Introduction

Few years ago in the pandemic I was stuck at home with more free time at hands, so I signed up for EDX CS50 course to study artificial intelligence in Python and JavaScript and I wanted to apply the knowledge to some game imitating free style wrestling. I’ve chosen three paths to this AI problem: on one path I compared wrestling to a maze, on another path I compared wrestling to a game of tic-tac-toe and the third path was set to compare wrestling to chess. The first 2 paths led me nowhere. But the third was some success. It took much longer then the cs50 course, and in this article I want to present some results.

I have been wrestling since I was 10, and still do at 54. Many chess players can say the same about their chess biography, but not too many wrestlers stayed on the mat for that long. I come from big wrestling family and with some chess connections. Both of my older brothers wrestled and my oldest brother Sanasar Oganisian won Olympic gold in 1980 in free style wrestling and numerous world and Soviet titles. The older brothers took chess lessons from my uncle Artashes Oganisian, who fulfilled the criteria for Chess Master in the Soviet Union in the 70ies, although he could not confirm it as rules required due to very poor health and remained a candidate master. His youth friends included Yerevan grand masters Rafael Vaganian and others, perhaps they know more about Artashes ability then I remember. Around 15 years old Artashes did tie with Tigran Vartanovich Petrosian in a simul given by Petrosian in Yerevan when he visited Yerevan after wining world title in 1963. And there is a newspaper article highlighting that in family archives. Artash also had a passion for yoga and overall India and spoke about history of chess. So chess was very popular in my family although wrestling was a key passion.

My dad taught chess my kids and then they met a brilliant chess coach in their school. They started winning some tournaments, but I was quite skeptical and discouraging about their chess carriers waiting when they will pick up a passion for wrestling which they also practiced.

With kids I maintained the line that chess is great fun, which they can stay with their whole lives, but there is no need to devote countless hours of practice to chess when they can be outside playing. Still the kids got me involved in chess a little. We frequently went to Moscow chess club on Gogol Boulevard to play blitz and at some point they introduced me to Lichess.

This was around the time when I set the goal to find some connection between wrestling and chess and took the JavaScript course to find some results.

While spending countless hours on lichess I was brainstorming for a wrestling chess connection, playing again and again. So I found some connections and wrote some code to implement it.

I will explain it later in detail

I defined 64 cubes in space by drawing 4 imaginary wrestlers each consisting of 16 cubes which were fixed and there was a strict rule which mapped the cubes to chess squares and which described each of 64 cubes.

For example an A1 square is fixed for white rook, so is A3. A2 square is fixed for white pawn so is a4. A8 and A6 are fixed for black rook and A7 and A5 cubes are fixed for black pawn. If for example a white figure moves in to the space of an black wrestler crossing the 4th rank it should navigate his space in a manner where cubes were defined for black. Test this:

Hands are heavy pieces, play for white and black does random moves
Hands are heavy pieces, play for white and for black
Hands are pawns and legs are heavy pieces, play for white and for black
Hands are pawns and legs are heavy pieces, play for white and black goes random

Freestyle wrestling and chess have a lot in common

Freestyle wrestling and its US version collegiate wrestling are direct descendants of Indian Kushti wrestling or Pehlwani and Persian version Pahlevani wrestling. This is where similarities begin, as chess has both Indian and Persian roots.

An attack in wrestling is initiated with bringing up your arms extending palms, and engaging feet, elbows and knees, controlling opponents neck, shoulders and legs, creating a solid stance and then trying to penetrate inside opponent’s joints to find weaknesses, inaccuracies and waiting for opponents mistakes and blunders. An attack can end in score, or touché it could also lead to steal mate or can cause a counterattack if the opponents’ defense is strong.

Wrestling attacks and moves can be abstractly represented by chess pieces moves on the chess board

I start this research project with the most obvious similarity between chess and wrestling. Wrestling deals with joints of the body. Chess deals with pieces. However I found out that there is a correspondence or a map between chess pieces and human body joints and what is most stunning that the symmetry of the human body is preserved when this map is applied to joints of the human body and corresponding chess pieces.

Correspondence of chess pieces and joints

The figure above shows one example of such correspondence where pawns are hands and heavier pieces are legs, neck and waist. There is another arrangement possible where hands are the heavier pieces and pawns are legs. I will consider it later in the study.

