Estimating Total Search Space Size for Specific Piece Sets in Chess
Azlan Iqbal

TL;DR
This paper presents a combinatorial method to estimate the size of the search space for specific chess piece sets, aiding in evaluating the feasibility of automatic chess problem generation.
Contribution
It introduces a precise, documented approach for calculating chess position search space sizes considering piece sets and legality constraints.
Findings
Provides a mathematical framework for search space estimation
Clarifies the impact of piece placement rules on search space size
Lays groundwork for optimizing automatic chess problem generation
Abstract
Automatic chess problem or puzzle composition typically involves generating and testing various different positions, sometimes using particular piece sets. Once a position has been generated, it is then usually tested for positional legality based on the game rules. However, it is useful to be able to estimate what the search space size for particular piece combinations is to begin with. So if a desirable chess problem was successfully generated by examining 'merely' 100,000 or so positions in a theoretical search space of about 100 billion, this would imply the composing approach used was quite viable and perhaps even impressive. In this article, I explain a method of calculating the size of this search space using a combinatorics and permutations approach. While the mathematics itself may already be established, a precise method and justification of applying it with regard to the…
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Taxonomy
TopicsArtificial Intelligence in Games · Sports Analytics and Performance · Data Visualization and Analytics
