# Chess Rules Irregularities

What are the consequences of smoothing out some of the irregularities of the rules of chess?

# Metrics for each change

Each change will be evaluated on a few axes:

• depth - how many levels of clearly superior strategy does this game allow?
• resemblance to standard chess
• opening structure/similarity, and if new openings show up
• piece valuation change from standard (1-3-3-5-9-*4)

# Future

To actually get real answers would require setting up a training run for an alphazero like engine based on the modified rules.

## Explanation of strategic depth:

What does the rating structure look like? i.e. tic-tac-toe doesn't have a very deep skill level tree, but chess does. ELO is in some sense an absolute scale; if you define random play as 1000, the higher the best known player's ELO is in this world, the deeper the game.

It's not clear what the result of this is for chess since ELO 1000's definition is not clear, and seems to be linked to the default skill of someone who only knows the rules. This is already a pre-selected group though, so the real depth of standard chess isn't known. Another way to think about this: how many skill levels can a game have, where level 1 is random play, and level N+1 beats level N X% of the time, X>51%). Question: as X varies is it all proportional? Or does choice of X matter? Default to X=75. The existence of draws complicates this, too. Perhaps a better system would be that level X+1 on average receives N points per game against level X, 1>N>0.5. This system is gameable to artificially introduce depth (at the worst, various AIs could communicate their level to each other through hardcoded move patterns, and then just let whoever had the highest level win. But there may still be some value in this as long as the engines aren't trying to artificially introduce levels.

# Main categories of rule variations

I will not explore variations involving more complexity to the rules, new pieces, etc. This comes out of realizing that for the game of go there are almost no meaningful ways to simplify the best rulesets; this process is already done there.

• Conceptual Changes
• Legacy Rules
• Irregularities in Piece Movement
• Board Statefulness
• Board Orientation

# Conceptual changes

## Win by complete army destruction, not king capture

In this variation, the King is just another piece; you win when the other player has no pieces left. This changes stalemate conditions quite a bit. I'd expect a lot of opening changes too since there isn't as much emphasis on king safety. Standard chess is a subset of this, where the game just stops early. What would the king's value be here? According to wikipedia, as a piece its value is approximately 4 due to its strong local area of control. However, that's still based on checkmate rules; in this variation the King's value would be higher.

#### No concept of checkmate. Win condition is now complete army destruction

• depth: You remove mid-game surprising checkmates. Also, a lot of material sacrifices resulting in checkmate are no longer sound. But, you convert a lot of pawnless draws into wins; i.e. N+B vs B is now a win if pieces can be trade off. Overall it's probably a less deep game since there are probably many fewer states that have meaning. I.e. board evaluation functions are simpler to write.
• resemblance: once a king comes off, it's not at all like chess. Also, there may not be much incentive to attack, since the opponent has no particular weak point. Would it devolve into just a series of defensive moves?
• openings: really unclear what good play looks like. The center is still valuable, so maybe there would be a rush to occupy it in order to defend oneself more easily later?
• valuations: king becomes more valuable as a fighting piece

### Self-capture

#### Allow capturing your own army

• description: you can capture any piece on the board which you attack, not just your opponent's. This implies removing the concept of check-mate and making king capture an optional move that's required to win, since the king would start in check.
• depth: You're increasing move options so it may be a deeper game.
• resemblance: Almost all the time it'd resemble chess, but there could be occasional amazing self-capture sacrifices.
• openings: I'd expect very little change
• valuations: When needed, a bishop can capture pawns right in front of it to escape; knights already have the ability to get out without this, so perhaps B would gain value relative to N? Rooks would also have a much easier escape route.

#### Pieces that conceptually attack themselves can capture themselves (commit suicide)

• description: Once you allow capture of one's own army, the next question is whether pieces can capture themselves. In this variation, the Q, B, and R can capture themselves. It doesn't seem reasonable to allow pawns or knights to capture themselves, though. For Kings I'm leaning towards no, since their movement pattern is a vector of length 1.
• depth: more options, more depth?
• resemblance: similar, just with even more surprising self-capture sacrifices
• openings: there may be ones which allow amazing sacrifices, but it's unlikely
• valuations: all pieces other than N & P gain a bit of value since they have more options.

