the rarest move in chess I know what you're thinking you think you have all the answers I was like you once it's got to be on bant Checkmate right you know the weird pawn move done in a way to cause Checkmate or uh wait maybe castling Checkmate is more rare or something with Pawn under promotion there's a simple way to get to the bottom of this let's just look at a bunch of games of chess whatever happens the least often must be the rarest right like if we ask a million people what their favorite type of pizza is we could find the most rare pizza topping which we already know is rhubarb if we want to do this we need some way of talking about moves like what is a rare move what even is a move what does it mean to play chess what are we doing again okay we're going to talk about moves in terms of standard algebraic notation that's the normal way people talk about chess moves like when they say E4 and nf6 it's what they're writing down on those little pieces of paper it's a simple notation you just say what piece moved where that's the basic idea at least we just need to give names to places and pieces so we give every Square on the board coordinates with a letter and number and we give every piece a letter of its own we can use these letters and numbers to write down moves like bc4 means the bishop moves to C4 and there's only a couple extra things to know X means capture nxf3 means the Knight captures the piece on F3 pawn moves don't bother with naming the piece E5 just means you move your Pawn to E5 you add a plus to indicate a check qa5 plus means your queen moves to A5 and the opponent's king is now in check and similarly the hash sign means Checkmate pound sign what uh what do you call this thing octo Thorp yeah means Checkmate kingside Castle is o- O queenside Castle is o d o- o you don't even need to say whose turn it is white goes first and then you alternate this means the same move can happen from either side like e takes D5 e takes D5 with this notation you can describe an entire game of chess instead of writing down how the board looks after every move which would be very tedious you just write down the moves in order and you can reconstruct the board at any point so if we want to find the rarest move it's sufficient to look for the rarest notation of moves well okay there's probably many ways you could do it but we're going to be looking for the rarest notation there's one last important application to mention about this notation you'll notice this notation is very implicit all you do is say the type of piece and the destination and infer which source piece you're talking about but what if two pieces could move to the same square like both of these Knights could move to E5 in cases like this we need to disambiguate moves if it's ambiguous which piece to move you include the file of the source piece like nde E5 if it's still ambiguous use the rank instead like an3 E5 if it's still ambiguous use both both like n D3 E5 okay now we can talk about rare moves at this point I thought okay like there's so many games of Chess happening all the time we can just take all the moves in a bunch of games count how many times we see each move notation sort by that count and see which one is at the bottom but it turns out there's a lot of possible moves at this point I went on a bit of a crusade to understand what is every possible legal move notation according to standard algebraic notation that way I could understand if I'd seen every possible move this was much more interesting than I expected I kept finding new edge cases and eventually had to write a program to help simulate all the possibilities but honestly that's a video of its own let me know if you'd be interested in seeing such a video once I understood every possible move notation I was ready to look for the rarest move but something wasn't quite adding up I downloaded all the Master Level games from lee.org I thought maybe it just wasn't enough games so I started downloading games from anyone on Lee but as I kept downloading more and more months of data it became clear that there was a problem eventually I had gone through all of the games ever played on leeches containing 5 billion games and 9 terabytes of data that's 16 games a second every second for 10 years out of all the possible moves a full 30% that were theoretically possible I never saw occur even once my dream of saying that a specific move like qa1 h8 was the rarest was shattered instead I found their entire cat cies of moves that are rare so I've identified four candidates for the rarest category of move in chess as we go through them place your bets for which one you think will be the rarest according to the data let's start with a warm-up to get acquainted with how these rare moves work generally rare moves require multiple unique circumstances to overlap together like most moves aren't captures and most moves aren't Checkmate but even less moves are both capture and Checkmate so so with that in mind let's start by looking at the queen recall how in our algebraic notation if it was ambiguous which piece would move we needed to disambiguate unsurprisingly rare moves are all based on disambiguations since they require pieces to be in certain positions which doesn't happen all the time you only have one Queen to start so to require disambiguation you'll need to promote a pawn once we have two queens if they both see the same Target Square we need to disambiguate with their file like qc6 if they both live on the same file then