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The rarest move in chess [video]

183 points18 hoursyoutube.com
shric16 hours ago

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.

jerf16 hours ago

"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

Retric15 hours ago

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.

zarzavat7 hours ago

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)

maverwa4 hours ago

I was wondering on how Stockfish encodes the destination and origin square in 5 bits each. I think they don't, at least the code on github uses 6 bits each, which actually gives you 64 possible values, so works out fine:

https://github.com/official-stockfish/Stockfish/blob/master/...

Thats 16 bits. Thank you for sending me down that (small) rabbit hole!

zarzavat2 hours ago

Yes you are correct, I had 2^5 = 64 in my head for some reason.

anikan_vader15 hours ago

Some sources do write ep after en passant captures. As you point out, it’s no more redundant than notating checks.

Sesse__14 hours ago

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.

yunwal14 hours ago

I see what you mean obviously, but neither of those moves could possibly give a discovered check, right? If the rook starts in the corner of the board, nothing can hide behind it or attack from behind it.

Sesse__6 hours ago

Point, I should have written Rbc2, not Rac1.

kristopolous16 hours ago

Right, you'd need to look at board state transitions as opposed to move notation.

I'd imagine remarkably foolish moves from board states that only quite sophisticated users would get to would be up there

SamBam11 hours ago

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.

bobmcnamara16 hours ago

Funny enough, en passant is the only capture that takes a piece not in the destination square.

Someone3 hours ago

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.

Dylan1680715 hours ago

That's arguable. The motivation for the rule, and especially the name of the rule, suggest the pawn is not all the way there yet.

CrazyStat15 hours ago

In what sense is the pawn not all the way there? It occupies the square, prevents any other piece from occupying the square, can deliver check or checkmate from the square, and can be captured on the square.

+2
Someone15 hours ago
+1
Dylan1680715 hours ago
billforsternz14 hours ago

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.

kristopolous13 hours ago

Rarest I think is pretty easy. It's just board state transition.

You'd probably need 15 orders more magnitude of data to get there, but the definition itself is pretty straight forward.

incorrecthorse3 hours ago

Board state itself becomes unique pretty quickly, so you would just end up with a gigantic lot of "moves" played only 1 time.

EDIT: so you could define "rare" moves as the biggest difference of occurrences between state N and state N+1.

philipswood9 hours ago

Thinking about it, one could also have a canonical state transition based on the game state transitions.(i.e. expand the game tree).

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.

kristopolous7 hours ago

You don't need to know anything before. Game theory has a word for this type of game called "perfect information"

https://en.m.wikipedia.org/wiki/Perfect_information

It might be interesting, but the previous board state should not be a relevant factor when considering rarest move

mrslave11 hours ago

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].

[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...

animal5311 hour ago

It's been a long time since I've last played chess, but I've really enjoyed Anna and her mum Pia commentating on each other's games recently.

Props to them and all the other chess creators for bringing more influence and people to the game.

venusenvy4747 minutes ago

I prefer Gotham Chess. He analyzes recent games and makes it exciting with the way he vocalizes his descriptions. https://youtube.com/@gothamchess

alberto_ol1 hour ago
xyst13 hours ago

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

groggo12 hours ago

Yes, the text bothered me a little once I noticed it though. It's just moving a tiny bit, not necessary.

kristopolous16 hours ago

His definition of rare is an artifact of the notation where board state requires disambiguation, as in it includes externalities.

I feel like the question remains unanswered

kevincox2 hours ago

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).

munch1176 hours ago

Kinda misunderstands algebraic notation: You are by no means required to use the minimal unambiguous notation. In fact, the canonical form is something like "Ng1-f3". "Nf3" is a context-dependent abbreviation of that.

Dig up an old chess book if you don't believe me. You'll find books that only use the long form.

dh56 hours ago

Notation has changed over the years. Even twenty years ago you could pick up (admittedly dated) books using descriptive notation (e.g. P-K4). It's pretty clear what is the accepted standard for notation today though.

paxys16 hours ago

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.

tavavex11 hours ago

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?

shric15 hours ago

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.

antaviana15 hours ago

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.

shric5 hours ago

Yes, I've done it many times!

At the time of writing based on total games played at https://database.lichess.org/ one in every 272,369 games are mine :p

elijahbenizzy15 hours ago

This is delightful. I think that the hardest part (that, honestly, he absolutely nailed) is defining "rare" and "move" -- not only did he come up with reasonably satisfactory definitions, but he also was able to walk us through his discovery process.