## Allow zero-length moves

Many chess pieces have "infinite" distance capability. I.e. if you put a bishop on a 20x20 board, everyone would assume that it could still move corner to corner. So, it can move any number of squares. But why can't it just move zero squares? Why out of all numbers is only zero excluded?

#### Allow zero-length moves

• description: Q, R, B can also move zero squares.
• depth: I suppose there are more move options, but zugzwang is removed as a concept which reduces strategic options
• resemblance: there might be some changes in endgame situations. It seems more likely to cause more draws
• openings: zero-moves wouldn't be used often, so no change
• valuations:

## Knight movement irregularities

Do knights move 2 squares in one direction, then 1 perpendicular, or the other way around? In regular chess it doesn't matter since they fly over, rather than move through squares. But this flying power is irregular. There are three variations: Knights can move either 2,1 or 1,2 Knighs can move 2,1 Knights can move 1,2

### Knights no longer jump, they move through space like any other piece and can be blocked

• description: knights no longer jump; they move either 2,1 or 1,2 squares. Are there differences among these options? Because they can now be blocked, it matters. In say the 2,1 situation, it's also possible for my knight to attack my opponent's knight, but not be attacked, if there is a piece blocking it. This breaks the normal situation where B,N,R,K,Q are all guaranteed to be mutually attacking.
• depth: hard to tell, really
• resemblance: knights are way less valuable everywhere.
• openings: it's now really hard to develop knights.
• valuations: this kind of knight is definitely less valuable. Unclear which type of knight is better.

## Promotion Changes

The rules around promotion add a lot of complexity to the game; you theoretically need 8 extra queens and every other promotable piece of each color on hand to be truly ready to play any possible game, for example.

There is also an issue with time around promotion - because it's rare and involves moving around off the board, in time-pressure situations it can be hard to resolve. Do you stop the clock while searching for the 3rd queen you just promoted?

This suggests a few simplifications:

#### Disallow promotion

• description: pawns just do nothing when they reach the back rank
• depth: much less depth; most pawn endgames are draws. Game becomes more like shogi where it's much harder to check-mate.
• resemblance: quite different; tournaments would probably have to adjust to lower draw counts, changing play style to a more risky one or reducing time allocations. Also, without promotions, a huge strategic part of the game would be missing.
• openings: giving up pawns wouldn't be nearly as bad; more gambits for attacking chances.
• valuations: pawns worth even less relative to other pieces. Pieces which can mate more easily (Q & R) become relatively more valuable.

### Other forced promotion types

If the mythology of chess supported it, pawns may automatically have promoted to kings, or rooks, or other pieces, exclusively. Rooks wouldn't change things too much, but minor pieces would greatly increase draws and lessen the value of passed pawn defense. Some of these changes make having multiple bishops of the same color much more likely, allowing B-B batteries, which nearly never happens in standard chess.

In Chess's historical context, it seems more natural for pawns to want to become kings than queens. But what do multiple kings mean? Do they compete with the other king? Or are they supporters of his war against the opponent? Can they be independently checkmated? The most natural interpretation seems to be that you lose when all of your kings are captured / capturable. You'd have to allow actual king capture within a continuing game. This is similar to how a campaigning general is effectively the king of his army; but if he dies, the king back in the capital still has power. Loss only happens when all such kings are dead.

#### option to promote to king

• depth: you have more options, having multiple kings greatly increases a single King's value, since it can now expose itself to capture. There could be a whole realm of unexplored strategic positions involving multiple kings.
• resemblance: once the 2nd king shows up, it's very different than regular chess
• openings: not much change

#### forced promotion to queen

• depth: nearly identical since 99% of normal promotions are to Queen anyway.
• resemblance: nearly identical
• openings: identical
• valuations: nearly identical

#### forced promotion to rook

• depth: is this actually less deep? Seems that many endgames that involve both sides promoting to Q now become a lot more interesting (or at least are not quick forced wins)
• resemblance: passed pawns aren't quite as dangerous now
• openings: there may be some change devaluing passed pawns
• valuations: pawns less valuable

#### promotion options are only R, N, or B

• depth: this may actually increase game depth since alternative options would be more worth of consideration. I'd expect players to take advantage of promotion to B or N much more often than they do currently.
• resemblance: endgames would have less emphasis on preventing promotion. Mutual promotion scenarios might be more common.