we need to use the rank like Q4 E6 but what if we promote another Pawn to make three queens then if there were two Queens on the same Rank and two Queens on the same file and they all saw the same destination Square we need to disambiguate with both the rank and file like qc8 E6 this move is immediately rare because it requires three queens arranged together however we can keep stacking Rarity Checkmate can only happen once per game so we expect the same move causing Checkmate Q Q C8 E6 mate to be even rare finally if we also capture a piece when causing Checkmate we get Q C8 takes E6 mate for a doubly disambiguated Queen capture Checkmate that is quite a move but this was just the warm up now we're ready for our first real candidate move let's talk about Bishops again we'll look at disambiguated moves wait a second why do you ever need to disambiguate Bishop moves each Bishop always stays on the same color when moving diagonally and since the two Bishops start on different colors it's always unambiguous which Bishop you mean to move the two Bishops live in entirely separate worlds well this would be true except for pesky Pawn under promotion if you promote a pawn to a bishop it can be on the same color as another bishop and therefore we may require disambiguation of course 98% of the time people promote pawns to Queens but you are allowed to promote to a bishop we've arrived at the rare move a rank disambiguated Bishop capture Checkmate remember that we first disambiguate with the file and only disambiguate with the rank if both Bishops are on the exact same file that is file disambiguation is preferred to rank disambiguation with eight columns you'd probably expect two pieces to be on the same file around 1/8 of the time that ends up being true here with rank based disambiguation about 1/8 as likely as file based as with the rare queen move we showed before we tack on capture and Checkmate to compound the Rarity such a move would look like this B2 takes E4 mate to recap this requires under promoting a pawn to have two Bishops on the same color this requires arranging them so that they're on the same file it must capture a piece and it must cause Checkmate that leaves us with a pretty darn rare move I bet on basant mate doesn't sound so rare anymore does it the next rare move might not surprise you it's the doubly disambiguated Bishop capture Checkmate if you under promote at least two pawns to Bishops both on the same color then it's possible to arrange your Bishops in such a way that they need both Rank and file disambiguation if we look back at how much rarer rank disambiguated moves are compared to file based well doubly disambiguated moves are even rarer the arrangement requires the Bishops to sit in a square around a Target Square only onethird of the corners of this Square actually requires double disambiguation since the others only see one Bishop on their same Rank and file as before also including a capture and Checkmate compounds the Rarity such a move would look like ba a takes C6 mate there's actually another rare move here something very interesting happens when we look at doubly disambiguated Bishop checkmates that are not captures because all three Bishops see the same Target Square it means both diagonals from that square will remain attacked no matter which Bishop you move there thus if there's no enemy piece being captured a doubly disambiguated bishop move won't attack any new squares so how could this possibly be a Checkmate turns out this can be a Checkmate but only via a discovered attack the bishop you move has to reveal another piece that actually causes the Checkmate I like this move because it's one of the few times that a move implies that it must be a discovered attack such a move would look like B C6 E4 mate finally we have our last rare move candidate a doubly disambiguated Knight capture Checkmate finally something other than a bishop two knights can require disambiguation and in fact disambiguating Knight moves is common but to get double disambiguation we again need to under promote a at least one Pawn it's kind of hard for Knights to cause checkmates because they don't control as many squares as other pieces for this rare move the Knight must be arranged in a specific rectangle and then capture a piece and cause Checkmate this move might surprise you in Rarity due to how Knight's move the rectangle of where the knights must be is quite specific and not as lenient as queens or Bishops the destination Square cannot be anywhere along the outer edge of the board and if you inset one more Square only allows half as many positions of knights this gives less leeway for such an arrangement such a move would look like n D4 takes E6 mate and that's our four rare move candidates side note I'm sure you've noticed all these moves require Pawn under promotion and having the opponent not resign these are highly unlikely situations to arise in high level games which in a sense contributes to the Rarity a move being rare doesn't mean it's good like getting struck by lightning under promotion itself is often been a sign of a game not being taken very seriously it's someone's always better to just promote to a queen I mean you could Envision cases where you must under promote to avoid stalemate to justify these moves being theoretically possible in a real professional chess game with no funny business but such a game would be so rare you'd never actually see it happen all right so far everything we've done here has been