Comment by quuxplusone | Hacker News Reader

Comment by quuxplusone | Hacker News Reader

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Mentioned in TFA: This version of chess is given by Martin Gardner in his "Mathematical Games" column of July 1980 (pages 27 and 31) — https://www.jstor.org/stable/24966361 — and the analysis of White's mate is given in the column of August 1980 (page 18) — https://www.jstor.org/stable/24966383.

I do wonder how things would change if the board were 9 cells long; 10 cells long; etc. Also, it seems "in the spirit" to permit castling if neither K nor R has moved yet: i.e., from the position

K _ R N r _ n k

White ought to be permitted to

_ R K N r _ n k

(Or maybe there's a stronger argument for R K _ N r _ n k, actually. The former was conceptually "rook moves halfway toward king, then king moves to the other side of rook"; but the latter is "rook moves two steps in king's direction while king moves to the other side of rook.")

I'm pretty sure this wouldn't change the analysis on the 8-cell board at all, though. I wonder if it would change the analysis on any size of board.

Maybe I'm not good enough at chess to understand the strategy here, but how would castling be useful in this 1-D game? Castling in a normal game protects your King and activates the Rook. In this 1-D game, your King starts out protected behind the Rook. If you castle and end up in a _ R K N position, your king is exposed and your Rook is trapped behind the King, useless, with no way to ever get it back out. The Rook seems essential for mate, and its power has been eliminated.

Exactly. Feels like R K N would be a more suitable initial position in which castling would swap the king into safety, provided it has not moved and is not in check...

Though maybe in that case the best first move for both is to castle and we are non the wiser (back to the original starting position)

I had claude code implement minimax (w/ alpha-beta pruning) for the general n cells version of the game.

I checked n=6...20. It looks like white wins for n=6 and n=8 with perfect play, otherwise it is a draw.

With random play, black seems to have the edge regardless of board size. About 2/3 of the games end in a draw, but black wins 20% and white 13%.

> It looks like white wins for n=6 and n=8 with perfect play, otherwise it is a draw.

For n=6 it's "1. N4 mate," right?

For n=7, "1. R5" is a stalemate; "1. R4 N4 2. N4 r4#" is a loss; "1. N4 n4 2. R2 r6 3. R3 r5 ..." is a draw by repetition; so yeah, it's a draw with best play.

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