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Comment by vinchuco | Hacker News Reader

I wish it had examples! I'd be more interested in a move that complicates the game. In fact, what is the most complicated position in chess? (Legal or not)

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Probably positions stemming from the Botvinnik variation of the Semi-slav. Conventional chess wisdom doesn't really help, and figuring a way forward is pure calculation.

Then also, maybe lines of the "Irrational system" of the French Defence, Winawer variation (lines of Qg4, and Black sacrificing both g7 and h7 pawns).

Playing with nuances about what "complicated" means, perhaps also Nimzowitsch's "Immortal Zugzwang" game, where White is absolutely helpless on an almost full board of pieces.

The "Legal or not" part of your question is interesting. I am guessing you mean a "legal" board is one which was derived from the starting position following the legal moves. How could this be determined, short of doing a brute force search from the starting position?

This is something I've thought about when looking at chess problems, whether such problems could actually occur in a real game.

I wonder if existing computer chess engines can be modified to do retrograde analysis, and then find some heuristic for positions that are "obviously" possible via legal moves, and then see if the retrograde analysis can reach one of those.

I have a feeling this is often tractable, because we could probably construct a cooperative scenario involving sacrifice of arbitrary pieces at the beginning of the game (maybe via a series of knight captures?), and then the main question is confirming how particular pawns moved past each other, and finding a way of ensuring that no stalemates occurred while positioning the kings.

Sounds computationally intensive. It reminds me of an experiment I read about some time ago, tangentially: http://theinvisiblegorilla.com/blog/2012/02/15/how-experts-r...

Thanks for the link! That in turn reminds me of how Fischer advocated randomizing starting positions in order to eliminate the role of opening theory.

https://en.wikipedia.org/wiki/Chess960

(because apart from the structure part that the link you gave mentions, experts seem to know a huge amount of explicit opening theory, in terms of memorized opening lines and particular chess masters' view of their tactical consequences)

I'm getting more curious about the reachability question.

There are some discussions at

https://chess.stackexchange.com/questions/4830/how-many-lega...

https://mathoverflow.net/questions/138133/what-proportion-of...

https://www.chess.com/forum/view/general/how-many-different-...

https://en.wikipedia.org/wiki/Chess#Combinatorics_of_chess_a...

That includes a retrograde solver for openings, but that's not exactly what I was envisioning -- I was thinking of a retrograde solver for endgames, which then needs something kind of akin to an inverse tablebase ("yes, this family of positions is known to be legal!" instead of "this position is a win for black").

It's an interesting question. It is easy to check when a position is unreachable, sometimes.

For instance a white king on H8 and black Rooks on A7, A8 (unless I'm mistaken).

It almost seems as if it is easier to find a position that is guilty (when it is), than to check that a position has a perfect record (check that it is legal).

I don't understand what "legal or not" means here. Does that include making the board 1000x bigger and increasing the number of pieces? Seems like by changing the rules of the game you could make a position arbitrarily complicated.

It's meant to be left for interpretation. But I was thinking not changing the board size. Add pinned pieces, compose tactics, make the game tree as wide as possible.

the starting position ?

No, add a pawn.

what ? You mean have a non-legal starting position ?

Well yeah, I could also add a rubiks cube to the white pieces.

Fair point. But we'll eventually settle on some rules.

The thought is like the following: people actually compose chess puzzles for fun, without regard to them appearing in an actual game: There's chess puzzle composition competitions.

Could one write a program to make a monster puzzle (or better, the most complicated) with forced moves?

That is: maximize X in "white to move and mate in X moves" restricted to board size and standard chess rules.

My wish was granted!

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