Human body has 18 key joints which are used when a human dances, wrestles or is playing twister. In the two arrangements I described above I only use 16 joints. In the first where hands are the pawns I assume that foot finger and an ankle is just one joint while palm and wrist are 2 separate joints. In the second arrangement where pawns are legs in reciprocity I assume that foot fingers and ankle are 2 separate joints while palm and wrist is just one joint. Both approximations are valid in my view.

4 right pawns are mapped to 4 joints of a right arm, 4 left pawns are mapped to 4 joints of a left arm and more expensive pieces rook, knight and bishop right and left are mapped to leg joints of right and left legs while king is mapped to waist joint and queen is mapped to neck joint. Notice that symmetry of joints is preserved. Right knee and left knee are identical in human body in this mapping they are mapped to bishops which are also identical except they never cross (a very old proverb in wrestling – that knees should never cross). Similarly the hip joints (thighs), knees and feet, right and left are identical and they are mapped to rooks, bishops and knights.

Notice that I in this mapping use joints of the body and not the body parts. But if one is to use body parts, then the mapping is one to one if legs are assumed to be pawns. Foot is a pawn e.g. D and E. calf is a c and f pawns, thigh is a b and g and hips are A and H pawns. Palms are Knights, forearms are bishops and upper arms are rooks. Queen is head and back is the king. So on occasions I will use the joints and bones interchanebly

In the arrangement where pawns are hands - E and D pawns are mapped to palms or hand fingers which are used frequently for wrestling grips.

Wrists are mapped to C and F pawns. Wrists are used in wrestling for making shwoongs keeping pressure on opponent’s neck or shoulders. They are also used for grips. B and G pawns are elbow joints. Which are also used for grips and in some moves or they can be a useful entry for attack or used for defense.

A and H pawns are shoulder joints. They need to be controlled.

There are more ways to map chess piece to joints. Combinatorics of such mappings is complex. In fact later in the study I will learn that perhaps mapping arm joints to heavier figures and leg joints to pawns is perhaps a better mapping for chess wrestling isomorphism. But lets stick to the historic order of events as they occurred in the discovery.

Chess and body symmetry is helping me to map symmetrical pieces to symmetrical joints.

Another note is that degrees of freedom of joints can be used to map joints with similar degrees of freedom chess pieces. But for now I are going to concentrate on that the mapping in the figure above as after several trial and error attempts this mapping seems to make some sense and degrees of freedom also do correspond.

Wrestling and chess similarities at large

I now take a step back to explore further similarities of chess and wrestling.

In the entry paragraphs I explained in wide sketches how freestyle. wrestling match begins with either feet steps or with hand moves. Similarly chess game is started with either knight moves or pawn moves.

An attack in wrestling is started with bringing up your arms extending palms, and engaging feet, elbows and knees, controlling opponents neck, shoulders and legs, creating a solid stance and then trying to penetrate inside opponent joints to start an attack. An attack in wrestling can end in score, or touché. An attack can stall if the opponents’ defense is strong. Be afraid of the counter attack then.

Knight is a foot or knight is a palm?

Knight is one chess piece which can start moving in the beginning of the game and make infinitely many moves. Similarly feet can make infinitely many steps on the wrestling mat avoiding contact with opponent. Palms can also do this.

What are the bishops? Are they knees or elbows?

While feet moves are important for stance in wrestling hands do the initial key work to start penetration into the quarters of the opponent. Waist and neck (or head) are engaged later on when a particular line of the attack is chosen. They are used for defense especially the waist need to be protected.

King is mapped to waist and a Queen is mapped to neck and they are key joints in wrestling. Neck can be used to make duck under and various other leg shoots. I was interchangeably using neck and head in terminology. Waist is so important for practically all wrestling moves. Waist should be protected in every possible way because if you give up your waist to an opponent you will be in big trouble. Because waist is part of the back I will frequently use the word back instead of the waist. But because I concentrate in our mapping of chess pieces to body joints it should be noted here is that when I say back I really mean the waist which has lots of degrees of freedom unlike other body joints. When I say foot I really mean the ankle joint and foot fingers and etc.

