The creator admits it early on -- it's measuring rarity based on the specific notation everyone uses, which greatly influences the classification of rarity.
Fundamentally all chess moves are a piece moving from one source to another destination including:
- castling as a king move with a distance greater than 1
- pawn moves to the 8th or 1st rank with the additional datum of a new piece
- en passant is the same as a regular pawn capture, it just requires the victim pawn to have moved two squares previously.
Algebraic notation also has an arbitrary and reasonable amount of extraneous detail despite dropping the source location if it's unambiguous.
For example, the captures (x), check(+) and checkmate(#) symbols are all unnecessary given the previous state of the board is always known. With en passant it's also unnecessary to have a special symbol indicating an en passant capture, and indeed there isn't one.
I was initially hoping to get some insight on e.g. which pairs of squares had the fewest moves for a given piece etc.
That being said, I thoroughly enjoyed the video. It was beautifully illustrated and explained everything clearly.
"I was initially hoping to get some insight on e.g. which pairs of squares had the fewest moves for a given piece etc."
This may not be quite what you were asking for, but it's close, and has the advantage that I can link it right now. Tom7's Elo World chess video has where pieces start and end up, and their survival rates, as a chart: https://youtu.be/DpXy041BIlA?si=Zdh6Rh6mekatp2-q&t=815
He did find a move that occurred a single time including the specific game that included it. He also showed many moves that occurred zero times from every single game played on lichess.org.
So, depending on your definition either could reasonably qualify. Which you pick as the rarest is simply an arbitrary definition.
You could consider different notions, but run into the issue of defining what is unambiguous. IE You could say e2 to e4 is unambiguous for a given game state but that would imply game state must be included in the definition for of a move. Defining what the minimum game state is for an unambiguous move would be a video of its own.
What occurred once is not what chess programmers would call a “move”, but rather what chess players would call “move”.
His definition of a move is one ply of algebraic notation. From a chess programming perspective algebraic notation is just a data format and doesn’t have any greater significance.
In programming terms a move is a data structure that allows you to derive one position from another according to the rules of chess.
In Stockfish a move is a 14 bit number, the first 5 bits are the destination square, the next 5 bits are the origin square, the next 2 bits are the promotion piece, and the last 2 bits are the move type (normal, promotion, en passant or castle)
Notating checks is not even redundant; it can disambiguate which piece is to move without additional information (e.g. Rac1 and Rhc1; only one of them might give a discovered check, so Rc1+ could then be an unambiguous notation where the check is not redundant). The PGN spec is clear that SAN disambiguates legal moves and not pieces (if moving one of those rooks would put yourself in check, you should not disambiguate when you move the other one), but I don't know whether it considers the check part of the move for those purposes.
Presumably there are a mind-bogglingly-huge number of unique board state transitions. It's virtually impossible for the same game of chess to be played twice, except for silly scholar's-mate type games. Almost every single game in a chess database will have many unique board state transitions.
It would be fun to have a chess variant where en passant applied to every move:
- you play bishop a3×e7 taking my queen
- I reply with bishop a7×c5, taking your bishop en passant, getting my queen back (your bishop got taken before it reached my queen)
- you reply with knight a4×b6, taking my bishop while it’s on route to intercept your bishop that took my queen. You get back your bishop, it does end up on e7, and I do lose my queen again
- I reply, taking your knight while it moves through a5. Your bishop dies again, I get back my queen.
- etc.
For knight’s moves, I think you’d have to either make a hard rule as to what square they move over, or let the player say how they moved on every move. Also, two pieces could be taken in one move (a piece on the target square and the knight that just hopped over it)
Standard chess already has some of this in the rules for castling. There, you aren’t allowed to move your king through a position where it would be attacked by an enemy piece. That’s like saying it can be taken en passant.
This video is really about the rarest Standard Algebraic Notation (SAN) corner cases, which is more than a little different from rarest moves. But the author basically acknowledges this, and 'rarest moves' is so hard to really define anyway. So kudos it's otherwise a great video.
I'm about equally impressed with the statistical analysis and the video construction and presentation. I can imagine tackling the former, but not the latter. I did notice a few mistakes in the video presentation though (eg a Bd4# that he presented as Be4#). I imagine at some point he just thought "I've polished this thing enough" and stopped.
Interesting, but I initially expected this to be about the unusual opening employed to victory by Magnus Carlson against Kacper Piorun on May 7, 2024[1] (1. a4 e5 2. Ra3).
