Wednesday, April 27, 2022

Sprouts 2022 Talks, Session 1

This past Saturday (April 23, 2022) we held Sprouts for the first time since 2019.  Here's some summaries of the talks from the first session:

Lexi Nash, "Enumerating Distance Games"

Lexi showed how to use a polynomial profile to count the number of positions on a graph with different numbers of colored vertices.  Then she showed how to use Auxiliary Bonds as a better counting method using Cartesian, Strong, and Categorical graph products.  Generating functions can be built from regular expressions of colors of nodes for distance games, and she showed many examples of this technique.

Khoa Bui, "Reinforcement Learning Based Artificial Intelligence"

Khoa talked about Google's AlphaGo player and how he used those characteristics to create an AI to play Ultimate Tic-Tac-Toe.  (This is the game played on a Tic-Tac-Toe board where each of the nine spaces consists of another Tic-Tac-Toe board.  Khoa refers to this kind of recursive game structure as "Stacked".)  He used reinforcement learning combined with a Monte Carlo Tree Search to implement his player.  He wants to apply these techniques to stacked versions of distance games.

Gracie Banning, "Kraken the Numbers!"

Gracie created an impartial game themed around a Kraken attacking people on a row of boats.  Each boat is a Nim Heap, and the Kraken eats from three adjacent piles in the list, taking any triple of this form (floor(k/2), k, floor(k/2)).  She showed values for many three-boat positions and proved that these formulas work by induction.  She also discovered that four-boat positions are zero when all boats have the same size.

Carolyn Curley, "Partisan Peg Solitaire"

Carolyn created a partizan game based off of jumping peg solitaire games.  Players can make jumps in directions based on their identity (Left - Vertical, Right- Horizontal).  She solved on and two-row positions by hand, as well as the 3x3 grid, where she found Up and Down values!  She investigated a bunch of 3x3 sub-boards, as well as what happens when they are surrounded by extra holes.  She looked at many other cases as well.

These were all great talks!  I'm really amazed at what great work undergraduates do in CGT.

The next post will cover the Keynote talk as well as the talks from Session 2.

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