Fastest checkmates

Any chess player has surely won with and lost at least one game to the most famous fast checkmate, Scholar's Mate:

When younger, we used to call this the "four move knockout", and delighted in beating unsuspecting players with it. At the time we didn't realize that in playing a game like this we weren't actually playing chess. Once we started playing opponents who had seen it before, we quickly found out it was a terrible way to start a game, mostly because it's almost always a mistake to bring the queen out too early.

The quickest game of chess is actually a win to black, and is known as Fool's Mate:

Played like this, I think it's fair to say this is almost certainly a set up (who moves pawns like this?) However, searching through my dataset of games I found a few plausible variations on Fool's Mate, such as this win for white:

Fool's Mate as a win for white is half a move longer than the win for black (i.e., five half moves). Another checkmate just as fast for white is called, for some unknown reason, the "Bongcloud Mate":

The king's position between the two pawns makes this a kind of epaulette mate. Incidentally, an epaulette mate provides the fastest checkmate in Chess960 which can occur in three half moves (i.e. a pawn move each from white and black, and the white queen delivers mate on the second move), but only if the king starts out in between the two rooks. No faster mate than Fool's Mate is possible in standard chess since the first check can only occur with a bishop or queen on the second move and, apart from the special set up of pawns in Fool's Mate, there is always a piece or pawn to block the check. Certainly I didn't discover anything quicker than Fool's Mate while looking for fast checkmates.

In a database of games played on a different chess website, the bongcloud game (also as a half-move longer win for white) popped up quite a few times, and similar to the basic Fool's Mate, it's probably played by cheaters for the purposes of sandbagging. It seems unlikely anyone would move the king so early on and with no particular reason. However I'd argue the following two games that I discovered are plausible, especially in bullet chess:

OK so white's choices might not be the wisest moves ever played, but trying to dislodge the black queen with g3 loses the rook after Qe4+ (yes, I have fallen for that at least once) . So with that sequence fresh in white's mind, moving the king can seem like a better choice at the time (especially when playing bullet chess).

Speaking of moving the king early, I discovered more than one checkmate in front of the pawns, such as this (chess.com opening explorer calls moving the king like this the "Fried Fox Defence"):

I don't really see that it really deserves the name "defence", but an internet search did show at least one person expounding the benefits of moving the king so early, mostly - I think - as a surprise opening.

I downloaded 1000 games through the chess.com API of recent games played in 2|1 tournaments that ended in a checkmate in six moves or less. (Castling becomes more common after move five or six and I found that the number of checkmating patterns explodes after move six). I then grouped the checkmates by final move, and double checked the mating pattern (i.e. mating pieces and friendly pieces blocking the king's escape).

There are quite a few different ways to lose to Scholar's Mate, and in the count I included a few variations that seemed similar enough, such as the king moving a square before dying (followed by Qf1#), as well as the queen being supported by a knight rather than the bishop. Grouped like this, Scholar's Mate was by far the most prevalent way to finish the game in under six moves, and it occurred as a white win nearly four times as frequently as a win for black.

Fool's Mate occurred 76 times with approximately equal wins for black and white. Most of these were not set ups (as far as I could see), and as mentioned above, there are quite a few plausible variations for Fool's Mate. I was surprised to see quite reasonably ranked players fall to some kind of variant, here's a favorite of mine that I discovered:

I categorized several games as "Bishop Scholar's Mate", where the mate is delivered by the bishop, supported by either the queen, or a knight on e5 or g5. These seemed different enough to regular Scholar's mate and included the mating pattern of white queen on f7, white bishop on e6 mating the black king on d7.

A handful of Fried Fox games popped up, and I wouldn't have believed these are legitimate games, but for the exhortation of the fried fox maneuver to which I linked above. Obviously, looking at games of less than six moves featuring fried foxes are always going to be catastrophic losses for the fox, but presumably the element of surprise is worth something. I'd imagine games starting like this are either complete disasters for white or black with very little in between.

The games that I categorized as irregular were typically games with random, nonsensical moves and relentless pawn storms down the board. In my larger database of games I noticed a few back rank mates with rook or queen in under six moves, but these were always as a result of a massive blunder and showed no common patterns that define and group the other fast checkmates.

Finally, I discovered a few games that were won by a knight, but there was no sequence of moves common to these games. Here is my favorite, which is a queen's gambit that goes badly wrong for white: