Searching Through 180,828 Mate in Two Problems - Part I

What are the hardest mate in two problems?

What are the hardest mate in two problems?

I have decided to find out. I've turned to the power of Stockfish 16 and Python for an in-depth analysis of a large amount of mate in two problems.

My quest involves a dataset of 180,828 composed mate in two problems that I recently discovered. But what are the components of a really difficult mate in two problems? We know the feeling when we cannot find the solution, but how do we measure it without solving them?

I have tried to think of some measurable data points that can be extracted from each problem.

A histogram of some of the analyzed data to see the distribution of the problems. It looks like most problems are solved, using the script I made, with around 500-1000 nodes. Some problems however need far more. We will find out if this is a good scoring metric for difficulty.

• Average nodes

  The average number of positions or "nodes" evaluated by the chess engine across different iterations or depths of analysis until a mate in two solutions is found.

• Legal moves in the initial position

  The number of legal moves available in the position before delivering mate in two. This should give us a feeling of how many options you have to pick from.

• Legal moves after the first move

  The number of legal moves available after the first move in the sequence leading to mate. This tells us something about how many variations you have to calculate.

• Unique final moves leading to mate

  The count of distinct moves that directly deliver checkmate in the final position. My thesis is that it is more complicated to find a solution with many unique checkmates vs. a position with only one variation in the end.

• Average time to fin mate in two for Stockfish 16 (s)

  The average time taken (in seconds) to analyze the position across multiple iterations or depths until a checkmate in two is found.

• Complexity

  A measure of the complexity of the position as a count of the number of pieces on the board.

• Diversity

  A count of different pieces present in the position.

• Open squares around king

  The number of unoccupied squares immediately adjacent to the black king indicates how exposed or vulnerable the king might be.

These are the metrics I could think of that might influence the difficulty of a mate in two problems. It takes some time to analyze all of this with my current home setup, so until it all has been processed let’s do a test.

To test the difficulty and find out more of the influence of these metrics I have composed a little test with four mate in two problems that I will ask you to solve. Write the first move of the solution and the time it took you.

I will reveal the results in the next part. Should you know or remember an incredibly challenging mate in two problem that has given you a headache please drop the FEN and details in the comments. I will then look at how the problems score in the next newsletter.

I think it will be a multiple series about the search for the ultimate mate in two problems, so I hope you will find this interesting!

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By the way, if you wondered why I didn’t send out a newsletter last week I can tell you that it was because I worked on a little puzzle book with 88 puzzles from the European Team Chess Championship. The puzzles are all positions where the player failed to play the best move according to Stockfish. The best move is at least +1 better than the second-best move in the position. I think it is a fun little collection with some atypical puzzles that you might find interesting.

I plan to do a free giveaway on the first days of the publication. I will send out a mail when it is out.

/Martin