All Questions
Tagged with mathematics chess-variants
16
questions
11
votes
2
answers
3k
views
When can legions of knights on an infinite chessboard checkmate a lone king?
On an infinite (perhaps only in one direction?) chessboard, what kind of configuration of (possibly a very large number of) knights could checkmate a lone king? I'm really thinking of an infinite-in-...
- 335
14
votes
1
answer
3k
views
Checkmate in ω² moves with finitely many pieces
The post Checkmate in ω
moves? has inspired a lot of discussion and mathematical research into positions on an infinite chessboard where white can mate in a transfinite amount of moves. The current ...
- 503
3
votes
1
answer
277
views
Mate-in-N problems where N scales indefinitely with board size
Motivation - Long range mating patterns
This question is inspired by my recent interest in infinite chess and the post on MathOverflow Checkmate in ω moves?. Since my chess endgame skills are quite ...
- 503
-1
votes
1
answer
480
views
What is white's increased advantage in chess90 as compared to chess870? (Chess960 can be split into 2 subsets, chess90 and chess870)
Here, it is shown 90 of 960 positions involve having to move a rook on 1 side in order to castle on the other side (unless the rook is somehow captured or something). These 90 positions come from 18 ...
- 2,172
2
votes
1
answer
748
views
How many Chess960 positions exist in which castling on one side does not require moving the rook on the other side?
Update: It's chess870 (or chess869). See answer.
Context/Motivation/Goal: In regular chess, you never have to move a rook (on 1 side) to castle (on the other side). My aim is to see how much of 9LX ...
- 2,172
14
votes
2
answers
798
views
If repetition loses, who wins KvK?
Suppose we're playing a version of chess where you lose if you repeat once an earlier position (position = arrangement of pieces + who's move it is). We're down to the wire, and we've just arrived at ...
- 13.1k
6
votes
2
answers
2k
views
Chess480: Why 480?
From wiki:
Lewis has named this chess variation "Chess480"; it follows the rules of Chess960 with the exception of the castling rules. Although a Chess480 game can start with any of 960 ...
- 2,172
7
votes
1
answer
964
views
Relation between ratings for Chess960 and standard chess
Is there any relation or any attempt at discovering a relation between Chess960 ratings and standard chess ratings? This can be for GMs, for (any)M's, for pro players, or for all players on lichess/...
- 2,172
1
vote
1
answer
75
views
What arrangement of 8 each of these 4 different compound leapers has the "strongest coverage properties" on a 16x16 board?
The 4 compound leapers I'd like to look at are:
(1,2), (0,3), (2,2); knight+threeleaper+alfil
(1,2), (0,2), (1,1); knight+kirin
(1,2), (1,3); knight+camel
(1,2), (2,3); knight+zebra
What arrangement ...
- 308
14
votes
7
answers
3k
views
Arrange 5 non-attacking knights on a 5x5 toroidal board
The celebrated British mathematician and lover of public transport, Simon Norton, passed in 2019. He was the subject of a wonderful biography. He was not a particular fan of chess, but here is a tiny ...
- 13.1k
5
votes
1
answer
660
views
Longest possible game of Horde Chess
The longest possible normal game of chess has been calculated, but I want to know what the longest possible game of Horde Chess is. What makes this an interesting case is the crazy amount of pawn ...
- 17.7k
7
votes
1
answer
301
views
16 roses, 16x16 board; maximum double-attacked squares while all 256 squares are attacked at least once?
The rose is a piece that is best described as a "circular nightrider", able to reach up to 32 other squares from the center of a 13x13 area by making consecutive knight jumps in a rotating fashion in ...
- 308
5
votes
2
answers
384
views
What is the maximum number of squares 8 queens and 8 nightriders can attack on a 16x16 board?
Including but still obstructed by occupied squares, what is the maximum number of squares on a 16x16 board that 8 queens and 8 nightriders can collectively attack at least once each? Even if attacking ...
- 308
4
votes
1
answer
687
views
Minimal number of moves before castling in Chess960
As you know, in the initial position Chess960 the king lies between the two rooks. Here are the rules for castling.
For a starting position P, let n(P) be the minimal number of moves that White needs ...
- 409
10
votes
4
answers
4k
views
How to calculate the number of combinations for Chess960 positions
Can someone derive how do we get the total number of 960 possible positions for Chess960?
- 219