On which squares has the opposing king never been checkmated?

[chessica]

Hi, I'm currently watching a few games that I play all the way to checkmate
If it is possible, I have two simple questions.


1. What is the distribution of checkmate positions on the board?
1.1. in normal chess
1.2. in FRC chess

2. Are there any fields where checkmates have never occurred? Results from 1.

[Ajedrecista]

Hello:

Hi, I'm currently watching a few games that I play all the way to checkmate
If it is possible, I have two simple questions.


1. What is the distribution of checkmate positions on the board?
1.1. in normal chess
1.2. in FRC chess

2. Are there any fields where checkmates have never occurred? Results from 1.

Someone wondered the same and collected some data over one million games borrowed from Lichess:

I looked at a million games played on Lichess and counted how many times checkmate occurred on each square

https://www.reddit.com/media?url=https% ... 300961.png

Which should answer your question 1.1. The short answer to the topic title is 'Nowhere': there have been checkmates in every square.

I expected more checkmates at the borders of the chessboard and less at the centre, which is exactly what results say. If we are going to trust this data:

Code: Select all

 3653    4714    6654    5756    14753   10901   26745   17271    |     90447
 1995     504     856    1526     2650    1647    2066    5990    |     17234
 2847     787    1066    1427     1430    1890    1533    5607    |     16587
 3084     671     862     839     1140    1587    1823    5538    |     15544
 3011     676     859     848     1148    1716    1848    5629    |     15735
 2620     688     842    1246     1394    1632    1539    5531    |     15492
 1916     465     699    1150     1667    1211    1560    6016    |     14684
 3458    4367    5860    4875     9066    9545   24937   17034    |     79142
-----------------------------------------------------------------------------
22584   12872   17698   17667    33248   30129   62051   68616    |    264865

This means that 'only' 264865 games out of the 1-million sample ended in checkmate (almost 26.5%). Computing percentages over 264865 and rounding up to 0.01%:

Code: Select all

 1.38%   1.78%   2.51%   2.17%   5.57%   4.12%  10.10%   6.52%    |     34.15%
 0.75%   0.19%   0.32%   0.58%   1.00%   0.62%   0.78%   2.26%    |      6.51%
 1.07%   0.30%   0.40%   0.54%   0.54%   0.71%   0.58%   2.12%    |      6.26%
 1.16%   0.25%   0.33%   0.32%   0.43%   0.60%   0.69%   2.09%    |      5.87%
 1.14%   0.26%   0.32%   0.32%   0.43%   0.65%   0.70%   2.13%    |      5.94%
 0.99%   0.26%   0.32%   0.47%   0.53%   0.62%   0.58%   2.09%    |      5.85%
 0.72%   0.18%   0.26%   0.43%   0.63%   0.46%   0.59%   2.27%    |      5.54%
 1.31%   1.65%   2.21%   1.84%   3.42%   3.60%   9.41%   6.43%    |     29.88%
------------------------------------------------------------------------------
 8.53%   4.86%   6.68%   6.67%  12.55%  11.38%  23.43%  25.91%    |    100.00%

The high count of g1/g8 mating squares might be explained by a lot of checkmates with a queen at h2/h8 squares plus a bishop in that diagonal or a knight at g4/g5 squares, since there was not a minimum Elo thresold in the sample games and that sort of checkmate patterns, along with back-rank checkmates, are very common in low rated matches... all together knowing that castling kingside is far more played than castling queenside, probably around 90% of the time.

Any insights are welcome.

------------

The code source of the Python script that was used is available here:

[python] king's square at checkmate

So it should be possible to work out some data for FRC.

Regards from Spain.

Ajedrecista.

[chessica]

Many thanks , the best place for the king is b2. It will be never mate.