A Program of Introductory Videos on Combinatorial Games
The fastest way to become acquainted with a new game is to watch it being played by two experienced players, and that's much more easily conveyed in an edited video than in any book or lecture. Elwyn will speak about his several introductory videos on Combinatorial Games. They assume virtually only fluency in the English language. A typical video shows a full game, sometimes played by real kids. The rules are explained and a post-mortem analysis of that particular game follows, which inevitably leads into some rudimentary CGT. Some videos have been used, with at some preliminary success, by some junior high school students as young as the sixth grade.
To watch these videos, visit the playlist's on Elwyn's YouTube Channel:
What happens when players move simultaneously in a combinatorial game?
This talk explores different interpretations for playing combinatorial games with simultaneous moves. Examining the overlap between economic game theory and combinatorial game theory, we begin developing possible directions for the theory of simultaneous combinatorial games.
This is joint work, in varying degrees, with Dr. Richard Nowakowski, Dr. Paul Ottaway, and Dr. Craig Tennenhouse.
Game trees and the value set of strong placement games
I will give an overview of ongoing research into the structure of game trees and the value set under normal play of strong placement (SP-) games. This work takes advantage of the one-to-one correspondence between SP-games and simplicial complexes with vertex set bipartitioned. Restricting this to impartial SP-games, we remove the requirement of the bipartition of the simplicial complex, allowing us to look at the correspondence between properties of simplicial complexes and possible nimbers.
A Generalized Upstart Equality
The Upstart Equality states that ⇑* = ↑ + ↑ + * = {0|↑} (or equivalently ⇑ = ↑ + ↑ = {0|↑*}). When we consider ↑* as *:1 it is natural to ask about games of the form {0|*:G}. We show that for all G, {0|*:G} - *:G = *:n for some integer n.
Extremal value games
Partisan short game values range from arbitrarily small infinitesimals to arbitrarily large numbers, while the sizes of all-small games are limited in both directions. We examine a pair of games that achieve extremal values, one an all-small loopy game with both the largest and smallest possible game values, the other a short asymmetric placement game whose positive values are arbitrarily small. This raises the question about other playable games that achieve extremal values.
Last updated: 2017-07-17 21:11