#### Promotion options: N or B

• depth: endgames don't resolve nearly as easily. Situations where both sides promote now are less likely to be forced wins; On the other hand, players may allow promotions more often and

#### Force promotion to N

With bishop promotion, you'd see more the previously extremely rare bishop battery.

# Legacy rules

### En Passant

#### Remove en passant entirely

• description: ruleset is simpler, with very little other effect
• depth: similar
• resemblance: high
• openings: nearly all identical - a very few lines of theory would have to be changed
• valuations: no expected change

### Castling

Castling involves a bunch of violations of the rules other pieces follow:

• it can only be done from certain squares
• involves two pisces moving at the same time
• ability to do it is stateful

#### Remove castling entirely

• depth: possibly even higher since average game complexity would be higher. but, maybe lower since the king being in the center could cause forcing lines to be easier to find.
• resemblance: it's still chess, but only a subset of games are now possible, involving more intense fighting and risk
• openings: rather large opening change since there's more of a requirement to protect the center
• valuations: rooks probably worth less since they're harder to activate and link

### Make Castling symmetrical

Official castling is arguably as logically complex as another variant, where on the queenside the king moves 3 steps instead of 2. The rule is "king moves til it's next to the rook, rook jumps over it".

#### Redefine castling as "king jumps sideways until next to its rook in the corner; rook jumps over the king

• description: the only change is to queenside castling, making it now go farther and protect the pawn on the last file. Queenside castling might become more common.
• depth: very similar
• resemblance: very similar
• openings: a few would change
• valuations: no expected change

### One-step pawn moves

#### Remove special-case two-step pawn moves

• description: old style chess; pawns always can just move one square a time. automatically removes en passant complications, too. The game would probably be a lot slower.
• depth: You're reducing move choice so it's probably not as deep.
• resemblance: It'd still look like chess, but just slower.
• openings: This would change nearly every opening, but middlegame and later would be nearly identical.
• valuations: Pawns are nerfed so they're probably worth slightly less. Seems harder to break positions up, so knights may gain value since more positions are likely to be closed. In contrast, there will be fewer pawns in the center on average, so piece density in the center might be higher.

# Board Statefulness

Knowing what is legal sometimes requires knowing past moves. That is, metadata about board history is required to know whether certain moves are currently legal.

### En passant

What happens if you remove the statefulness rule of enpassant?

#### En passant is no longer limited to immediately after the opponent's pawns 2-step move; as long as a pawn might have just moved en passant, it can be taken en passant.

• description: not a very good rule since now pawns are even more irregular in how they can attack. There are also some complications where there is a piece obstructing a potential prior 2-step move; if you move your obstructing piece out of the way it might re-enable the opponent to take en passant.
• depth: similar
• resemblance: high
• openings: nearly all identical - although there must be some theory that relies on the one-time opportunity to take en-passant.
• valuations: no expected change

### Castling & Statefulness

There is lots of state here: has the king ever moved? Has the rook ever moved? Do we really gain much by imposing these restrictions? They seem mostly symbolic/historical. i.e. a king can run away easily if his attackers haven't come close to breaching his hideaways yet. Castling requirements which depend on board orientation will be discussed later.

#### Remove statefulness from castling. You can castle whenever your king and rook are in the appropriate positions.

• description: This could introduce some interesting endgame situations; rather than being conceived as a breakable one-time-only plan for a king's escape, castling is now more like a feature of the board, where there's something like a tunnel on the back rank that the king can use anywhere.
• depth: probably similar
• resemblance: rook endgames might change; one player may try to maneuver the situation into one where they can castle. There are some problems where the right answer is castling, which can result in a checkmate or other advantage, but these almost never happen in a real game since it's so easy to make castling unavailable for the opponent. In this variation, there would be legitimate real endgames which rely on setting up a position to castle. I.e. if you are near your own back rank, you might as well keep your king on his original square so that you have more move options.
• openings: ones where one side gains an advantage by forcing the king or rook to move would not be as valuable.
• valuations: rooks and kings gain endgame power so they might be more valuable.

## Board State memory

### 3-fold repeats

This is hard to remove, since infinite repeats wouldn't be detectable.

