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The rarest move in chess [video]
- AnimalMuppet 2y 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.
- f154hfds 2y agoIt'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".
- AnimalMuppet 2y agoHuh. 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.)
- LeifCarrotson 2y agoInteresting, 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.
- tavavex 2y agoOn 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.
- shric 2y agoThe 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.
- kristopolous 2y agoRight, 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
- SamBam 2y agoPresumably 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.
- kristopolous 2y agoI bet it's way less than you think - orders of magnitude. What could happen versus what does happen are entirely different. Doing some algebraic permutations computation here would be like claiming a 50,000 letter English document has 27^50,000 possibilities. I mean no, there's words, and they only go in certain orders and there's all these rules. Here's another approach: humans are pretty lousy when remembering large amounts of anything so let's say there's in practice, only been 100,000 unique games played over and over. Without the help of a computer or careful tabulation, I'm pretty sure no human would realize it because no human can remember 100,000 unique games. Anyways, it's worth digging into the data to see what the variation really is. I bet the 90th percentile is embarrassingly small with a long tail that's far shorter then most think edit: so I actually took 7.7 million games from https://www.ficsgames.org/download.html https://www.ficsgames.org/download.html and did some basic processing on them. These are people ostensibly with ELOs over 2000 which is pretty decent just to see if I'll eat crow on this one. Going in, I was expecting a uniqueness level to be something like 50-70%. Actual percentage of unique games over 7.7 million? 98.7%. Alright fine. Although I could try to do 1 billion games, I expected the distribution to be readily visible around 7 million. Now as an artifact of the data, I made the games as compact as possible, potentially leading to ambiguity maybe. So a game might look like so a3a5b3b6Bb2Bb7c4e6Nc3Nf6d4Be7Nf3O-Oe3c5d5exd5Nxd5d6Nxe7+Qxe7Bd3d5O-Odxc4Bxc4Nc6Qe2Rad8Rad1Ne4h3Nd6Ba6Bxa6Qxa6Qb7Qd3f6Qc3Rfe8Rd3Ne4Qc4+Kh8Rxd8Nxd8Rd1Qe7Qd5Nf7b4axb4axb4cxb4Qc6h6Rd7Qf8Qxb6Rd8Rxd8Qxd8Qxb4Qe8Bd4Kg8Qc4Nd6Qd5Kh8Nh4Kh7Qb3Qe4f3Qe6Qd3+f5e4g6exf5Nxf5Nxf5Qxf5Qxf5gxf5Bf2Kg6g4fxg4hxg4h5Kg2hxg4fxg4Ne5Kg3Nf7Kh4Ne5Be3Nxg41/2-1/2 Given this we can just run uniq with incrementing numbers and find out how things increase. I'm doing this on a pretty old laptop (3rd gen intel) so excuse me for cutting things a bit short number of characters / unique entries / percentage duplicates 99 7470034 0.039416039621657628 98 7462496 0.040385363441781119 97 7454437 0.041421683508957363 96 7446241 0.042475620631500677 95 7437517 0.043597454142611958 94 7428583 0.044746291899176449 93 7419379 0.045929849399894973 92 7409325 0.047222709798876217 91 7399016 0.048548361067336399 90 7388091 0.049953224789125783 89 7376939 0.051387278814333581 88 7364995 0.052923177422393386 87 7352785 0.054493281408027117 86 7340118 0.056122151775432672 85 7326671 0.057851323625950024 84 7312421 0.059683754567414482 83 7297272 0.061631789397747494 82 7281670 0.063638076243272224 80 7247260 0.068062914748240111 79 7228770 0.07044057426456829 78 7209233 0.072952869233227302 77 7187947 0.075690070989017588 76 7166719 0.07841981442939705 75 7144539 0.081271977115830896 74 7119854 0.084446261873027284 73 7094951 0.087648579608837096 72 7068178 0.091091363720824936 71 7039566 0.094770627867995505 70 7009607 0.098623104961001351 69 6978335 0.10264442288391196 68 6944221 0.10703119826195528 67 6909408 0.11150785919986417 66 6871309 0.1164070722832925 65 6831848 0.12148142718723132 64 6790088 0.12685141428305979 63 6744878 0.13266504255419009 62 6698251 0.13866088518630681 61 6648086 0.14511168505848671 60 6594883 0.15195314634822232 59 6540926 0.15889156573829932 58 6481469 0.16653723917595897 57 6419070 0.17456122923325301 56 6355249 0.18276807660975847 55 6282195 0.19216221064468775 54 6209896 0.20145925798763076 53 6133584 0.21127234360201919 52 6048154 0.22225792783565479 51 5963420 0.23315401228435984 50 5870519 0.24510030469790289 49 5770633 0.25794480975187595 48 5668750 0.27104611232094422 47 5558836 0.28518013439112821 46 5443035 0.30007117547551587 45 5323607 0.31542861845637304 44 5192507 0.33228698311784588 43 5064129 0.34879532132158775 42 4925937 0.36656565792950735 41 4777302 0.38567887708631909 40 4626169 0.40511331817237839 39 4465105 0.42582480288508218 38 4301802 0.44682420429097458 37 4126391 0.46938059333470927 