I spent some time considering words to describe a chess position with many legal moves. “Complex” doesn’t quite capture the situation since we would usually describe a complex position as one with many tactical interations. Ramified seems to make the most sense, as it describes “branching out”.

The opening position in chess has 20 legal moves. From there, the number of legal moves in a position tends to increase as pieces move towards the center of the board, before decreasing as the number of pieces on the board drops in the endgame.

People have composed artificial positions with a huge number of legal moves. The most ramified artificial position I have found has 218 legal moves. But it’s hard to imagine how such a position could come about in a real game, which is what I’m interested in. So I churned through all of the positions in all of the Lichess games which took place in 2023 in search of the most ramified chess position. Here is what I found.

Most games max out around 16 moves in

In the chart below you can see the maximum moves at any point in the game. The x-axis represents half moves. (In other words, if white makes a move and black makes a move, that’s two half moves.) Each game starts out with exactly 20 possible moves for white, which quickly increases in the middle game before gradually decreasing again.

The colors represent the percentiles, since at every slice along the x-axis there is actually a distribution of positions and associated legal moves. Interestingly, we can see that for the 10th percentile the bottom really falls out after 40 moves or so, with positions so constrained that there are only a handful of legal moves. These likely represent positions where the king is in check.

100+ move positions are rare

Each line represents the chess position in a chunk of 5000 games with the most legal moves.

Each line represents the chess position in a chunk of 5000 games with the most legal moves.

To parse the games, I wrote a multithreaded rust script with python bindings to process chunks of 5000 games at a time. Within a chunk of games, it was pretty typical for the maximum number of legal moves in any position in any game in the chunk to be between 70 and 100.

Here is a typical position with 84 legal moves for white:

Very few ever exceed 120

When you get past 100, most of the positions have several queens. There are exceptions, however. This 112 move gem has zero.

Here is a typical 120-move position with six queens:

The 147 move position 🤯

Here it is, the 147 legal move masterpiece.

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