So Long Sucker: Endgame Analysis

So Long Sucker is a strategy board game that requires 4 players, each with $c$ chips of their designated color, and a board made of $k$ empty piles. With a clear set-up comes intricate rules, such as: players taking turns but not in a fixed order, agreements made between some players broken at any time, or a player winning the game without any chips in hand. One of the main points of interest in studying this game is finding when a player has a winning strategy. The game begins with four players who get successively eliminated until only the winner is left. To study winning strategies, it is of interest to look at endgame situations. For that, we study the following game set-up: there are two players left in the game, Blue and Red, with only their respective chip colors. In this paper, we characterize Blue's winning scenarios and strategies for this game set-up through a delicate case analysis.