Games@Dal 2016 talk: "A unique form for hereditarily transitive games" - Neil McKay
Neil McKay spoke about a new term: Transitive Games. A game, G, is left-transitive if all positions that could be reached from a series of left-only moves from G are also (immediate) options of G. Right-transitive is defined analagously, and a position is transitive if it's both left and right-transitive. Games are hereditarily transitive if their subpositions are also transitive.
The ruleset MAZE is transitive, because players can move as many spaces in their direction as they want during their turn. (At some point, I should write a Game Description post about MAZE and MAIZE.)
Neil defined closures for (hereditary) left-transitivity, by recursively adding, as new Left options, all Left options of Left options. Again, the right closure is analagous. Speaking in terms of rulesets, MAZE is the hereditary transitive closure of MAIZE. It's still not known which rulesets have a transitive version that's equivalent.
2 weeks ago