Monday, July 4, 2022

The Weirdest Chess Move, Part 2

This is the second part of a two-part post. For the first, see here.

In the previous post, I discussed some candidates for chess's weirdest move, where "move" here means a move written in algebraic chess notation. Our first two candidates, while rare, have come up in some historical games. Without further ado, here is chess's (notationally) weirdest move:

The weirdest move: Bf3g2#

At first glance, this looks rather innocent. It is a checkmate, but other than that it's just a bishop move, right? However, there's something strange here: both the starting square f3 and destination square g2 are listed for the bishop. Usually, only the destination square is listed in algebraic chess notation. But I'm not changing the notation rules here! There is a technicality that we'll use to our advantage.

The position above comes about in is a very common line in the Queen's Gambit Declined opening: 1. d4 d5 2. c4 e6 3. Nc3 Nf6 4.Bg5 Nbd7. Black has just played the move "Nbd7", moving the queen's knight from its home on b8 to d7, where it reinforces the pinned knight on f6. The notation "Nbd7" is used instead of "Nd7" because there are two black knights that could legally move to d7 on this fourth move! The other knight move would be denoted Nfd7 (a very bad move since white would win the queen). When additional information is required to disambiguate a move, chess notation rules hold that information must be provided about the piece's initial square. The way this information is provided is as follows:

Suppose that a player may move two or more of the same piece to the same square. Then the notation for the move must include one of the following three pieces of information:
  1. The file (column on the chess board, labeled a-h) where the piece originated, such as in the example Nbd7 above
  2. The rank (row on the chess board, labeled 1-8) where the piece originated, if specifying the file does not disambiguate the move
  3. Both the rank and file, only if neither the rank or the file alone can disambiguate the move
We saw an example of (1). As an example where (2) applies, see the following diagram:
Special notation disambiguating moves happens very frequently for rooks, because they are often "connected" on the same rank or file. In the above position, white has just played "R1h5". Both white rooks could move to h5, and they are both on the h file, so the originating rank (the first rank in this case) is provided before the destination square instead.

Though situations (1) and (2) are common enough, applying (3) is almost never necessary. This is because this would require one player to have at least three of the same piece, requiring a promotion of some kind. How rare is it for a player to have three of the same piece? Let's take a look at a few notable examples. There's a line where this can occur straight out of the opening: the famous Lasker Trap.

The game begins 1. d4 d5 2. c4 e5 3. dxe5 d4 4. e3 Bb4+ 5. Bd2 dxe3, arriving at the following position.


So far, only white's fourth move e3 can be considered a mistake, and not a major one. It appears that white can win a free piece by taking the bishop on b4, but this falls right into the Lasker trap! After 6. Bxb4, black responds with exf2+. In this position, white can't take the pawn, and must move the king to e2 (see below).



White has just played 7. Ke2. If white instead took the pawn with Kxf2, the king would no longer be protecting the queen and black wins with Qxd1. The winning move for black is now 7. ...fxg1=N+, underpromoting to a knight! This remarkable underpromotion occurs only seven moves into the game. If black promotes to a queen, the position is equal after white inserts Qxd8+, since after the white queen is captured, white can take the promoted piece on g1, leaving roughly equal material. This means that black must promote with check. After 7. ...fxg1=N+, If white takes the new knight with 8. Rxg1, the skewer 8. ...Bg4+ wins the white queen, so white plays 8. Ke1.



Black can then play 8. ...Qh4+, as shown above. White is lost here: they are down a piece, their king is completely exposed, and black's new knight will be saved. Most importantly for us, the final position features three black knights! They're nowhere near each other, though, so there's no need for disambiguating notation.

A few other quick examples of extra pieces: there have been a few historical games where a player had three queens (requiring two promotions!), and only one game I could find where a player had three rooks, see below. The game was a tournament game between Grigory Serper and Catalin Navrotescu in 1988.



In this position, black can promote and gain a huge material advantage. However, promotion to a queen results in a draw! This is because of a neat stalemate trick: white can perpetually check the black king with their two rooks. If the black king actually captures both, it's stalemate because the new queen on g1 takes away all squares from white's king, and both pawns are locked! Therefore, the winning move is "g1=R", which leaves five rooks on the board! The rook promotion was actually the last move of that game: white resigned. None of the games I found required rule (3) above to disambiguate a move, however.

Moreover, I could not find a single historical game in which one side had three bishops, which is the situation required for our candidate weirdest move. In fact, even more is required than that: one side needs to have three bishops of the same color for rule (3) to apply, which requires at least two bishop underpromotions!

This is the main idea behind my candidate for weirdest move, but I'll quickly run through the other features that led me to the specific choice of "Bf3g2#". First: the choice of squares.



In order for rule (3) to be required to disambiguate, at least three bishops must be able to access the destination square. This means the square in question cannot be a corner or an edge square. The next most unusual choice is a square close to the corner such as g2, since this greatly constrains the positions of the bishops (all three must start among the four squares h1, h3, f1, f3; we'll use the configuration above). Further, the bishop that moves must be on the same file and the same rank as another bishop. We can't have the bishop move from h1, however, because it is impossible to deliver a checkmate with Bh1g2 if it is not a capture. This follows from the fact that the bishop does not attack any square it didn't before, and also could not have gotten out of the way of another piece. Therefore, if we stick to a checkmate without capture, the bishop that moves must start on f3, as shown.

The choice of corner (g2 instead of say, b2) is not particularly important, but with the white pieces is marginally weirder since the promoted bishops would have to retreat back toward white's side of the board and occupy the king's most common position (after kingside castle). Finally, let's consider the checkmate. In a similar vein to the comment above, after moving the bishop from f3 to g2, it doesn't attack any squares (not occupied by white pieces) that it didn't before. Since the move to g2 wasn't a capture, in particular, the bishop already saw the h1 square on the previous move. But then, how can this be a checkmate?

One can see that these conditions force the move to be a discovered checkmate, which is the final bit of weirdness; the bishop on f3 must be blocking a piece that then delivers checkmate to the enemy king. This setup feels even more contrived than having the bishop capture a piece to deliver checkmate, hence my choice of "Bf3g2#". Finally, just to prove that the move could happen, here's a (highly artificial) chess position using the move.

In this image, white has just delivered checkmate with our weirdest move, Bf3g2#.

This example serves to illustrate the huge variety of chess positions that have never been seen in a game before. Maybe this "weirdest move" will appear in a game someday. But I wouldn't bet on it.

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