DeepAI AI Chat
Log In Sign Up

A complete solution for a nontrivial ruleset with entailing moves

by   Urban Larsson, et al.
IIT Bombay
Dalhousie University

Combinatorial Game Theory typically studies sequential rulesets with perfect information where two players alternate moves. There are rulesets with entailing moves that break the alternating play axiom and/or restrict the other player's options within the disjunctive sum components. Although some examples have been analyzed in the classical work Winning Ways, such rulesets usually fall outside the scope of the established normal play mathematical theory. At the first Combinatorial Games Workshop at MSRI, John H. Conway proposed that an effort should be made to devise some nontrivial ruleset with entailing moves that had a complete analysis. Recently, Larsson, Nowakowski, and Santos proposed a more general theory, affine impartial, which facilitates the mathematical analysis of impartial rulesets with entailing moves. Here, by using this theory, we present a complete solution for a nontrivial ruleset with entailing moves.


page 1

page 2

page 3

page 4


Impartial games with entailing moves

Combinatorial Game Theory has also been called `additive game theory', w...

A tutorial for computer scientists on finite extensive games with perfect information

We provide a self-contained introduction to finite extensive games with ...

Quantum Combinatorial Games: Structures and Computational Complexity

Recently, a standardized framework was proposed for introducing quantum-...

Fairer Chess: A Reversal of Two Opening Moves in Chess Creates Balance Between White and Black

Unlike tic-tac-toe or checkers, in which optimal play leads to a draw, i...

Sprague-Grundy values and complexity for LCTR

Given a Young diagram on n boxes as a non-increasing sequence of integer...

Forced Capture Hnefatafl

We define a new, partizan, loopy combinatorial game, Forced-Capture Hnef...

Sampled Fictitious Play is Hannan Consistent

Fictitious play is a simple and widely studied adaptive heuristic for pl...