# Chess on an Infinite Plane (game: bowlinggreen - vickalan)

n13

7...C(-2,7)

-2,2

8...C(-1,5)

c-13

You already have a knight on (1,3). Your chancellor can't go there. Will you make another move?

c-1,3

Oh, sorry. I missed the "-". So your move and my move:
9.C(-1,3)...Cx(-1,3)

-2x-13

10...(7,6)

r-21 or r-12

11.R(-2,1)...N(1,6)

r-27

12...N(3,5)

c73

i meant 83 sorrry

xman720 skrev:

This is really cool, I'm going to follow this for sure. From my own experience, the problem with open play chess is that it's super difficult to checkmate an opponent's king (example: king + two rooks is draw by insufficient material) so the extra material/pieces is really helpful. For clarification, how far away are the hawk/pawns?

Also, I recommend that within the normal 8 x 8 chess board, players use normal chess notation for shorthand and only revert to raw coordinates outside the 8x8 board.

Maybe I misunderstand you? It seems trivial to mate with K+2R vs K:

* Contain the opponents king in a n*n square (n > 6) with rooks on opposing corners. Rooks defend each other when necessary (https://en.lichess.org/analysis/2R4R/3k4/8/8/8/8/8/K7_w_-_-) and return to opposite corners when the opponents king threaten to escape in that direction (https://en.lichess.org/analysis/2R4R/8/8/5k2/8/8/8/K7_w_-_- - next moves might be X. Kb1 Kg4 Y. Rc3).

https://en.lichess.org/analysis/7R/8/8/8/6k1/2R5/8/1K6_b_-_-

* Move your king towards the edge of the square

* Resize the square to a corridor with dimensions n*5 (rooks defend each other at the top, king guards the opening at the bottom)

* Force the opponents king towards your own

* Checkmate

Zharptytsia wrote:
xman720 skrev:

This is really cool, I'm going to follow this for sure. From my own experience, the problem with open play chess is that it's super difficult to checkmate an opponent's king (example: king + two rooks is draw by insufficient material) so the extra material/pieces is really helpful. For clarification, how far away are the hawk/pawns?

Also, I recommend that within the normal 8 x 8 chess board, players use normal chess notation for shorthand and only revert to raw coordinates outside the 8x8 board.

Maybe I misunderstand you? It seems trivial to mate with K+2R vs K:

...Checkmate

Good work!
Thanks for analyzing it. You show it's easy to checkmate with (K+2R) vs (K).

I didn't yet study the possible ways to checkmate on an infinite plane. I'm sure most of the basic checkmates are not possible on an infinite board. I hope to study them or find answers:
1. King-Two Rooks vs. King (8 x 8: possible)(infinite plane: you found it's possible)
2. King-Queen vs. King (8 x 8: possible)(infinite plane: I don't think possible )
3. King-Rook vs. King (8 x 8: possible)(infinite plane: I don't think possible)
4. King-Two Bishops vs. King (8 x 8: possible)(infinite plane: how many bishops are needed?)
5. King-Two Knights vs. King (8 x 8: Not possible) How many knights are needed on an infinite plane? (The Formation Chess version start with 14 knights for each color)
6. King-Rook-Bishop vs. King-Rook (8 x 8: usually not possible, so probably never possible on infinite plane)
7. King, Knight and Bishop vs. King (8 x 8: very difficult to checkmate, so probably not possible on infinite plane)

If anyone does more research on this I hope it can be shown here: (chess on an infinite plane).
bowlinggreen wrote:

i meant C(83)

13...Bx(8,3)