In old-school chess AIs, zugzwang is also of interest because it can break null-move pruning[0], which is a way to prune the search tree. "Null move" just means "skip your turn", and the assumption that skipping your turn is always worse than the optimal move. But in zugzwang positions, that assumption is wrong, so you have to avoid doing null-move pruning.

Stockfish's heuristic for "risk of zugzwang" is basically "only kings and pawns left over", alongside logic for "is null-move pruning even useful right now" [1]:

    // Step 9. Null move search with verification search
    if (cutNode && ss->staticEval >= beta - 16 * depth - 53 * improving + 378 && !excludedMove
        && pos.non_pawn_material(us) && ss->ply >= nmpMinPly && !is_loss(beta))
    {

[0]: https://en.wikipedia.org/wiki/Null-move_heuristic

[1]: https://github.com/official-stockfish/Stockfish/blob/1a882ef...

Relevant for a lot of geopolitical and corporate strategic situations as well. The whole Mideast situation we're in now is because we were in zugzwang and a couple leaders felt the compulsion to move. Taiwan is a similar situation: the best policy is "strategic ambiguity", which is holding for now, but is a bit of an unstable equilibrium.

More relevant to a business site, this is the situation many large corporations find themselves in. Say you're Google and you own an immensely profitable monopoly. The very best thing you can do is nothing; anything you do risks upsetting the delicate competitive equilibrium that you're winning. If you're an executive, how do you do nothing? You can't very well hire thousands of employees to do nothing and pay them to do it. But if you don't have thousands of employees, and your job is doing nothing, how do you justify the millions that they're paying you?

The strategy many executives use is to set different parts of their organization at odds with each other, so that they each create busywork that other employees must do. Everybody is fully utilized, and yet in the big picture nothing changes. Oftentimes they will create big strategic initiatives that are tangential to the golden goose, spending billions on boondoggles that don't actually do anything, because the whole point is to do nothing while seeming like you need thousands of people to do it. And the whole reason for that is because most people are very bad at sitting still, and so if you didn't pay them a whole lot to do nothing useful, the useful stuff they'd be doing would be trying to compete with and unseat you. (You can also see this in the billion dollar paydays that entrepreneurs get when they mount a credible threat of unseating the giant incumbent.)

Would it be a fair analogy that the president is in a constant state of Zugzwang - ever subsequent move he makes only ends up making things worse.

The metaphoric meaning of being under “Zugzwang” in German is very similar to “forcing someone’s hand”, from the perspective of the one whose hand is being forced. It means being forced to act, as opposed to not taking action.

Interestingly, many people will refer to zugzwang when one player only has losing moves and would love to skip their turn altogether, but that's not zugzwang. As a non-example of zugzwang, consider the position with White having a Kb6 and Rc6, and Black just has Kb8. When White moves 1. Rc5, killing a move, Black has no choice but to move 1...Ka8 followed by 2. Rc8#. However, Black is not in zugzwang, because the position is not mutually bad for either player. As a true example of zugzwang, consider the example where White has a Kf5, pawn on e4, Black has a Kd4 and pawn on e5. Now this position is zugzwang because whichever player has to make the next move loses defense of their pawn and with it, the game. For instance, if it's White to move, the game could continue 1. Kf6 Ke4 2. Kg5 Kf3 3. Kf5 e4 and Black will simply march his e-pawn to the 1st rank, promote to a Queen, and checkmate shortly after.

While normal Go allows passing one's turn, and thus has no zugzwang, there is a No Pass Go variant [1] that forbids passing, where the first player in zugzwang loses the game.

[1] https://senseis.xmp.net/?NoPassGo

In MTG control decks and a subset of that, prison decks are the prime and extreme example of that. Especially something like Lantern Control. It's not about winning, it's about trapping your opponent _not able to_ win.

Sounds like a quagmire.

Zwischenzug (https://en.wikipedia.org/wiki/Zwischenzug) is also a good one and is equivalent to intermezzo as an "in-between move"

i feel like Musk does it on a daily basis with all the heavy artillery he has on the board

Go is a turn based game without this feature (or bug?) because you aren't forced to move, you can instead pass. Both players passing in a row implies neither player thinks they can improve their position and the game ends.

I recently happened upon a comment (not on HN) that seemed to treat 'zugzwang' as a synonym for 'deadlock'. Possibly because 'zugzwang' sounds really cool and makes your inner voice sound intelligent to your inner ear.

It's kind of an illusion when you think about it. "Whose turn it is" is an inseparable part of the game state. If any move makes the game state worse this turn, then the game state was already bad before this turn.

Do corporations get drawn to AI from a compulsion to make a move addressing it?

"Fear of missing out"

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The only way to win is not to play.

Sounds a bit like a Xanatos Gambit

https://tvtropes.org/pmwiki/pmwiki.php/Main/XanatosGambit

Differences being Zugzwang explicitly doesn’t allow a non-move, and I guess assumes a zero sum game? Whereas a Xanatos Gabmit is flexible enough to accommodate both non-moves, and a non-zero-sum setting.

Either way, for your opponent, all roads lead to ruin.