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1D Chess

rowan441.github.io

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Re: 1D Chess

#181

Post by garaetjjte »

tylervigen wrote: post #79
stavros wrote: post #75

Earlier quoted context omitted.

Wait, how is the "put off checkmate" objective scored? Turns before checkmate? Or what? Is it just a joke?

I have never played it, but I could imagine a scoring mechanism that would make it interesting, and perhaps is implied by the rules: The score value starts at 1. Every additional "check" multiplies the score value by 2 (so 2, 4, 8, 16...). The first player to say "checkmate" receives the score. Track your summed score between games; the player with the highest overall score at any given time is "winning."

Isn't that just iterated prisoner dilemma?

Re: 1D Chess

#182

Post by pedrosorio »

quuxplusone wrote: post #14

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…

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%.

Re: 1D Chess

#183

Post by daynthelife »

otherme123 wrote: post #148
daynthelife wrote: post #127

It frustrates me that the site does not give the strongest defense for black. The position is mate in 6, not 5: 1. N4 N5 2. Nx6+ K7 3. R4 N3+! 4. K2 N5 5. N8! Kx8 6. Rx5#

You give "3 ... N3" a !, when it is literally the only legal move the black has.

The site plays Kx6 instead. You're right though that I was generous with the exclams; all the moves are easy to find in reality.

Re: 1D Chess

#184

Post by daynthelife »

splonk wrote: post #169

It's interesting that the page actually uses minimax to determine black's play. I kind of assumed it would be a simple lookup table given the small state space of the game. I suppose it makes it easier to add more variants.

It clearly doesn't use minimax, since it doesn't play the best move for black in the critical line, leading to a mate in 5 instead if a mate in 6.

Best line is N4 N5, Nx6+ K7, R4 N3+!, K2 N5, N8! Kx8, Rx5#. The site has black instead play Kx6 on the third move, allowing a faster mate.

Re: 1D Chess

#185

Post by ctool »

A workable minimalist variant is slimchess, which contains one of each piece on a 3x8 board. It's the smallest chess board that can preserve all the rules (including castling).

Re: 1D Chess

#187

Post by jamie_ca »

stavros wrote: post #119
jamie_ca wrote: post #117

Earlier quoted context omitted.

Give two players cards, "Check" and "Checkmate". Both players choose a card. Players then in turns reveal their card, and if Check, make another choice. The player first revealing Checkmate wins if their opponent's currently-chosen card is also a Checkmate.

But then this just gives the win to the first person to open their card, since in that round they had both selected Checkmate. Or, you have an incentive to rush to open your card when you know you've selected Checkmate, as you want to be the first one to open.

Maybe I should've worded differently for clarity, the game doesn't go forever:

The player first revealing Checkmate ends the game. They win if their opponent's currently-chosen card is also a Checkmate, otherwise the opponent wins.

Re: 1D Chess

#188

Post by quuxplusone »

pedrosorio wrote: post #182
quuxplusone wrote: post #14

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…

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.

Re: 1D Chess

#189

Post by questerzen »

The given best-game solution is not optimal: Black can delay mate for another move to give a forced win in 11 ply rather than in 9 ply. Optimal is: N4 n5 N6+ k7 R4 as given, but Black can delay mate with ... n3+, rather than ...k6. The remaining moves are then: K2 n5 N8 k8 R5#. Perhaps your minimax code doesn't include moves-to-mate in the move score?

Re: 1D Chess

#190

Post by asdofindia »

hackyhacky wrote: post #42

If you enjoyed this, you might like Mind Chess, which can be played without a board and pieces [1]: Consider Mind Chess. Two players face each other. One says "Check." The other says "Check." The first says "Check." This continues until one of them says, instead, "Checkmate." That player wins -- superficially. In fact, the challenge is to put off checkmate for as long as possible, while still winning. This may be bet…

There's a fantastic game like Mind Chess and Rock-Paper-Scissors called "Hand Cricket". It is like cricket, but played by showing a number with the fingers of your hand. (Showing just a thumb is 6, folding all fingers is 0, and 1-5 is 1-5 fingers as usual).

Both players play a number simultaneously. If the numbers are the same, the batting player gets out. Otherwise, whatever number the batter showed gets added to their score. The innings continues till the batter gets out. And then the roles reverse, the other person becomes batter.

After both innings, the person with higher score wins.

It's spooky because you have 7 different choices for each ball but people still get out rather quickly.

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