The quickest selfmate in 1

Question

How quickly can a legal game reach a position where one side must give checkmate?

This is in effect Evergalo's reading (see his (now deleted) answer) of Rewan Demontay's Question 33154; that question actually asked something else, but the selfmate question is nice too. Evergalo offered a game that reaches such a position in 6.0 moves, i.e. after Black's 6th:

[FEN ""]

1. e3 d6 2. Ke2 Qd7 3. Kd3 Qh3 4. Qh5 Kd7 5. Ke4 Ke6 6. d4 Qf5+ 7. Qxf5#

I found a solution in 5.5, that is, after White's 6th move (actually two very similar positions, which together can be reached in 660 ways according to Popeye 3.41).

Is 5.5 moves the quickest possible?

If so, are there other solutions in 5.5 ?

Has this puzzle appeared before?

Answer 1

Going to the dusty databanks in my skull, this indeed has been written about before. It appears in Journey Entry #153 of Tim Krabbe's Chess Diary. Since you define the ply count to the position before the selfmating move, the given examples are valid (although, Krabbe does not count the forcing move either, leading to counts of 5.0). This answers your second and third wonderings.

Here are the given games, which, unsurprisingly, all have Fool's Mate setups. All are 5.5 moves, the same as yours. I can offer no proof of optimality, however. I do think, though, that it seems unlikely that faster can be done.

[Title "Pim Blijlevens, Tim Krabbe's Website #153, 12/10/2001, PG in 6.0"]
[FEN ""]

1. f4 e5 2. g4 Ke7 3. Nc3 Kf6 4. Nf3 Kg6 5. Nd5 Nh6 6. Nh4+ Qxh4#

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[Title "Pim Blijlevens, Tim Krabbe's Website #153, 12/10/2001, PG in 6.0"]
[FEN ""]

1. e4 f5 2. Ke2 g5 3. Kf3 Nc6 4. Kg3 Nf6 5. Nh3 Nd4 6. Qh5+ Nxh5#

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[Title "Sasho Kalajdzievski, Tim Krabbe's Website #153, 12/11/2001, PG in 6.0"]
[FEN ""]

 1. e4 h5 2. f4 g5 3. Kf2 f5 4. Kg3 gxf4+ 5. Kh3 a6 6. Qxh5+ Rxh5#

Answer 2

For the record, my solution was

[Title "Help-selfmate in 5.5+0.5, NDE Dec.2020"]
[FEN ""]

1. Na3 Nc6 2. d3 Nd4 3. Kd2 Nf3+ 4. Kc3 b5 5. Nxb5 Rb8 6. Nxc7+ Qxc7#

(264 possible games), and the same with Nf3+ changed to Nb3+ (396 games; the simple ratio 264:396 = 2:3 corresponds to the counts of 3-move Knight paths from b8 to f3 or b3).