Thursday, June 15, 2017

Game Description: Cutthroat and Impartial Cutthroat

A long time back, while going through Lessons in Play, I got hung up on the definition of Impartial Cutthroat in section 2.2.  I completely forgot about this until recently, when a student asked me to explain what was going on.  Today, I had a look back at Cutthroat and Impartial Cutthroat and confirmed my understanding with Richard Nowakowski.  In this post, I'll try to clarify both games.

Cutthroat is a partisan game played on a graph where each vertex is colored Blue or Red.  In addition, each connected component of the graph must include vertices of both colors.  Each turn a player chooses one of the vertices of their color and removes it from the board, including all incident edges.  Then, remove any connected component that includes only vertices of one color.

Here's a whiteboard sketch of a Cutthroat game tree I made today:

 
Notice that Red has an immediate move to zero by choosing the lower red vertex.  (The remaining two connected components are both mono-colored, so they are immediately removed.)

I've added this as it's own entry in the ruleset table.

Impartial Cutthroat is a bit different.  On one hand, it's the same game if you assume that players can choose vertices of any color AND all vertices are given a unique color.  

Another way to explain it is that a position is an uncolored graph where each vertex must have at least one neighbor.  On a player's turn, they choose a vertex and remove it and all incident edges.  Afterwards, all vertices with no neighbors are also removed.

Yet another way to explain Impartial Cutthroat is by considering it as a variant of Node Kayles.  In Kayles, a player chooses a vertex, then removes that vertex and all of its direct neighbors.  Here, there are two differences:
  • The player must choose a vertex that has at least one neighbor.
  • Only the chosen vertex is removed, not any of the neighbors.
Because of this similarity, I've included it in the ruleset table as a variant of Node Kayles, instead of a standalone game or a variant of Cutthroat.

Monday, May 1, 2017

Sprouts 2017: Overall Awesomeness

I spent all Saturday at Sprouts 2017, and it was excellent!

Craig Tennenhouse organized an amazing experience.  Everyone got a Gamester Pen, a program with a CGT quick-reference-page, a grid-lined notebook decked out with a gamey cover, and a nametag with the logo.

 Official Sprouts Notebook

His students gave amazing talks.  Each had created their own game, complete with actual pieces they had 3-D printed or otherwise manufactured!  It was clear they had spent lots of time analyzing their games, and had learned CGSuite to help get results.  One student had learned about Atomic Weights and applied that theory to their analysis!

Infinitiles

My student, Matt, also gave an excellent talk.  He discussed AI methods to play Chess and Go.  After all the talks, we got into working groups and looked at a few games more deeply.  I am definitely convinced that undergraduates can contribute to this field!

I'll post comments about the individual talks, though that may have to wait until the semester wraps up.  In the meantime, I've already started dreaming about Sprouts 2018.

Sunday, April 23, 2017

Sprouts 2017: A CGT Conference for Undergrads

Exciting news for New England Gamesters: Craig Tennenhouse is organizing the first Sprouts, a conference for undergrad CGT research.  (I helped by making the website.)  Sprouts 2017 will take place at the University of New England (Biddeford, ME) on April 29.  The basic plan is to continue hosting Sprouts every year at either UNE or Plymouth State (NH).

I know this announcement is a bit late, but things have come together only recently.  Inspired by our desire to get our gamester undergrads involved in research, we're harnessing the opportunity presented by Craig's research class.

Hopefully in the future, we'll be able to get the word out sooner to attract visitors from the region.

Monday, January 2, 2017

CGT Facebook group

Simon Rubinstein-Salzedo started a Combinatorial Game Theory Facebook group!  Join us here: https://www.facebook.com/groups/413534538978745/

Happy New Year!