What is the farthest away a game can be from a guaranteed checkmate?

Question

What is the maximum number of moves away from checkmate that a player can be where checkmate is guaranteed? There are many positions that are a guaranteed win for a player if played perfectly, right? (Obviously there is not a guaranteed win from the first move). My question is: What is the furthest amount of moves one can be from guaranteed checkmate, when the shortest amount of moves to checkmate is taken?

Let's assume you are white and have, say, a bishop and a knight left and black is down to just the king. (there is a way to get checkmate with a bishop a knight, so checkmate is assumed to be guaranteed). Now, one set of moves could take say 40 moves to get checkmate from this point, but the least number is say 19 moves away. Now, my question is asking what the most amount of moves to guaranteed checkmate is, but you have to take the route to checkmate that has the least amount of moves, so 19 would be the case from the point where the bishop and knight are the only pieces other than the kings left.

I apologize for the lengthiness of this question, I couldn’t think of a good way to ask what I’m asking. This question derived from wondering if black or white could win every time from the first move but obviously that isn’t the case. The main question is at the end of my first paragraph.

Edit: 50 moves without a pawn push or a capture does not trigger a draw.

Answer 1

The position with the longest known sequence away from checkmate has a mate in 595 moves. It is a computer-verified extension of the 8-piece table record found by Lutz Neweklowsky.

By "verified," I mean Stockfish agrees with the moves that occur until the 8-piece position occurs, and then we know 100% it is correct from there. While we can't know defintely the first 4 moves are 100% the best, since 14-piece databases aren't here yet, it is best to accept them as it is at the limit of our technological capabilities.

[Title "Mate In 595 Moves"]
[FEN "7R/8/8/8/q7/p2B1KB1/P2pRQn1/3knB2 w - - 0 1"]

1. Qxe1+ Nxe1+ 2. Bxe1 dxe1=N+ 3. Rxe1+ Kxe1

Answer 2

I doubt that anyone will be able to give you a definitive answer beyond this one, but the longest known win from the end of a game is a famous 549-move 7-piece tablebase win. Until we get to 8-piece tablebases, this is probably the longest anyone can prove.

You can see that position, and all 549 moves here.

Answer 3

UPDATE:

An important update on 8-Men Tablebase by Marc Bourzutschky.

http://arves.org/arves/index.php/en/2-ongecategoriseerd/1509-8-men-tablebase-first-explorations?fbclid=IwAR2BwvtDqDsu_2HIZjzHKWGgzJg42e1SX1SugBV_fLxr8KfQ3rfp3iOt1C4

This is worth reading in detail, but one point demands quotation:

An important question is at what point the chess board becomes so crowded that adding more pieces does not lead to longer winning lines due to the increased likelihood of shortening captures. My results suggest that we may already be at or close to this saturation point: the longest winning line for 8-man endgames without pawns appears to be “only” 400 moves. [...] After generating about 15% of the pawnless endings I’m quite confident to have captured the longest ones. While 15% seems like a small subset at first blush, most other piece configurations have large material differences between White and Black so that long lines are unlikely.

Q: How long is the longest forced checkmate in chess?

A: We will probably never know but the naive extrapolation based on multiplication by number of moves is no longer impossible. It is even conceivable that we already know the longest forced mate in all of chess, which occurs with 7 pieces.

50/75 move-rules don't apply

Firstly, let's definitively remove one distraction: 50-moves (or 75-moves). The Codex for Chess Problem Compositions states:

Footnote 12.

Presently the rules defined in the 1 Jan 2018 version of the FIDE Laws are valid. > Relevant for compositional chess are articles 1 to 5, 9.2 and 9.3.

This includes 50 moves-rule, but excludes 75 moves-rule. However:

Article 17 – 50 Moves-Rule

Unless expressly stipulated, the 50 moves-rule does not apply to the solution of chess compositions except for retro-problems.

These conventions are specifically crafted to support the kind of endgame analysis being discussed in this SE question.

The answers are very different from a superficially similar SE question where the 50 move-rule is taken into account.

Extrapolation from 7-man

The 7-man case is solved at 549 moves, and ingenuity has pushed this back a few more moves (as of Jan 2021, 535 moves). The real breakthrough will come from tablebase development for the 8-man case. We don't know what the answer will be, but there is some intelligent extrapolation possible from existing results.

The Lemonosov webpage stated as long ago as 2014:

Many show interest in what to expect from 8-man endings. First, take note that the longest 6-man mate took 262 moves (KRN-KNN). Moving to 7-man endings doubled [the value].

Of course, as the number of pieces increases, it maybe that the opportunity for stalemate increases and tends to dominate. There is no indication that this is happening at 7-man database level. We are not just limited to the 32-piece starting position, of course, we are looking at any legal position where no captures have yet taken place. So chess as whole might be a draw, while at the same time there might still be some very long forced checkmates in 32-man positions.

I imagine (and it can't be more than this) that such positions might lead themselves very quickly to exchanges, because the board is so cluttered). But I have no idea, and (absent some stupendous breakthrough in quantum computing) humanity will never know.

Answer 4

Here you can find a mate in 555 moves by me (Lutz Neweklowsky).

In this kind of chess compositions we don't have a 50-move-rule.