Anti puzzle

Find the worst move

In this case the worst move is the same as a selfmate in one (S#1). 

What is the formal definition of "worst move"?

Good question! I have never read a formal definition and I have it from casual conversation. This is a bit of a problem in the fairy variants of chess since nobody is authorized to define them though they commonly remain with the original author. They get recognition after design, consensus and growing popularity. I'll ask my dutch friends about "worst move". My understanding is that the worst move leads to the worst result when followed by the "best play" by both sides thereafter. Intuitively we add to that "fastest mate" and "forced mate" but they may not be part of the definition. For instance, 1.Qh4 can be viewed as a worst move as well since it also permits black to mate in 1. Note that the overlap with selfmate would take away from the individual significance of the worst move type.

Btw, there are books and websites with lists of thousands of popular fairy variants. These lists are inherently incomplete as dozens of new types are invented every year. Not to mention the tons which silently disappear as everyone forgot about them. I'll look for a decent internet list (I knew a german one but lost the link).

Qd1 is just as bad for White, as Black can just mate by Qf2#

Yes, unless a move which forces your opponent to mate you is considered worse than a move which permits the mate! That's why the precise definition of "worst move" matters!

Yeah, I confused helpmate with selfmate.

Here is a puzzle showcasing the difference between helpmate and selfmate from the same position.

In the selfmate variant, Black actively does everything he can to not checkmate White as long as he can do so.

Good examples @KlekLegacy!

The language and instructions for the helpmates are a bit different. The leadership is not attributed to either black or white. So we say Helpmate in 1 (H#1) and not "white gets helpmated in 1". Also, black is assumed to start, not white, so a H#1 consists of a black move followed by a white move which checkmates black. If white starts it is still black who gets mated but a half (0.5) move is added to the assignment. Like H#1.5 means a white move, a black move and a white checkmating move. - white actually plays 2 moves.

A special case is duplex. When you specify duplex as in H#1 duplex then you indicate there are 2 puzzles with 2 same length solutions from the same diagram - one where black starts and white mates and one where white starts and black mates! Note that helpmates often have more than 1 solution like H#2 4 solutions.

Selfmates follow the expected natural pattern. S#3 means white starts and gets mated by black's 3rd move!

Addendum: This is culture, not logic or necessity. Though you can always see a logical thought if you want to. Like the minimum number of moves for a directmate problem is "one white checkmating move" but "just one white move" for a helpmate problem is weird. After all "where is the help if only white plays?". A minimum of one white and one black move is required to manifest the cooperation. These two minima have been numbered as the first in their type and thus we get "#1" and "H#1" with different solution lengths.

Another thing of course is that you cannot solve a helpmate in chess.com's Puzzle GUI as it insists on playing the "opponents" moves. But in Helpmates there are only "friends" and you gotta play both sides. This is a massive omission since there are many occasions and instances where you want the solver to play both sides!

Thanks for the culture clarifications and color conventions for helpmates. Like you said, «this is culture, not logic or necessity», but following standards for everyone can help to make things clearer and to prevent confusion.

Yes! These things were arbitrary when they were invented and defined but as time goes by they have found consensus and have become the laws of (that part of) the composition domain. Of course, you need not be part of that but that requires re-explaining your case for every puzzle. Your treatment is not more intuitive than the standard convention and people will only understand it because you provided the solutions with the puzzles (by reverse engineering). Once you present them as pure puzzles for solving, they will ask you for a handbook describing your annotation system.

Btw, the difference probably only concerns the helpmates. The selfmates are generally not contentious.