36 3948981 0.49219403707682896 35 3770310 0.5151696348833128 34 3581328 0.5394711411415466 33 3387960 0.5643366503548165 32 3202702 0.58815928132701434 31 3008299 0.61315788289287476 30 2810171 0.63863548833641626 29 2617450 0.66341779875536144 28 2413377 0.68965988152851743 26 2044415 0.73710531205655982 25 1849362 0.76218749819167997 24 1674682 0.78464988674290859 23 1499682 0.80715342462054207 22 1324053 0.82973784664289008 21 1167329 0.84989124361622848 20 1005747 0.87066933880105002 19 862832 0.88904701374837569 18 733254 0.90570966192613567 17 599187 0.9229495579983682 16 489782 0.93701812692123954 15 395141 0.94918816879710877 14 300280 0.9613865008348812 13 233128 0.97002168698093183 12 167915 0.97840753392729818 11 115118 0.98519678700915769 10 78474 0.98990889924908909 9 46588 0.9940091724420389 8 26581 0.99658190548385495 7 14316 0.99815908200996462 6 5390 0.99930689103336889 5 2659 0.99965807481590496 4 408 0.9999475346088339 3 180 0.99997685350389731 2 20 0.99999742816709969 1 9 0.9999988426751949 It would be interesting to see later, when I crunch larger numbers on a more capable machine, if these distributions generally hold. Of course it won't, it's not possible. But I'm wondering if it's greater than what the Shannon limit would predict. An ancillary analysis would be to compare it to the possible legal permutations at a character count although this would of course require a board and rule model. I would expect those percentages to decrease as the length increases and perhaps such a function can give more predictive heft to the actual "language" of chess in practice
- kristopolous 2y agoHis 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
- kevincox 2y agoThe 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).
- matt-attack 2y agoAgreed. 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.
- thih9 2y agoA 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 https://en.wikipedia.org/wiki/Joke_chess_problem
- paxys 2y agoThe 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.
- shric 2y agoHe 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.
- antaviana 2y agoIn 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.
- shric 2y agoYes, I've done it many times! At the time of writing based on total games played at https://database.lichess.org/ https://database.lichess.org/ one in every 272,369 games are mine :p
- tavavex 2y agoI 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?
- CalChris 2y agoDid 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.
- yunwal 2y agoZugzwang has no notation. The author states in the first 2 minutes or so that the video is about the rarest edge cases in notation.
- CalChris 2y agoNf3 can be ambiguous but resolved by the position itself. That ambiguity has no notation either. FWIW, I wrote the XBoard PGN parser.
- yunwal 2y agoRight, the video talks about that and doesn’t consider the ambiguous but resolved by position one different from any other Nf3
- mathgradthrow 2y agoparent 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.
- yunwal 2y agoStalemate doesn’t have notation either, so the OP doesn’t consider it different than any old bishop underpromotion
- bitcurious 2y agoFun 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.
- elijahbenizzy 2y agoThis 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!
- none_to_remain 2y agoDo chess players actually consider this "double disambiguation" from the notation to be a different "move"?
- bongodongobob 2y agoNo.
- billforsternz 2y agoThis 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.
- kristopolous 2y agoRarest 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.
- philipswood 2y agoThinking 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.
- kristopolous 2y agoYou 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 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
- incorrecthorse 2y agoBoard 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.
- pimlottc 2y agoThe game and move in question is here: https://lichess.org/NoXEwGi8#136 https://lichess.org/NoXEwGi8#136
- yunwal 2y agoI wonder if the winner was specifically going for wacky notation when he played that, or just going for a crazy checkmate.
- mehmetalianil 2y agoI 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.
- billforsternz 2y agoAnother 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.
- jameshart 2y agoYou’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.
- billforsternz 2y agoWell, only one of the other bishops would have to be pinned else single disambiguation would do, but otherwise - fair point!
- xyst 2y agoI 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
- groggo 2y agoYes, the text bothered me a little once I noticed it though. It's just moving a tiny bit, not necessary.
