Post #1810167

2026-04-30 11:43 UTC

Once at university we accidentally invented Hexagonal Quantum Chess. Chess-like games on a hex board have been thought of before, of course. But one afternoon we had a hex board and some pieces and nothing better to do, so we tried to make up one of our own. Our pawns were very powerful, because they could make _either_ of the diagonally-forward moves, so a pawn had a large area of potential influence. But we constrained the initial two-space move to go directly forward. (Diagram on left.) This led to an ambiguity in the en passant rule. (Diagram on right.) The pawn that just moved forward 2 must have either zigged left-right via cell a, or zagged right-left via b. But it's not clear _which_ it did. So if an opposing pawn lands on a, does it capture? If cell b was occupied by something else, that's the easy case: the pawn had no choice but to go via a, and a capture on a must succeed. But if both cells were free, what rule do you choose? FAVOUR THE ATTACKER: the capture always succeeds. FAVOUR THE DEFENDER: the capture always fails. At that point, someone mentioned quantum mechanics, and we realised there are several more possibilities. CLASSICAL: when you make the double move, you state out loud which cell the pawn went through. Then a capture on that cell succeeds, and one on the other cell fails. HEISENBERG: flip a coin. SCHRÖDINGER: when you make the double move, you write down _in secret_ which cell the pawn went through. Again a capture only succeeds if it's on the right cell. But the opponent doesn't know which, until they look. Luckily we ran out of afternoon before attempting to play the final possibility: MANY WORLDS: fork the game and play out both versions.

Replies (7)

@fraggle@social.coop 2026-04-30 11:46

@simontatham@hachyderm.io have you seen "5D Chess with Multiverse Time Travel"? https://en.wikipedia.org/wiki/5D_Chess_with_Multiverse_Time_Travel

Open ##1810166
@jleedev@mastodon.sdf.org 2026-04-30 11:52

@simontatham@hachyderm.io I'm only passingly familiar with Diplomacy lore, but once a decade the errata are amended to resolve yet another paradox or ambiguity.

Open ##2589860
@casar@mastodon.social 2026-04-30 12:42

@simontatham@hachyderm.io This brings back some nice memories on high school times when we invented and played or own kind of card games during national championship in mathematics. Tarot by 6 players using two decks of cards was really fun to play.

Open ##2589861
@UnassumingKiwiReborn@kolektiva.social 2026-04-30 13:28

@simontatham@hachyderm.io You could just rotate the hexes by 60 degrees to eliminate the ambiguity

Open ##2589898
@mjd@mathstodon.xyz 2026-04-30 14:09

@simontatham@hachyderm.io Barely related but possibly interesting anyway: https://blog.plover.com/games/double-chess.html

Open ##2589901
@gclef@social.vivaldi.net 2026-04-30 14:17

@simontatham@hachyderm.io Another en passant alternative: "En Tanglement" where neither piece is removed from the board, instead they become entangled — black moves to a and white moves to b.

Open ##2589912
@SchwarzeLocke@ohai.social 2026-05-02 09:47

@simontatham@hachyderm.io It must be classical, because black is observing how white moves. The attack is not really happening afterwards, black is declaring that the board does not reflect the real state because they saw white pass a and attacked - the attack is not a killing from behind. There is one alternative though: white needs to declare an attempt before executing the move, black notes in hidden knowledge whether they attack if a is passed, then white flips a coin for the way.

Open ##2589913