It's even more interesting because an unknown IRL Chess.com player named Viih_Sou (since revealed to be Brandon Jacobson[2][3]) used this opening to defeat Daniel Naroditsky on May 2, 2024[4] only to be subsequently banned for violating the Fair Play Policy[5].
Why would that be the rarest chess move? It's a pretty common way to try to start a chess game, so much so that kids have to be taught not to do it because it's flat-out terrible.
I just want to say that the format of this video is beautiful and easy to follow along. A topic that is easily boring and dry is presented in a way to keep the viewer interested
The problem is that there must be hundreds of ways to describe "a move" from the complete board state before and after to the distance that the piece moved (moving moving a bishop and queen 2 diagonally is the same move).
So while I agree that the notation is pretty arbitrary and puts lots of emphasis on how implicitly a move can be recorded I don't think it is fundamentally worse than any other definition. Yes, personally I would have picked something more directly tied to the game than if the notation requires more disambiguation, but I don't think it really makes the video any less interesting or the result and less useful (probably no use either way).
Agreed. Just the notion of double disambiguation is meaningless to a chess player who doesn’t use the notation. This is fundamentally not about chess. But about one particular way that certain people use to write down chess moves.
Another count against statistically analysing SAN strings to death is some of the rules of that format. There's a lot of weight given to disambiguation in this video. In SAN you must not (if you're following the rules, some software including ChessBase doesn't follow the rules) disambiguate if one of the pieces is pinned to the king. So 1.d4 e6 2.c4 Bb4+ 3.Nbd2 Nf6 4.Nf3. Not 4.Ngf3.
This muddies the waters I think, these doubly disambiguated moves he lovingly isolated would be recorded differently if a marginally involved piece was pinned.
More significantly, there's no SAN notation for stalemate, or en-passant (or many other things of course) of great chess significance, perhaps more worthy of analysis.
The video was still a great technical achievement, and very entertaining for a chess nerd like myself.
You’re welcome to scan the game archives to determine the actual game state and find the case where someone had three Bishops on the same color, positioned in three corners of a square, moved one to create a discovered checkmate, but the move was notated without disambiguation because the two other bishops were pinned.
The problem with using a dataset consisting of all games on lichess.org is that most/all instances of these moves are most certainly from people who are trying them out in a noncompetitive game just to see what happens. In fact he himself likely polluted the data further just to make this video, maybe even enough to change the answer.
There needs to be a minimum bar for the data to be meaningful, e.g. by restricting to players above a certain rating threshold, or considering tournament games only.
I don't think including "noncompetitive" games is an issue. For a game with so many possible states, it only makes sense to ask about what moves have been played at all, and not the context that these moves were played in.
Plus, restricting the dataset introduces more biases and ambiguities. What exact ELO should be "good enough" for consideration? Why not a point higher or lower? Should they have accounted for time control too, because people in speed chess play worse and can get into weird situations they otherwise wouldn't have been in?
He stated that he tried using master tournament games but the dataset was way too small.
But yes indeed, the single example game he showed was indeed a result of the winner playing very silly moves and the loser allowing it rather than resigning.
In bullet games at Lichess it is not that uncommon to play on lost positions to try to either flag the opponent or to offload as many own pieces as possible to seek a stalemate with the frenzy. Conversely, the winning side then tries to delay the win by promoting a bunch of unneeded pieces and sort of demonstrating who is really in charge. It’s even fun.
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Fundamentally all chess moves are a piece moving from one source to another destination including:
- castling as a king move with a distance greater than 1
- pawn moves to the 8th or 1st rank with the additional datum of a new piece
- en passant is the same as a regular pawn capture, it just requires the victim pawn to have moved two squares previously.
Algebraic notation also has an arbitrary and reasonable amount of extraneous detail despite dropping the source location if it's unambiguous.
For example, the captures (x), check(+) and checkmate(#) symbols are all unnecessary given the previous state of the board is always known. With en passant it's also unnecessary to have a special symbol indicating an en passant capture, and indeed there isn't one.
I was initially hoping to get some insight on e.g. which pairs of squares had the fewest moves for a given piece etc.
That being said, I thoroughly enjoyed the video. It was beautifully illustrated and explained everything clearly.
