Chess on an Infinite Plane

another bump

Recently in my game v. Aiden a point was brought up about an infinite mating pattern- without a fifty move rule this could make a game go... forever. We are deciding if the mating pattern person should win or the game should draw. To make the forced draw valid we must add a 50+ move rule, which I have no idea why it was erased in infinite- we need the rule more than ever here!

I agree in practice that a 50-move rule is needed (or "x"-moves), because there may be some endings where a king is bound to keep walking away, but never be put in checkmate.

Tomato showed an example (here - post 223).

In theory one player can just keep moving his king one square every move, but it is never a repeated position, so he is never bound to admit a draw.

The dilemma is that I want this game to be mathematically "correct". What if there are legitimate checkmates that require 1000 moves? Or 50,000? This is an unresolved problem.

This is an example of an endgame (by HorribleTomato) where Black's king is eternally forced to move one square away at every move:

The pgn notation takes a form like this (a-f are variables for coordinates, not file and ranks):
White.....Black
R(a,b).....K(c,d)
Q(e,f).....K(c,d+1)
R(a,b+2)...K(c,d+2)
Q(e,f+2)...K(c,d+3)
R(a,b+4)...K(c,d+4)
Q(e,f+4)...K(c,d+5)
R(a,b+6)...K(c,d+6)
Q(e,f+6)...K(c,d+7)

It might be easiest to say that if king is forced to make a one-square move in the same direction for five consecutive moves then the game has ended in a stalemate.

Thanks to @HorribleTomato for providing this interesting endgame example.

But now I'm thinking White could have won in the example above if there are only those pieces. White could have moved his king to g12 prior to the force, eventually leading to a mate. So if there were other pieces, White would either need to play otherwise (stop the repetition), or the game ends due to "translational repetition".

So now we must add that rule "if the exact pattern is followed, even down the board, 5 times IN A ROW, the game is considered drawn" 

Umm... that's what I just said, 2. This is kinda far off, but summer's coming, and during summer I think there should be a 2 day vacation per game (summer) that is a total of 5 days break, about a vacation. I'm sure I'll have one during summer, and I'll have games too. So... :/

I'm OK to call it a draw by perpetual check. Can I say the infinite chess committee is: hitthepin, HorribleTomato, and vickalan?

Then the committee has decided that forcing a king to move "one square in the same direction for 5-consecutive moves" is "draw by repetition"?

Also, I'm OK with any time-control (including having a bank of spare days for vacation). That's usually between opponents, although if games are in a tournament we probably need an upper limit.

No, the pieces attacking the king AND the king move in the same pattern for 5 turns. 

Tug may join also.

*facepalm* I presume you somehow posted offline (online 40m ago, posted 20m)

@AlphaToOmega V. @Hitthepin 

Someone asked for all the files required to initiate a game, and create board updates. So all required images (plus a few more) are below:

Note: making board updates can be more complicated than games on fixed board sizes. Based on where players move pieces, it may be necessary to "stitch" more board space to one side.

This may or may not be easy based on the graphical software you are using, but good luck. For infinite chess you have to "go outside of the box" so to speak.

The normal lead image:

Board (starting position):

board (empty - could be useful if you need empty squares for stitching):

That was me.

I think I need white queen on dark

white king on light

Black queen on white

and

Black king on black.

Paints on desktop works, right?

Continuing:

Chancellor:

Hawk:

Guard:

Template of all pieces (sized to fit to board):

move diagram for hawk (normally not required, but good if you need to explain it):

Good luck! Let me know if anything else I can do.