Unraveling Go gaming nature by Ising Hamiltonian and common fate graphs: tactics and statistics

Go gaming is a struggle between adversaries, black and white simple stones, and aim to control the most Go board territory for success. Rules are simple but Go game fighting is highly intricate. Stones placement and interaction on board is random-appearance, likewise interaction phenomena among basic elements in physics thermodynamics, chemistry, biology, or social issues. We model the Go game dynamic employing an Ising model energy function, whose interaction coefficients reflect the application of rules and tactics to build long-term strategies. At any step of the game, the energy function of the model assesses the control and strength of a player over the board. A close fit between predictions of the model with actual game's scores is obtained. AlphaGo computer is the current top Go player, but its behavior does not wholly reveal the Go gaming nature. The Ising function allows for precisely model the stochastic evolutions of Go gaming patterns, so, to advance the understanding on Go own-dynamic -beyond the player`s abilities. The analysis of the frequency and combination of tactics shows the formation of patterns in the groups of stones during a game, regarding the turn of each player, or if human or computer adversaries are confronted.

Go game formal revealing by Ising model

Go gaming is a struggle for territory control between rival, black and white, stones on a board. We model the Go dynamics in a game by means of the Ising model whose interaction coefficients reflect essential rules and tactics employed in Go to build long-term strategies. At any step of the game, the energy functional of the model provides the control degree (strength) of a player over the board. A close fit between predictions of the model with actual games is obtained.