Games@Dal 2016: Alda and Carlos talk about Short Sums

Games@Dal 2016 talk: "Some notes on Disjunctive Short Sum" - Alda Carvalho & Carlos Santos

Alda and Carlos presented their work on Disjunctive Short sums.  They started from Paul Ottaway's definition of the difference from a short sum (to a normal long sum): The game ends when a player chooses a component in which they have no legal move.  This doesn't make a difference in Normal play (because players don't want to choose one of those games) but it's important for Misere.  In misere, this is equivalent to: The game ends when there is a component in which the current player has no legal move.

Now, instead of starting from zero as the terminal position, they start with two games that have no options: Infinity (Inf) and negative Infinity (-Inf).  Inf is the game with no options for Right, and -Inf has no moves for Left.  These are the only games born on day 0.  Then the day 1 games are:

• Inf* = {Inf | Inf}
• +/- Inf = {Inf | -Inf}  (like a switch)
• 0 = {-Inf | Inf}
• -Inf* = {-Inf | -Inf}

They showed a bunch of the birthday lattice for day 2, which is very large, then started talking about Color Nim: a short disjunctive sum of Nim games.  Another way to say this is that each pile has a color (not necessarily unique) and the game ends when one of the colors is gone.  In the Misere case, this means that each color behaves like Penultimate Nim.  (For some reason, Penultimate Nim kept coming up at this meeting!)