Highest number of mates

Question

In chess, what position has the highest number of checkmates in 1 move for a given side? You can have as many of each piece as you want, except for the king (you get exactly one). Bishops can be same color. Other color can have only the king, or other pieces if you want to. Rules same as chess rules. Pieces can be:

Queen
Rook
Bishop
Knight
Pawn
1 King (a must)

Answer 1

The highest number of one-move mates that I have found is currently 91. It is based off of the following idea:

RB.....K
........
......Q.
........
........
........
........
........

Here, each dot or letter represents a square on the board. There are 7 positions that the bishop can move to, so I would count this as 7 different moves that end in check mate, ie. 7 different 1 move mates. When counting the total number of moves that mate from each piece in the board, I will represent it like this:

07.....K
........
......0.
........
........
........
........
........

I found the following board based off of this idea that has a total of 91 different moves which result in checkmate:

B..RQ.BQ
Q....R..
..RB....
RB.K.B.Q
Q......Q
.R......
B..B..R.
Q..QQQQB

Where many pieces have several possible mates (a=10, b=11):

0..03.02
2....8..
..7b....
03.K.a.1
3......3
.a......
0..7..9.
2..13220

There might be a small permutation of this board which increases in incrementally, but I am interested in what other ideas people have from scratch.

Answer 2

A bit late to the party, but here's 142 checkmates:

The K in the middle is the black king. Every number is a white queen, with the number indicating the number of ways to mate with that queen. I got this through the following reasoning:

1. arbitrarily choose black to be mated
2. The question asks for the highest number of mates for 1 side, not both sides, so clearly the mated side should only have a king and no other pieces, as any other pieces would just get in the way.
3. the black king should be in one of the center squares (doesn't matter which), as that allows the greatest scope for mating
4. the black king should not have anywhere to move, to allow maximum mates. note this would be stalemate in a real game, but there's no stipulation it has to be a realistic position.
5. Queens and knights are the only pieces worthy of being considered for white, as they can emulate the moves of every other piece, whereas the reverse is not true.

From the above, I devised a kind of modified greedy algorithm (manual as i cant be bothered to code it), as follows:

1. assign a number B to each square which is not yet taken, where B represents the number of mating moves which either end on that square or pass through that square. Thus B represents the number of mates which would be subtracted if you put a piece on that square. Initially all squares are 0.

2. For each square which is not on a checking line, work out A-B=X, where A is the maximum number of mates you could add by adding a piece. Thus X is the 'net profit' from adding a piece. (queen or knight, although I soon worked out that only queens are really effective - knights cost more than they contribute in the long run).

3. add a piece to whatever square has the most profit. in the event of a tie, favour corner squares first, side squares second and other squares third, since corner/side squares will interfere less with the greedy algo going forward.
4. repeat from 1 until there's no more profit to be had.

The 142 solution above is one of the local maxima using this algo. I can't prove it's the global maximum.

Answer 3

Without a king the maximum is 143 mates in one, which was achieved in 1947.

Nenad Petrovic, Sahovski Vjesnik 07/1947

Thanks to @JSI in the comments, with a slight modification to the 1947 position, the highest possible is 142 mates with a king.