completely theoretical if we want to get a real answer for what's the rarest move we need to look at the data from all the data lead chess makes available I found 342 billi moves so can we talk about rare moves let's talk about rare moves some starter stats Pawn mates are not really uncommon with about 0.01% of moves being a pawn mate very few of these are on pant mates but it's still on the order of tens of thousands of occurrences castling with Checkmate o- mate and o-- mate make up 0.00001% of moves I found about 50,000 instances out of the 342 billion interesting ly long Castle Mates is twice as common as short Castle mates probably because the Rook ends up more in the center where the king starts out these moves are pretty rare but it's just the beginning a king move that captures a piece and causes Checkmate like King takes A1 mate is actually even rarer than either of these with just 13,677 occurrences just 1/4 as many as Castle checkmates this is probably rare because such a mate requires a discovery since the king can't directly threaten the other king and with that we're ready to see which of our candidates is actually the most rare place your bets now first up is our warm-up move doubly disambiguated Queen moves there were 42 billion Queen moves out of which I found 63,9 doubly disambiguated Queen moves but our idea was to look for captures with Checkmate when looking at doubly disambiguated Queen capture checkmates I found drum roll 179 just 179 times in 342 billion moves that's 0.005% now that's pretty rare as we talked about it requires two pawns to promote then sit in a square then capture a piece and cause a Checkmate in one move that's a lot to ask for okay but again that's just the warm-up now for our first real candidate for rare move it's rank disambiguated Bishop capture checkmates I found 2,294 disambiguated Bishop moves of which only 22,35 were Rank disambiguated and how many of those cause capture and Checkmate a measly 26 yep that's 0.00000000 8% of moves since Knights can require rank disambiguation without Pawn under promotion the equivalent knight move happens 200 times more often than our rank disambiguated Bishop capture Checkmate we're getting into pretty rare territory now and now let's talk about non capture Bishop double disambiguated checkmates these were the ones that required a discovered attack after under promoting at least two pawns and how many of these did we find dral one yep that's right I found exactly one of these on January 22nd 2022 n Marcus n and Maus played a Blitz game which ended in bf1 G2 mate indeed they had three Bishops in a square and moved the corner ring a discovered attack via a queen wow so that's it then one out of 342 billion 0.003% this must be the rarest move well let's keep going let's now talk about Knight double disambiguations I kind of thought these were an underdog in the race like it's just a knight move but these are truly very rare the constraints on how you have to position the knights make it harder to execute than you might expect I only found 1,973 night double disambiguations and how many of these were capture and Checkmate none zero I never found any but judging from the ratio of capture checkmates from other moves we probably need to look at several billion more games before we'd expect to see one by chance so maybe we can expect one of these on Lees at some point this decade so is this it what could be rarer than never well finally we have the bishop double disambiguation capture Checkmate these are much rarer than single disambiguation I only found 665 Bishop double disambiguations and care to guess how many of these are captures and checkmates that's right none of them okay well we went looking for rare moves but it ended up being so rare that all we found is a bunch of zeros now how are we supposed to Crown a winner if it's a tie for Z out of 342 billion well ideally we just keep analyzing data until we had some hits but I went through all the data there was just.com has something like 8X more games but unfortunately the data is not available to download and we just won't know without the data in my view doubly disambiguated Bishop capture checkmates seem likely to be rarer than doubly disambiguated Knight capture checkmates of all the pieces Bishop double disambiguations occur significantly less than the others with onethird as many as Knight double disambiguations I found three Knight double disambiguation captures but zero Bishop double disambiguation captures Bishop double disambiguation requires at least two Pawn under promotions instead of just one and they have to be on the same color so we'll unconvincingly give the crown to Bishop double disambiguation capture checkmates great job there's an argument to be made here that if a move has never happened can you really call it rare like the minimum threshold should be one like let's say spaghetti monsters invaded Earth and beat Magnus Carlson at chess the word I would use to describe that wouldn't be rare though since we only have data from Lees we have to assume these moves have happened somewhere at some point in history so I think it's safe to call them rare moves this was so much more complicated than I ever expected it to be I can't tell you the number of times I remade this video upon finding a newer even rarer move or postpone to analyze just one more month of data my code is available if you'd like to analyze it yourself you can look at some extra details of the statistics there too thanks for watching
