have bottom position. A player can actively attempt to assume a position, but he is not guaranteed his desired position if the other player wants the same position. As soon as one player establishes bottom position (either voluntarily or by being forced there by the other player), the other player assumes the top position by default.


Awarding Points based on Top and Bottom Positions

The only way for either player to score points is for the players to establish top and bottom positions. Therefore, it is very important (and strategic) for each player to know what position he has so he can predict how many points he can score.


Before awarding points to a player, the referee must know which position that player had at the time of the point-scoring action. A player’s position determines which of his actions will score points and how many points will be awarded. The referee is responsible for tracking which player has which position so that he can accurately award points. This means that the players’ positions are very important to the referee in determining the winner if there is no submission achieved.


Using Dominant Positions to Advance

A player with a dominant position allows him to easily progress to a submission hold, because it is achieved by passing the opponent’s guard. A dominant position can be entered from either bottom or top players. A player who achieves a dominant position can be awarded points, depending on the rule set.


Progressing in the Bottom Position

For the bottom player to progress, he can:

  1. Achieve Guard. If the bottom player is under the top player’s dominant position, he can attempt to establish or re-establish his guard. Although achieving guard will give a bottom player a higher chance of submitting his opponent or scoring points, the action of achieving guard itself usually does not score any points because it is considered a defensive action.

  2. Reverse the positions. If the bottom player has guard at the time of the reversal, he is considered to have performed a sweep, and points are awarded in most rule sets. If the bottom player does not have guard at the time of the reversal, he usually receives no points. No matter how many times a bottom player gets onto his knees, or how long he stays on his knees, he is still considered the bottom player if his opponent has not been seated.

  3. Submit the top player. The bottom player can achieve a submission, which ends the match. Although it is more common for a guard player to be able to submit the top player from within his guard, the bottom player without guard can also submit the top player.

  4. Reset the positions. If the bottom player chooses to stand up onto his feet and his opponent also stands onto his feet, and both remain standing for 3 seconds or more, the positions become vacant where neither player has top or bottom.

Progressing in the Top Position

For the top player to progress, he can:

  1. Pass the bottom player’s guard. It is difficult for a top player to submit the bottom player when the bottom player has guard. Thus, the top player usually attempts to pass the guard.

  2. Submit the bottom player. The top player has an easier time submitting the bottom player once he has passed the bottom player’s guard. The top player can also attempt to submit the bottom player from within the guard, although submissions under these conditions are uncommon.

  3. Yield top position. If the top player sits down onto the mat and allows the bottom player to come onto his knees or feet, he is yielding the top position. If the top player has not yet passed the bottom player’s guard at the time he sat down, and he allows the bottom player to quickly assume top position, a sweep occurs, and the new top player will be awarded points for the sweep. No matter how many times or how long a top player sits down, he is still considered the top player until his opponent gets up from the seated position onto his knees or feet to establish the top position.


When positions have not been determined

When both players are reset to standing, the top and bottom positions are not determined. This happens on 3 occasions:

  1. At the start of a match when both players are facing each other on their feet. The top and bottom positions are established only when one player pulls guard or a player performs a take-down on the other player. The top and bottom positions are not determined when both simultaneously sit down to assume bottom position, which is known as double guard pull.

  2. When the bottom player stands up onto one or both feet (usually for a minimum of 3 seconds).

  3. After a referee reset when both players were ordered to stand up after a time out during the match.


girl and boy start standing in bjj match
BJJ Match Starting in the Standing Position

A submission is hard to achieve when both players are standing, or when both players are on their knees. Also, points cannot be awarded unless the positions have been determined. Thus, for the game to progress from standing, the players need to establish their roles either by pulling guard or by taking down the opponent.


Importance of Positions in Training Matches

In a BJJ class where mat space is too limited for standup scuffles, BJJ practitioners often start on their knees instead of on their feet. Training in a practice BJJ match is often known as rolling or sparring.


During a roll, the primary goal varies for each player, depending on what he is working on within his training regimen (e.g., developing a submission technique, refining strategies, developing a sequence, etc.). In any case, players should get in the habit of realizing who has what position at any point during the roll to help them understand what’s required to progress the game.


In BJJ classes, instead of rolling, students are often asked to play the game of “sweep or pass.” This is where the players’ positions are predetermined, and no submissions are allowed. When the option of a submission is taken away from the game, then the only actions that will progress the game are for the bottom player to sweep the top player, or for the top player to pass the guard of the bottom player. The game of “sweep or pass” helps to develop the BJJ practitioner’s skills in getting to the submission hold, instead of focusing on submission techniques.


Rule sets without points (Submission-only rules)

There are many rule sets that do not award points, so the position of either player does not directly determine the winner if there is no submission. In this case, the positions only matter strategically for setting up a submission, and neither player is rewarded or penalized for achieving a dominant position.


In many Submission-only rules sets, the only way to win is to submit your opponent. Both players lose if there is no submission, which encourages the players to actively pursue submissions regardless of their position.


Some Submission-only rule sets allow for the referee to determine the winner if there is no submission. This can result in a player’s position mattering, because his ability to aggressively pursue submissions usually depends on his position. Also, sometimes the referee selects a winner simply based on how long a player remains in a dominant position.


Leg Entanglements

A popular type of rule set for No-Gi BJJ matches is one that favors battles of leg entanglements. This type of rule set allows for knee reaping9 and heel hooks. For No-Gi matches where the players tend to be more advanced, knee reaping and heel hooks add more attacking options but require more understanding of how to navigate leg entanglements. Adding knee reaping and heel hooks induce battles that are centered more around strategies for leg entanglements than around strategies for sweeping and passing the guard.


man applies belly down footlock to grimacing opponent
Belly-down Footlock

Maintaining a submission hold while in a leg entanglement is usually achieved by a seated player, regardless of his assigned position of top or bottom. Quite often when the legs are entangled, both top and bottom players end up in the seated position. If the match does not use points, the top and bottom positions don’t matter because both players in a leg entanglement have opportunities to submit his opponent, and the player who has the better strategy for leg entanglement often gets the submission. If the match uses points, the top and bottom positions matter only if there is no submission by the end of the match.


Conclusion

In conclusion, BJJ is generally a game where the players vie for a position that prevents the legs of the other player from impeding access to a submission hold. Although the primary goal of a match is to achieve a submission, it matters greatly if a player can prevent his opponent from using the legs to impede a submission hold.


The top player usually needs to pass the legs of the bottom player to achieve a submission. Thus, the main goal of the top player who is not in a dominant position is to pass guard of the bottom player so that he can secure a dominant position.


The bottom player who has guard can easily use his legs to prevent the top player from getting a submission, while having easy access to submission holds of his own. In essence, the guard player can be considered to have passed the guard of the top player by the nature of having guard from the bottom position. This is why it is common for bottom players who have guard to get submissions.


A player normally prefers either the top or bottom position when it comes to executing submissions. If a player who prefers the top position ends up being in the bottom position, it is common for him to attempt to sweep the top player, then pass the guard to set up his attacks. If a player who prefers the guard position ends up in the top position, it is common for him to attempt to pass the guard then yield the top position before setting up his submissions.


Some players prefer submissions from the leg entanglement, so it does not matter to him whether he plays top or bottom position because he can be seated in a leg entanglement from either top or bottom position. Thus, the standard BJJ game theory still apply when knee reaping and heel hooks are added to the rule set because the game is still about preventing the legs of the other player from impeding access to a submission hold. However, submission techniques with knee reaping and heel hooks allowed are abundant while the legs are still entangled, whereas submission holds where knee reaping and heel hooks are not allowed usually require the legs of the players not be entangled.

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