Two talks were given in the second session at Sprouts 2017.
Kristen Falcinelli: Undecidability demonstrated by a tiling game
Kristen showed a new game, Infinitiles, where players each have their own library of Wang Tiles. The starting position is a finite or infinite grid with at least one tile already on the board. Each turn consists of a player choosing one of their tiles, then placing a copy of it onto the board somewhere adjacent to one of the tiles already on the board. The placed tile must match all the other tiles it touches.
Kristen was able to find many values in the game: all integers, all switches, *, Up, Down, and 1/2. One issue she found was that on an infinite board, it is undecidable to determine whether the game will finish on an infinite board!
Ashlee Tiberio: Also Kanye: Examining patterns in a strip game variant
Ashlee created a grid game similar to Drag Over, but in two dimensions. On a grid with red and blue pieces, you move by choosing a row or column, then you move all pieces in that space. If it's a column, you move all pieces up ("North"); if it's a row, you move all the pieces left ("West"). If the pieces fall off the board, they are removed. You can only make a move if you have pieces left on the board.
Ashlee found number values for all 1-by-n strips where either all spaces had a token (of the same color) or one space had a token. She also found values for 1-by-n strips with two tokens of separate colors.
Ashlee also noted that the misere version of this game should be called "Imma Let you Finish".
My Last Visit with John Conway
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