Computationally Estimating the Solvability of Forced Mate Sequences

In automatic chess problem composition, there may be a need to classify or label problems in terms of solvability (i.e. how difficult it is for the typical player to solve) for more efficient human consumption. Automatically classifying a chess problem as being easy, moderate or difficult therefore helps in that regard. In this article, we explain a formula for this that relies on five variables, i.e. chess engine solving time, total piece count, total piece value, move length and an adjusted number to represent the variations possible. The method was tested on samples of forced mates (3, 4 and 5-movers) including both published chess problems by human composers and computer-generated ones. Statistical analysis of the results was significant and as expected based on the groups tested. Such problems may therefore then be classified as ‘easy’, ‘moderate’ or ‘difficult’ based on percentile. The lowest third of scores is considered easy, for example. Longer sequences that do not end in checkmate (such as studies) is still an open problem in terms of solvability using this approach mainly because even good chess engines often cannot solve them conclusively enough to establish the time variable and the number of variations possible.