In this mapping knees are mapped to bishops (a very old proverb in wrestling – that knees should never cross), but in fact they can cross and even touch each other. In the next mapping that I will consider, where leg joints are pawns and heavier figures are the arm joints, the bishops are mapped to elbows and one knows for sure that no matter how hard you try you can never make your elbows touch each other in their focal points.

Time to show some results

I have used three.js javascript library popular for 3d animations and chessboard.js and chess.js libraries to write code that connects chess moves and human joint moves.

Wrestling space

There are several versions of 3d chess: one is famous Kubikschach which uses 8x8x8 cube for chess space and there is a version with 5x5x5 chess space called Raumschach. There is also Star track chess which uses 64 squares arranged in 3d dspace. Our versions of chess wrestling space also uses 64 cubes. Using the naive approach I organized 3d chess wrestling space into 4 sets of 16 cubes arranged in 3d space.

Each set of 16 cubes is a wrestler shown in the figure below. It is an abstract schematic representation of a wrestler which only shows the body joints. In the middle there is neck and waist or head and back doesn’t really matter how you call it. On the right and left sides there are arms and beneath are legs.

There are 4 such imaginary wrestlers in our space. 2 stand in the initial positions representing chess figures on first and second ranks for white and on the 8th and 7th ranks for black. And they are visible when game starts.

The other 2 wrestlers are placed between the first two by transaltion. So if you move all white pawns on 4th rank and all figures to the 3rd rank you will reconstruct the second white wrestler. These two wrestlers are invisible. But if you move your pieces to where they are, their cubes will start populating with pieces on the move.

Moves in Chess Wrestling

The 64 cubes I defined by drawing 4 imaginary wrestlers in space each consisting of 16 cubes are fixed and there is a strict rule which maps the cubes to chess squares and which describes each of 64 cubes.

For example an A1 square is fixed for white rook, so is A3. A2 square is fixed for white pawn so is a4. A8 and A6 are fixed for black rook and A7 and A5 cubes are fixed for black pawn. If for example a white figure moves in to the space of an black wrestler crossing the 4th rank it should navigate his space in a manner where cubes were defined for black.

Say for example a2 white pawn goes to a3 then to a4 then to a5 and then goes to a6

If a2 pawn is a shoulder, as in the arrangement when pawns are hands. When it goes to A3 it is occupying square on the second imaginary wrestler for white which is fixed for rook a1. So when it move to A3, the shoulder becomes the hip, perhaps shoulder goes down to the level where the hip is. A2 A3 places the A2 pawn on the imaginary wrestler cube fixed for right rook. When it moves to A4 from A3 it becomes again the shoulder joint of second imaginary wrestler for white. When it moves to A5 it becomes the shoulder joint of second imaginary wrestler for black, because a5 square is defined as black’s wrestler shoulder. You can picture that if you imagine that your shoulder is occupying space near your opponent’s shoulder. He could have placed his shoulder in that space, but now he can’t because your shoulder is already occupied it first. When it moves to A6 it becomes the hip joint of a second imaginary wrestler for black because A6 is fixed for black rook which is defined as hip joint. You can imagine that you bent down your shoulder to the level of your opponent’s hip. He could have put pawn A7 onto that cube but he can’t because your pawn (shoulder) is there. But he can use B7 pawn to take your pawn. B7 pawn is elbow in this arrangement. You can imagine that you hook this low hanging shoulder of your opponents which hangs at the level of your hip with your elbow. This grip or hook becomes taking in wrestling and corresponds to taking piece in chess. So the shoulder is no longer important. White wrestler lost control of its right shoulder. It’s been hooked with an elbow, and elbow is directing this shoulder where to move.

This arrangement abstractly resembles wrestling. In the beginning of the wrestling match – two wrestlers are separated by roughly 2 steps. Each can make roughly one step forward without encountering opponent’s body parts. If you make another step forward most likely will be penetrating into the other wrestler space. Your opponent with first moves will come closer to your. After rank 4, you will have to place your arms on another wrestlers shoulders or go for a collar tie or grab his wrists or penetrate with under hook or over hook or take Russian 2 on one or simply start pushing into the chest.

