Friday, August 12, 2016

Games@Dal 2016: Neil talks about Transitive Games

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.


  1. Maze and Maize are fascinating games. So simple, yet intriguing, that I independently thought of them while doodling in a CGT class years ago before I even learned of their existence last week! In fact, my impetus was to see if I could come up with an interesting game where left or right could make any number of consecutive moves without an obvious winning strategy. (Though my equivalent version was played on a dual graph, with the pieces travelling down lines branching out like roots instead of a grid with walls like a maze.)

  2. Cool! It's definitely a good game for learning about outcome classes.