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Trappist-1. Chess game with no boundaries. includes Guard, Chancellor, Hawk, and Huygens. () [All Comments] [Add Comment or Rating]
H. G. Muller wrote on 2022-06-22 UTC

There is nothing 'unknown' about the set of prime numbers; it is in fact very well known that there is no such thing as a 'complete' set of them, as the set is infinite. There exist simple (albeit inefficient) algorithms to determine for any given number whether it is prime or not.

It is also a misconception that the presence of a Huygens would make a game unsolvable due to the properties of primes or any other of its properties. E.g. it is very easy to prove a game with a starting position of King + 2 Queens vs King + Huygens on an infinite board is won for the Queens. It is even possible to give a detailed algorithm for how to do this, in a number of moves that only grows logarithmically with the distance between the Huygens and the Kings. If the Huygens has the first move, this number can of course be made arbitrarily large, by moving the Huygens far away after it runs out of safe checks (because the King approached it).

All this would still be true if the Huygens was a Rook, rather than a subset of it.

Gavin Yancey wrote on 2022-06-21 UTC

I wrote a digital implementation of this a few years ago. It's somewhat incomplete and probably a bit buggy, but likely good enough to play.

Code here:

I'm currently hosting it at -- although don't expect that to be highly available.

David Haft wrote on 2021-06-14 UTC

Does anyone know if there is a digital implementation of this game, (not on a truly infinite board for obvious reasons), perhaps on Zillions of Games, or playable in a browser?

V. Reinhart wrote on 2017-03-08 UTC

Hi Fergus, Thanks for your comments.

About the piece images, I think the ones used make a lot of sense, because they match your abstract styles very well. The orthodox pieces all follow the normal shapes in your set. But since some unusual pieces are used, I selected piece shapes that best represent what they do.

For the guard (or "mann") I used the circle shape with triangle, to indicate it moves both orthogonally, and diagonally. It is a very basic shape just as the king (which has the same moves).

Your set does not have a hawk, so I used the tall triangle shape because it appears "sharp", just as a hawk has sharp talons and beak.

Also, there is no huygens, so I chose the pyramid shape piece with the "+" shape cut-out. The pyramid is a symbol of mystery, just like prime numbers, and the "+" shape represents the orthogonal moves of the huygens.

I hope you'll agree that these images are good choices for both "Trappist-1" and "Chess on an Infinite Plane".

Last, on the topic of playing on an Infinite Plane, a player can move a piece 50-million squares away. There is no problem with that (although the play would be questionable at best). If someone does this, the piece simply is not shown in the chess diagram. There is only a supplemental note added to the game status such as "white rook is in square (50,000,000, 2)". (file and rank of the piece). But in actual play, I don't believe there is ever any reason to move a piece this far away because there is nothing of interest so far out. The piece would be less effective at attacking because it could not create forks.

In all the games played so far, the farthest span of pieces ever played was 36 ranks I believe. Then the distant pieces moved back in. (I'll send you a link if you'd like to see the game's moves).

Anyway, thanks so much for your comments. I really appreciate them. There's currently several games in progress.

Fergus Duniho wrote on 2017-03-08 UTC

Suppose a player decides to move a Rook 50 million spaces away. How can something like this be handled in this game? Must players impose limits on their moves apart from what is actually legal to make the game playable?

Fergus Duniho wrote on 2017-03-08 UTC

Some of my Abstract pieces were designed with specific powers of movement in mind. This set includes a piece for the Rook+Knight compound you are calling a Chancellor. It is called a KnightRook. The piece you are using is the Dragon King, which moves as a Rook or a Ferz. The piece you're using for the Guard is for a Ferz. The Abstract set includes another piece for what you're calling a Guard. It is called a Centurion in the set. Your Hawk and Huygens are not represented in the set, but the images you used for them are for diagonal moving pieces. So some other images would be more suitable.

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