While connection to wrestling is abstract and requires imagination and interpretation. The map of chess board pieces to 64 cubes is a legitimate chess variant and is isomorphic to chess. So you can scrap the board and used the cubes to make chess moves.

You can test the chess wrestling play for white and black

Hands are heavy pieces, play for white and black does random moves
Hands are heavy pieces, play for white and for black
Hands are pawns and legs are heavy pieces, play for white and for black
Hands are pawns and legs are heavy pieces, play for white and black goes random

Mate on f7

By moving pawns and pieces you can try to extend arms and make steps with legs and etc. But one immediate study I want to perform is how mate of F7 corresponds to a lethal attack in wrestling.

I initially arranged wrestlers such that pawns were being arm joints and heavier pieces were leg joints. In that arrangement I found that mate on F7 is difficult to describe in wrestling terms. Because a bishop in this arrangement is a knee joint a knight is a foot and the f7 pawn is a wrist and white queen is neck (head). So if black wrestler is standing straight you can’t use a knee joint or a foot and a head to attack his elbow joint and to cause any damage to black wrestler’s king because you are attacking his hand.

However if you arrange a wrestler where legs are pawns and arm joints are heavier pieces the mate on f7 makes perfect sense. In wrestling it is called John Smith’s low head single shot

You can watch John Smith explaining this shot on youtube

John Smith in wrestling in wrestling is someone like Garry Kasparov or Mikhail Tal in chess or may comparison to Bobby Fisher is even better due to John's ability to win against strongest Soviet wrestlers.

There are different ways to perform this shot. The way John Smith explains it in this video is he uses his right palm which is a knight (in the arrangement where hands are heavy figures) to support an attack on ankle joint and he attacks the ankle joint f7 pawn with his head (queen). In other versions of low single you can use your king size bishop (which is your right elbow) to place it in a position where head attack will lead the opponent lose control of his center of gravity.

But it requires a better interpretation. If you use your king side bishop from h5, the move which Smith showed is possible to do. Because you just lowered you right elbow and can use it to go behind the ankle at the time when you attack the ankle with your head. But if you place your king side bishop on c4 or sort of move your elbow to the left to the level approximately where your left ankle (c4 is fixed for c2 pawn, which is left ankle) is or very low almost on the mat. Then when you jump forward with your head attacking ankle on f7, your right elbow on c4 is coming from left to right in sort of diagonal manner. It is still possible to do such low single shot but just awkward and nobody does it like that.

The left and right hand side of a wrestler also requires interpretation. If king side pawns represent right leg of a white wrestler, the king side pawns of black wrestler represent left leg of black wrestler. Another point is that you can't take heavy pieces with your legs. So pawns can't take heavy pieces but only pawns which represents various leg sweeps and hooks. So placing black king on d file is may be better representation of initital position, and adjusting the rules where pawns can't take heavy pieces (only in very special situations, when defending from leg shots, actualy i used to do it a lot) is also needed.

Coming back to the first arrangement where hands are the pawns and legs are pieces. And if I define f7 and c7 pawns as shoulders (and not the wrists) it is sort of possible to connect f7 mate to a wrestling attack. It is called a wizard in freestyle wrestling or uchi mata in judo.

But the relationship is vague.

In this arrangement the key is the attack by knee joint on space between hips or directly on the waste , lifting the waist up. The head (queen) is not used here. So again a bad connection to chess

Another possibility comes from Sumo wrestling. If you observe how Sumo match starts – you will notice that the first move that sumo wrestlers do is they touch the ground with their knuckles is some sort of ritual. It doesn’t help them with anything (may be I am wrong). But for a moment they become posted on 4 ends like dogs or bears or lions. Imagine that 2 wrestlers start their match like that and remain on their 4 posts to the ground like dogs. Then a similar attack as Smith’s low single is possible to perform on a elbow or wrist of an opponent.

Legs are pawns and hands are heavier pieces

I was trying to look at various abstract possibilities for mapping chess pieces and body joints and the relation where legs are pawns and hands are heavier pieces makes more sense than other maps but the map is still a much open question.

The 64 space cubes arrangement is also an open topic.

What’s a check in wrestling?