### “meaningful move history"

I.e. the "50 moves without a capture or pawn move" rule also seems hard to remove, since it opens up infinite repeats or continued play to cause your opponent to flag.

# Board Orientation

Some rules depend on knowing the board orientation. There are two kinds of board symmetry we could remove knowledge of:

• knowing which side is the top/bottom. i.e. allowing pawns to promote on either edge of the board. You often see trick endgame problems where the pieces are laid out to deceive you about board orientation. This happens because the common practice of always having your own pieces at the bottom; in problems you might assume the player "to move" started at the bottom of the board, but that isn't guaranteed.
• more rarely, the board might be rotated 90 or 270 degrees so that the promotion zones are on the left and right.

### Remove board orientation requirements from castling

This means that you can castle on either end of the board. The concept is that the ability to castle is a feature of the board, like a tunnel - from specific starting squares, any pair of K & R can castle. The extension of this, allowing cross-color castling, is infeasible because both before and after castling, the rook always attacks the king.

#### The only requirement for castling is piece position

• description: setting up castling could be done during an endgame
• depth: there are a few more options for endgames now.
• resemblance: opening would be similar, but endgames could be pretty different. A king on his opponent's back rank would now sometimes find it useful to use the opponent's "castling tunnel" during the endgame
• openings: no big difference.
• valuations: rooks & king even more valuable.

### Pawn movement

Out of all pieces, pawns are the only ones where you need to know which way the board is facing to know how they're allowed to move. Legacy chess variants retain this property even for other pieces; i.e. shogi/xiangqi have pieces which require knowing board orientation.

So removing it would imply pawns could move and take both up and down, and could even promote on either end of the board.

Changing this would probably make a huge difference to the game, since you'd be able to move your knight out of the way and then immediately move a pawn backwards to promote.

An even greater change would be to remove the requirement to track which part of the board are the top/bottom vs which are the sides. This would allow pawns to move one square in any direction orthogonally, and attack any direction diagonally; and when they were on a square which could be considered a "2nd rank" they can move two squares towards the center. The problem with this is that the a and h pawns should have already promoted since they start in what could be considered a promotion zone. There are some somewhat consistent rules making promotion optional and available as an instantaneous move during your turn.

#### Remove the concept of vertical orientation of the board

• description: pawns would be able to move up and down, and promote on either back rank. They can also take in both directions now.
• depth: lots of parts of original chess are now gone; most games are a mass of queens fighting. Seems likely that one side would have a strong material advantage after this, so there wouldn't be as much endgame variety. Also, endgames involving pawns would not happen anymore, since the pawns would have promoted.
• resemblance: it'd probably be pretty crazy since most pawns would promote quickly.
• openings: totally different, probably, involving lots of quick pawn promotion
• valuations: pawns are now worth nearly a queen each. Since this change only effects pawns, though, once they are gone it would be normal chess, albeit with lots more queens.

#### Remove all board orientation-specific rules

• description: pawns can take in any diagonal direction, and move any orthogonal direction.
• depth: similar to the above, but with even faster pawn promotion.
• resemblance: totally different.
• openings: totally different
• valuations: pawns even more valuable; but total material value on the board is so much higher that as part of an army, a pawn on its own still isn't worth that much.

# Next steps

## Actually test these

You'd have to write a fast board evaluation function for each rule variation, then train an alphazero like engine. Goal would be to have lots of sample games for each variation, as well as an average of (summed material => win percentages) from random states within those games to reveal piece variation. For openings, you could just compare common variations openings

## Evaluation of the criteria per variation:

• depth: You'd have to have a way to differentially power your ai to find levels such that level N+1 beats level N at a specific rate. But because of the way alphazero-like engines work with a policy network, even with no power behind the value network the level is extremely high.
• resemblance: just compare random positions from variation games with standard chess positions.
• openings: same as resemblance, just focussed on the beginning of the game.
• valuations: from variation positions with known winrate evaluations, sum the pieces on either side and solve to get approximate piece variations. I.e. in regular chess K+P vs K has some low winrate. But if pawns can promote on any board edge, K+P wins at a much higher rate. Cancel the K values to realize that in this variation, pawns are really valuable.