The rest is a fun programming problem (which he largely glossed over), and it's clear he put a massive amount of care into the video. Thank you!

alberto-m4 hours ago

Chess historian Tim Krabbé ran an analysis with a different notation, using an extended algebrical system (start and end square + kind of captured piece, if any). Here his results: https://timkr.home.xs4all.nl/chess2/diary_6.htm (entry 105).

His site is a trove of information for people liking chess trivia.

bmacho4 hours ago

tl;dw

Creator of the video uses the standard chess notation, which encodes if a move

  - is a capture
  - is a check
  - is a checkmate
  - needs a disambiguation
  - and other things
It is arguable how much the rest of the board is part of a move (see the current top comment), but let's say moves are different if their standard chess notation is different.

Then it turns out that bishop double disambiguation moves are very rare. They require 2 same color bishop underpromotion for the start. And they doing captures and/or checkmates are even rarer. A lot of them never ever happened on lichess.

That's about the content. Now about the format.

The video features hands expressive hands all along, which makes it stimulating to watch. If you are into presentation, go and check it out.

billforsternz14 hours ago

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.

jameshart14 hours ago

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.

Rarestest move for sure.

billforsternz11 hours ago

Well, only one of the other bishops would have to be pinned else single disambiguation would do, but otherwise - fair point!

thih916 hours ago

A different take on rare chess moves and perhaps more rare than what is presented in the video: https://en.wikipedia.org/wiki/Joke_chess_problem

pimlottc14 hours ago

The game and move in question is here: https://lichess.org/NoXEwGi8#136

yunwal13 hours ago

I wonder if the winner was specifically going for wacky notation when he played that, or just going for a crazy checkmate.

pimlottc11 hours ago

I wonder too, if the first promotion had been a queen (or a rook), that would have been checkmate right there.

kevincox2 hours ago

Yup. They were clearly not "playing seriously". They had a few obvious opertunities to win that they didn't take to get an odd checkmate in the end.

none_to_remain15 hours ago

Do chess players actually consider this "double disambiguation" from the notation to be a different "move"?

bongodongobob14 hours ago

No.

bitcurious15 hours ago

Fun video. An interesting follow up would to do this would be to ‘disambiguate’ every move, such that a move was a single piece’s movement and reflected less of the state of the game.

CalChris16 hours ago

Did he include under-promotion captures resulting in zugzwang? If you’re not including zugzwang then you shouldn’t include checks and mates. The problem becomes a lot simpler.

yunwal13 hours ago

Zugzwang has no notation. The author states in the first 2 minutes or so that the video is about the rarest edge cases in notation.

CalChris13 hours ago

Nf3 can be ambiguous but resolved by the position itself. That ambiguity has no notation either.

FWIW, I wrote the XBoard PGN parser.

mathgradthrow12 hours ago

parent is referring to stalemate. Underpromotion to a bishop to achieve stalemate was my guess for rarest, since you can always stalemate with a queen just as well as a bishop, so theres no reason to underpromote if you goal is a draw on the turn in which the promotion occurs.

mehmetalianil14 hours ago

I find it odd that now that this video is out, all of these moves will be executed and it will be impossible to know for sure anymore.

ViktorRay17 hours ago

This video is excellent. It’s one of those videos that will become a classic of YouTube in the future. The kind that’s recommended to millions of people

hoseja5 hours ago

Chess dot com needs to release the data.

pbj196812 hours ago

DAE learn about castling from Battle Chess?

skilled16 hours ago

Watched this earlier today myself, fantastic work by the author.

AnimalMuppet16 hours ago

"doubly disambiguated bishop capture checkmate"

It's a 30 minute video. If you care that much about the topic, enjoy. If you just wondered what the move was... you're welcome.

f154hfds16 hours ago

It's a 17 minute video.. that's quite the round up. Just saying because for me the difference from 15 minutes to 30 minutes tends to go from: "yeah I'll check this out" to "boy this is an investment".

AnimalMuppet15 hours ago

Huh. I stand corrected. Not sure where I got 30 from.

(I wasn't rounding that far, I was giving what I thought was an accurate number. Accuse me of bad info, not bad math.)

LeifCarrotson15 hours ago

Interesting, I'd assumed it was going to be a pawn promotion to something esoteric like a knight that didn't create a check, but that's a couple layers deeper.

Thanks for the TLDR.

tavavex11 hours ago

On a scale of billions of games, your situation would be be fairly common. The author of the video got to the conclusion by stacking multiple insanely rare occurrences - the player would need to underpromote to a bishop (the rarest promotion) and then capture and checkmate while these bishops are placed in a specific configuration. The author get into weird territory fast when fishing for the strangest game out of billions.