For a man to become unstable and lose ground and fall - he or she must be in a state of unstable equilibrium. This is when your center of gravity loses support. When you standing straight the center of gravity is supported with your legs. But when you start moving and say for example you bend forward, then your center of gravity moves away from support, when you post your hands on the ground - center of gravity is supported again, but as you now bent like a horse shoe it is located outside of your body. If a net force acting on your center of gravity is non zero you will be moving.

From the F7 mate example there was no direct attack on the king - the waist but the black wrestler lost control of its center of gravity and had to fall on his butt.

So it is possible to map a check in chess to a state of the unstable equilibrium of a wrestler where he will lose control of his center of gravity or he will give up control of his center of gravity to another wrestler.

In normal conditions no wrestler wants to lose control of his center of gravity. But he may be tricked in to losing this control by very simple threats and tricks.

Say for example you start pushing with your left arm into opponent’s right shoulder, forcing him to move his right leg to step back. The other wrestler lifts his right leg off the ground and is about to post it a step back. But you don’t wait for that and you start pulling his right shoulder towards you where you were previously was pushing it back. The other wrestler’s right leg was about to post a step back and is still in the air. When you pull in his shoulder he has no support anymore and is likely to come off balance and fall on his knees right in front of you or if he manages a big step forward with his right leg he may be in stable equilibrium again. But he will be all exposed to further attacks.

So most likely a check is a state of abstract unstable equilibrium where king the waist where normally center of gravity is located in a man becomes unstable and could fall.

So it is illegal to move your king to the field where your king is checked. If you do such move in chess it is illegal and you will lose your game because you made an illegal move. There are opaque less historical wrestling styles like BJJ or grappling where this is allowed. You can start your match by falling on your back right in the beginning and proceed from there. This is why I concentrate on freestyle wrestling in this article and disregard various other martial arts which deal with submission goals. Free style wrestling is unique style and is a descendant of ancient styles of Kushti, which originated in India approximately at the same time as chess.

If you find yourself in a condition where you can not move your waste anymore this means your opponent controls your center of gravity.

But if you additionally lying on your back and can’t move then you have been checkmated or pinned. Touché.

There are some wrestling tactics however where it is allowed to go briefly off the balance. Just as in chess you may plan on a tactic where you will be checked but will be able to move away from check and execute your tactic.

The mate

The mate in wrestling is touché. It is when you are laying on your back, your opponent has complete control of your back. This is when you are pinned. Your back can’t move. There are no moves left for your back. Opponent’s hands are holding your arms, your neck or your knees or thighs. Your center of gravity is completely made incapable of moving by your opponent joints. The referee checks whether both of your shoulder blades are on the mat and calls it over. Touché!.

It is likely that this additional check of whether or not both your spatulas are on the mat was not part of a rule in ancient times. It is likely that all you had to do is to make opponent lose his ground, take control over his center of gravity. In the mate on F7 example John Smith kind of taken the control over his opponents back. He was pressing with a side of his neck and head on the opponent’s ankle forcing him to fall on his butt. Chess rules call it over. It’s a mate. But in real wrestling with modern rules, the wrestling goes on from that position it is far from over, but on the rules developed so far in this discussion the match should end. It is possible that the opponent prepared previously a room for his back to escape, created other support, or protected his ankle with other pieces like knights for example. John Smith prepared a shot for an ankle but the opponent used his left arm (knight) to prepare to take on Jon’s head or take his knight (arm) out with his arm (night).

The similarities so far

So far I observed the correspondence between chess pieces and body joints. I also noted that the beginning of the wrestling match and chess game is similar. The strategic goals in wrestling and chess are also similar and involve penetration into opponents’ quarters. The goal of a chess game and the goal of wrestling match are also identical and it is to pin the opponent or to checkmate the opponent. Both wrestling and chess (free style wrestling I mean) originated in India at about the same time. The chessboard could be represented by 64 cubes arranged in space to resemble 4 imaginary wrestlers 2 in their initial positions and 2 where the initial cubes translate when an imaginary wrestler moves on step forward.

Further similarities

Exploring further similarities I posit that one chess game is just a very slow version of one wrestling attack. And similarly a wrestling match is number of chess games played between opponents. Some of these games are very short and end in tie. For example in a match two wrestlers make few steps cross their arms and make few grips and then unable to find weakness return to their initial position – this is represented as a very quick chess game where only few pawns have been moved and some heavier pieces got engaged but the opponents quickly agreed to a tie. In the next instance the opponents start from the initial position trying to penetrate or start a more complex attack if it ends in tie again the wrestlers start a new chess game.

