Research & Open Access

Board Games Theory & Computational Analysis

A mathematical monograph series analyzing state-space complexity, combinatorial graph topologies, bitboard solvers, and stochastic Markov decision processes.

Peer-Reviewed Research Monographs
Computational Solvers • Bitboard Topologies

Algorithmic Architecture of Solved Checkers Engines: 32-Bit Bitboards, Mandatory Capture Branching, and Retrograde Analysis

An architectural decomposition of the algorithms that weakly solved English Checkers: dense 32-bit register representations, mandatory capture branching collapse, alpha-beta NegaScout pruning, and 39-trillion retrograde endgame databases.

Tabletop Systems Lab • October 2026 Read Paper →
Discrete Mathematics • Graph Theory

Combinatorial State Spaces and Topological Graph Representations of Abstract Board Games

A formal graph-theoretic framework distinguishing state-space from game-tree complexity across classical board games. Analyzes DAG transformations, monotone progress functions, and dihedral quotient graph reductions.

Tabletop Systems Lab • October 2026 Read Paper →
Stochastic Systems • Probability Theory

Stochastic Markov Decision Processes and Expectiminimax Optimization in Classical Dice Games

Formulating imperfect decision-making under environmental uncertainty: 21 macroscopic polyhedral dice distributions, expectiminimax chance trees, absorbing Markov racing models, and Janowski doubling cube options.

Tabletop Systems Lab • October 2026 Read Paper →