This may not be quite what you were asking for, but it's close, and has the advantage that I can link it right now. Tom7's Elo World chess video has where pieces start and end up, and their survival rates, as a chart: https://youtu.be/DpXy041BIlA?si=Zdh6Rh6mekatp2-q&t=815
So, depending on your definition either could reasonably qualify. Which you pick as the rarest is simply an arbitrary definition.
You could consider different notions, but run into the issue of defining what is unambiguous. IE You could say e2 to e4 is unambiguous for a given game state but that would imply game state must be included in the definition for of a move. Defining what the minimum game state is for an unambiguous move would be a video of its own.
His definition of a move is one ply of algebraic notation. From a chess programming perspective algebraic notation is just a data format and doesn’t have any greater significance.
In programming terms a move is a data structure that allows you to derive one position from another according to the rules of chess.
In Stockfish a move is a 14 bit number, the first 5 bits are the destination square, the next 5 bits are the origin square, the next 2 bits are the promotion piece, and the last 2 bits are the move type (normal, promotion, en passant or castle)
I'd imagine remarkably foolish moves from board states that only quite sophisticated users would get to would be up there
- you play bishop a3×e7 taking my queen
- I reply with bishop a7×c5, taking your bishop en passant, getting my queen back (your bishop got taken before it reached my queen)
- you reply with knight a4×b6, taking my bishop while it’s on route to intercept your bishop that took my queen. You get back your bishop, it does end up on e7, and I do lose my queen again
- I reply, taking your knight while it moves through a5. Your bishop dies again, I get back my queen.
- etc.
For knight’s moves, I think you’d have to either make a hard rule as to what square they move over, or let the player say how they moved on every move. Also, two pieces could be taken in one move (a piece on the target square and the knight that just hopped over it)
Standard chess already has some of this in the rules for castling. There, you aren’t allowed to move your king through a position where it would be attacked by an enemy piece. That’s like saying it can be taken en passant.
I'm about equally impressed with the statistical analysis and the video construction and presentation. I can imagine tackling the former, but not the latter. I did notice a few mistakes in the video presentation though (eg a Bd4# that he presented as Be4#). I imagine at some point he just thought "I've polished this thing enough" and stopped.
You'd probably need 15 orders more magnitude of data to get there, but the definition itself is pretty straight forward.
EDIT: so you could define "rare" moves as the biggest difference of occurrences between state N and state N+1.
This would include not only the board state, but all the moves made up to reaching it.
It has a useful meaning for openings.
But it is so sparsely populated by actual games that "rarest" becomes too easy - many moves have been made only once under this definition.
It's even more interesting because an unknown IRL Chess.com player named Viih_Sou (since revealed to be Brandon Jacobson[2][3]) used this opening to defeat Daniel Naroditsky on May 2, 2024[4] only to be subsequently banned for violating the Fair Play Policy[5].
[1] https://www.chess.com/analysis/game/live/108840009759?tab=re... [2] https://www.reddit.com/r/chess/comments/1claxsm/its_me_viih_... [3] https://en.wikipedia.org/wiki/Brandon_Jacobson [4] https://www.chess.com/analysis/game/live/108394316331?tab=re... [5] https://www.chess.com/blog/Utkarsho/a-grandmaster-account-ge...
I feel like the question remains unanswered
So while I agree that the notation is pretty arbitrary and puts lots of emphasis on how implicitly a move can be recorded I don't think it is fundamentally worse than any other definition. Yes, personally I would have picked something more directly tied to the game than if the notation requires more disambiguation, but I don't think it really makes the video any less interesting or the result and less useful (probably no use either way).
This muddies the waters I think, these doubly disambiguated moves he lovingly isolated would be recorded differently if a marginally involved piece was pinned.
More significantly, there's no SAN notation for stalemate, or en-passant (or many other things of course) of great chess significance, perhaps more worthy of analysis.
The video was still a great technical achievement, and very entertaining for a chess nerd like myself.
Rarestest move for sure.
There needs to be a minimum bar for the data to be meaningful, e.g. by restricting to players above a certain rating threshold, or considering tournament games only.
Plus, restricting the dataset introduces more biases and ambiguities. What exact ELO should be "good enough" for consideration? Why not a point higher or lower? Should they have accounted for time control too, because people in speed chess play worse and can get into weird situations they otherwise wouldn't have been in?
But yes indeed, the single example game he showed was indeed a result of the winner playing very silly moves and the loser allowing it rather than resigning.