But suppose that one wrestler is lucky and starts a complex attack penetrating through opponents defense. This attack represents a sequence of moves by joints of an attacker’s body and a sequence of counter moves by the defendant body joints.

Evaluating stability of center of gravity of a chess positions

Using the tools developed here it is possible to evaluate center of mass and the center of gravity of abstract white wrestler and black wrestler and see how far from the equilibrium they are. It is interesting to see the results and compare it with the position evaluation by the engine. I have not done it yet. But possibly will do it in the future if time permits. This is an idea of evaluating position by geometric and mechanical measures. So you map standard chess position to 3d chess wrestling position, calculate the center of gravity of both wrestlers and determine in what state of equilibrium they are. Whether black are about to collapse.

Promotion of Pawns

The algorithm that I described for chess wrestling board stipulates that all 64 cubes arranged in space are mapped to very specific black or white chess pieces or body joints. So if a white pawn travels to the 8th rank it will become a piece or will stand on a field which mapped to the particular piece. There is some similarity with pawn conversion rules in chess. But perhaps old Indian associations were such that you grow another arm or something to resemble an Indian God or Goddes with multiple arms to aid you in wrestling once you were able to reach the 8th rank.

The chess board, the wrestling mat the Akhara

Kushti is very tightly attached to Indian religion. Akhara in northern Indian villages is a place where wrestling is practiced, learned and taught. It consist of a several mandatory items like water well, some shrines but the central item of the Akhara is wrestling pit. Wrestling Akharas are as old as India itself.

Here is how Joseph S. Alter in his 1992 brilliant book “The wrestler’s body The Identity and Ideology in North India” describes one of the present day wrestling Akhara in northern India:

“The akhara precinct is almost completely shaded by two large trees: a thick, broad nim that hangs low over the pit and a tall pipal that rises above the well. Under the shade of these trees, in the shadow of bazaar buildings, set against the temple skyline, stands the pit. It is the focal point of the akhara complex. Seven by seven meters square and a quarter-meter high, the soft red earth forms a large raised arena. Six cement columns stand at the four corners and at the center of two sides, supporting a tin roof which creates a canopy under the heavy branches of the nim. The columns are thickset, made of poured concrete and painted yellow. Each one is decorated with a mural drawing: a thickset wrestler lifting a nal (stone weight) over his head; another wrestler swinging a pair of joris; two wrestlers locked together measuring each other’s strength; Lord Hanuman flying through the air carrying a mountain in one hand and a mace in the other; Shiva bedecked in peacock feathers holding a flaming jori in either hand. Vases of flowers supported on the backs of jumping monkeys decorate the inner face of the four corner columns. Intertwined blue cobras drinking from bowls of milk are juxtaposed on the center posts. “

The historic Jarasandha's Akhara at Rajgir, mentioned in the Mahabharata.

Here is one possible way that chess was invented

Sarabjit Pahalwan was a great wrestler. He was a very devout believer in Hanuman. He would sit at the akhara temple and worship for two hours straight. He only did 200 bethaks per day but was a great wrestler. He was a Hanuman pujari and from this he derived his strength. He would worship with such feeling that tears would come to his eyes. But one day he fought with a lion in the jungle and the lion bit off his right leg and Sarabjit Pahalwan although he was able to survive could no longer wrestle. This worried and saddened him.

Ananta was a sannyasi a religious guru in Sarabjit’s village, he was a great theoretician of wrestling and a great mathematician as well. Seeing Sarabjit sadness he started to think of an imaginary wrestling system. After 5 years of hard work he finally came up with chaturanga rules and tought it Sarabjit Pahalwan who then became a very skilled chess player and maintained his chess Pahalwan status until his death. The rumor is that he berserked all of his king side pawns in each game to show that he could wrestle with just one leg.

Over the years the original connection of chess and wrestling was lost. But could possibly been reinvented recently.

Krishna and Radha playing chaturanga on an 8×8 ashtāpada

Below are video examples of chess move animations in Blender