- pbj1968 2y agoDAE learn about castling from Battle Chess?
- mrslave 2y agoInteresting, 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=review https://www.chess.com/analysis/game/live/108840009759?tab=re... [2] https://www.reddit.com/r/chess/comments/1claxsm/its_me_viih_sou/ https://www.reddit.com/r/chess/comments/1claxsm/its_me_viih_... [3] https://en.wikipedia.org/wiki/Brandon_Jacobson https://en.wikipedia.org/wiki/Brandon_Jacobson [4] https://www.chess.com/analysis/game/live/108394316331?tab=review https://www.chess.com/analysis/game/live/108394316331?tab=re... [5] https://www.chess.com/blog/Utkarsho/a-grandmaster-account-gets-banned-for-cheating-in-chess https://www.chess.com/blog/Utkarsho/a-grandmaster-account-ge...
- filleduchaos 2y agoWhy 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.
- thebruce87m 2y agoCan you explain the ban to a layman?
- munch117 2y agoKinda 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.
- dh5 2y agoNotation 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.
- munch117 2y agoAlgebraic notation hasn't changed notably in the last (at least) 50 years. The abbreviated form that most people use today was also the form that most people used 50 years ago. (A change to indicate draw offers is the only one I can remember.) The point is that there are multiple ways of writing the same move, and none of them are more correct than the other. Basing your definition of a move on the precise text that the computer happened to spit out when the games were retrieved, that's just being lazy.
- hoseja 2y agoChess dot com needs to release the data.
- alberto-m 2y agoChess 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 https://timkr.home.xs4all.nl/chess2/diary_6.htm (entry 105). His site is a trove of information for people liking chess trivia.
- bmacho 2y agotl;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.
- animal531 2y agoIt'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.
- alberto_ol 2y agoFor those who, like me, don't know who are Anna and Pia https://en.wikipedia.org/wiki/Anna_Cramling https://en.wikipedia.org/wiki/Anna_Cramling https://en.wikipedia.org/wiki/Pia_Cramling https://en.wikipedia.org/wiki/Pia_Cramling
- venusenvy47 2y agoI prefer Gotham Chess. He analyzes recent games and makes it exciting with the way he vocalizes his descriptions. https://youtube.com/@gothamchess https://youtube.com/@gothamchess
- aaron695 2y ago[dead]
- stevage 2y agoBy coincidence, I was exploring a couple of very related questions a few months ago: - [what are the commonest checkmating moves](https://chess.stackexchange.com/questions/44959/what-are-the-commonest-checkmating-moves-in-the-lichess-or-similar-database https://chess.stackexchange.com/questions/44959/what-are-the...) - [Have any full rank-and-file piece specifications ever been required in a masters level game of chess?](https://chess.stackexchange.com/questions/44961/have-any-full-rank-and-file-piece-specifications-ever-been-required-in-a-masters https://chess.stackexchange.com/questions/44961/have-any-ful...) I think this question here is perhaps the more interesting one though, and it's so well explored.
- foobarian 2y agoHuh. I wonder if the set of possible checkmate positions is quite limited compared to the full game.
- alhirzel 2y agoI am all about the hands used in this video! The bandage after getting hit by lightning is very immersive. I bet this video will have a Streisand-like effect [1] on the indicated capture scenarios. [1]: https://en.wikipedia.org/wiki/Streisand_effect https://en.wikipedia.org/wiki/Streisand_effect
- psuter 2y agoGreat investigation and excellent production value! Brings back good memories too, as 10 years ago my first contribution to lichess was to improve the PGN notation for disambiguation. [1] [1] https://github.com/lichess-org/scalachess/blame/master/core/src/main/scala/format/pgn/Dumper.scala#L21 https://github.com/lichess-org/scalachess/blame/master/core/...
- gweinberg 2y agoOP misses a couple important things when he's discussing notation: when a pawn gets promoted, you have to specify what it gets promoted to, and also if the move results in stalemate you note that. Stalemates are much rarer than checkmates, and underpromotions are very rare also, so I imagine the stalemates analogous to the checkmates he considers must be rarer still, if they ever happen at all.
- bjourne 2y agoIf you define a "move" as a piece moving from one square to another, which I think is the correct definition, then the rarest move is probably an illegal move. Like black king jumping from b4 to h8 or something. Or a piece moving to an already occupied square of the same color. In over the board chess illegal moves happen all the time in bullet chess, but not online of course.
- deleted 2y ago[deleted]
- ViktorRay 2y agoThis 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
- skilled 2y agoWatched this earlier today myself, fantastic work by the author.