Longest depth for a half-point zugzwang

Question

What is the maximum depth of a half-point zugzwang? Depth is defined as the number of fullmoves it takes for the winning side to win. I know 245 is possible. (Ignore 50-move, 75-move rules).

[Title "WTM draws, BTM loses in 245 fullmoves"]
[FEN "4n3/2n5/8/8/8/3K4/5k2/2R1N3 w - - 0 1"]

Answer 1

TLDR: Your shown position is probably the deepest depth half point zugzwang known till date. But that might change as we move to higher-piece tablebases or as more research goes into the existing 7-piece tablebase.

Terms I'll be using (for those unfamiliar with them):

• half point zugzwang - (WTM draws, BTM black loses) or (WTM white loses, BTM draws)

• full point zugzwang - (WTM white loses, BTM black loses)

• DTC, DTM, DTZ - link (Note - the papers referenced below and this answer considers a full move (1 move by each) as 1 depth but lichess and Syzygy tablebase consider a half move as 1 depth)

Greatest depth 6-piece zugzwang

Latest data I could find regarding zugzwangs was of 6-piece tablebase.

According to this paper, the maximum possible zugzwang DTC of a 6-piece tablebase is 226. And the pieces involved are KNN, KRN. Unfortunately, they do not provide the fen notation of this position and instead direct towards this website which no longer seems to host their data. Hence I could not verify if the position provided in the paper is the same as that of this question. But it does seem likely that both are the same since the pieces involved are the same and I verified that the question's position is shown as DTZ 450 by Lichess (meaning the no. of moves after which the game can be won by a checkmate is the same for both).

Interestingly, the same paper also mentions that there is unique zugswang position with the pieces KNN, KRB with a max DTC of 213. While trying to search for this position, in another paper, I came across the following 2 positions:

[title "BTM draws, WTM Mated in 225"]
[fen "k4b2/3K4/1r1N4/5N2/8/8/8/8 b - - 0 1"]

[title "BTM draws, WTM Mated in 225"]
[fen "k2r1b2/8/3NK3/5N2/8/8/8/8 b - - 0 1"]

Issue is, both of them are mate in 225 and have the same DTZ of 419 according to Lichess. Since, the original paper mentions that the position with DTC 213 is unique and 419 < 2 * 213, I believe that a better mate than 225 should be possible with KNN, KRB. Though it seems unlikely that this better mate would be better than OP's 245.

Hence, we could safely assume that your position is the best we can do with 6 pieces.

Greatest depth 5 or lesser pieces zugzwang

If we go to 5 pieces or less, the maximum possible depth of zugzwang seems to be decreasing (paper). The best we can do with 5 pieces is this mate in 105 zugzwang:

[title "WTM draws, BTM Mated in 105"]
[fen "8/8/8/p7/K7/4k3/8/6NN w - - 0 1"]

Greatest depth 7 or more pieces zugzwang

Since we don't have any such data available for 7-piece zugzwangs, for now, your mate in 245 zugzwang is the best we have. Though, we can't say for certain if the 7-piece solution is going to be larger or smaller than the current one since after a threshold, the probability of zugzwang decreases as the no. of pieces increase.

Some interesting facts indirectly connected to the question (sources - above mentioned papers + this one):

• full point zugzwangs are rarer than half point ones and are more focused upon due to their chess study aesthetic
• currently known max. depth full point zugzwang:

[title "WTM Mated in 17, BTM Mated in 103"]
[fen "8/8/8/8/p4p2/k1P5/2K1P3/8 w - - 0 1"]

• 5 or lesser pieces full-point zugzwangs aren't possible without a pawn
• Pawnless zugzwangs are just 5.26% of the total. Presence of at least one pawn increases the density of zugzwangs by a factor of 4
• Zugzwangs are also more frequent when Knights are present (always the tricky piece)
• Finally, all of the above data is subject to the condition that we aren't checking a subclass of zugzwangs. Tablebases assume that castling is not possible (source). However, a zugzwang may become a non zugzwang and vice versa depending on castling. A case where castling makes a difference:

[title "WTM draws, BTM w/o castling: Mate in 54, BTM with castling: draws"]
[fen "1KQNk2r/7r/8/8/8/8/8/8 w - - 0 1"]