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MatPlus.Net Forum General Longest helpmate?

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### Longest helpmate?

And I don't mean "longest helpmate *correct as a problem* ".
Those values are easily googled (48; 111 if illegal position).**
But rather along this question*
https://chess.stackexchange.com/questions/18587/helpmate-of-arbitrary-length
- it doesn't matter whether there are several possibilities to reach
the goal, it's just that the distance-to-mate N under help-play is maximal.

* With the same intent - I am an arbiter and N>50 (75?) would make epic
trolling material :-)
** Never trust anything googled - seems to be Madrasi? YACPDB 409595 -
and notation/position won't match...R must be K

Do you mean for fairy helpmates?
I bump you to Madrasi h#52: https://pdb.dieschwalbe.de/P1287073

Nope, I exactly mean NOT fairy and was a bit miffed
Google tricked me :-) Orthodox, please. And again,
rather "shortest mate line possible down the game tree"
than "helpmate". Illegal position would be
acceptable, but that's a different record.

If you mean a game in which both sides help prolong the inevitable but agree to arrange a checkmate, wouldn't it'd just be the longest game possible?

8848.5 moves: https://wismuth.com/chess/longest-game.html

Related question (or is this THE question): What is the longest possible helpmate if you do not require a unique solution?

So, you're looking for a position where there is no helpmate in under 28 moves (you want something longer than Bernhard Hegermann's record), but you care nothing about whether the solution is unique.
In other words, what's the longest number of moves for a Shortest Helpmate problem (akin to Shortest Proofgame problems, where the move order and transpositions are of no concern)?

Answers in any of these three varieties:
1) no promoted force and legal position,
2) promoted force and a legal position, and
3) an illegal position (no care about promoted force).

What are the records here?
Has any composer explored these questions at significant depth?

Or in mathematical terms:

Let S be the set of non-dead positions (including illegal positions).
Let M(P) be the minimal number of halfmoves needed to reach a mate (any king, so black mating white is also fine) in a position P from this set.
Obviously, the minimum of M is 0 (all positions that are already mate), but what is the maximum?

Examples:
* M(P) of the Vielvaeterproblem is 1 if white has the move, and 4 if black has the move. In both cases the sequence is unique.
* M(P) of the start position is 4 (1. g4 e5 2. f4 Qh4#), in this case the sequence is not unique.
* For any random position in the set: Try to find the shortest helpmate, mating the black king, and the shortest helpmate, mating the white king. M(P) is the minimum of these two (use infinity for when it's not possible to mate the black or the white king. Since the position isn't dead, it's not possible for both values to be infinity)

A related problem is to find max(M(P)) for any position P in the set S' of legal non-dead positions.

Well said, Joost.

1) Ottó Titusz Bláthy, 56 Magyar Sakkvilag 01/02/1924, Helpmate In 40
(= 8+10 )

https://pdb.dieschwalbe.de/P1379073

2) Karl Fabel, Schachmatt 1948, Helpmate In 48
(= 11+10 )

https://pdb.dieschwalbe.de/P0569740

3) James Malcom & Arno Tüngler, Matplus.net Forum 1/30/2020, Helpmate In 111
(= 14+31 )

https://pdb.dieschwalbe.de/P1372555

Wow. Thank you, James!

THX, Malcolm. Fabel missed the 50 by >< that much
(the 111 will probably not occur OTB that soon :-)).
Indeed, Kevin and Joost's reformulations were
my intent. That the h48 is not completely exact
is irrelevant for OTB trollolo purposes :-)

Note that both the h#40 and the h#48 feature a capture long before the end, so if you intend to do some trolling via the 50 move rule, you are much farther from your goal than you might have hoped.

--

By the way, has anyone checked these composition to see whether black can mate white at an earlier stage? Because that would decrease M(P) as it measures the distance to mate, not the distance to mate of the black king.

In the position of Malcom & Tüngler, White can be mated in 107.5 moves.

There is no magical switch however that turns the diagram from Black to play to White to play. So that isn't a cook.

EDIT: Wait, you said "White can be mated". So it would be kind of a Duplex?

As I understand it, we are looking for positions, under Kevin's system, that have the longest shortest possible help play for either side to be mated. Neither side has any intention to prolong.

The positions I posted are the longest with Black specifically to be mated--not quite the goal, but a starting to point to adapt from.

So, from that stance, unless we can prove which side is to move, as in the h#111 that is a h#107.5 for this goal, we mjst find the shortest possible mates in the h#40 & h#48 positions, as are starting points for this challenge.

It would be a duplex if the numbers of moves match.

You're still looking at the helpmate that is required to show that a position is not dead as a composition. For the determination whether a position is dead or not it doesn't matter which king is mated, as long as at least one king can be mated.

To whom do you speak, Joost?

To Viktoras, I do wonder what the duplex record would be, both sides having the same number of moves...

My question was poorly conveyed -- I was primarily interested to know the record for a given side to move (that has been answered).
The duplex question is interesting, but hardly the droids I'm looking for.