Allis has determined that the player who goes first in Connect Four always has a winning strategy. We consider the discrete bidding variation of the game instead of alternating turns. In discrete bidding, each player holds an integer number of chips, and the players bid for the next turn. Whoever wins the bid takes a turn and gives his chips to the other player; thus, the total number of chips stays constant. Introducing bidding to the game alters a player's strategy, as multiple moves in succession are now possible. Develin and Payne have completed an analysis of Tic-Tac-Toe using discrete bidding and have determined a winning strategy. We analyze bidding Connect Two on all board sizes and bidding Connect Three on a 3-by-3 board, which will give us insight into the strategy for Connect Four.

Author Bio

Kenny Goodfellow is a 2011 graduate of Juniata College with a Bachelor of Science in Physics and Mathematics. During his time at Juniata College, he worked as a teaching assistant for the introductory physics lab, a tutor for a variety of physics and mathematics courses, and a tour guide. He participated in research internships in optical physics at Juniata College during the summers of 2008 and 2009 and at Rensselaer Polytechnic Institute during the summer of 2010. The research for this paper was done to graduate with distinction in mathematics at Juniata College and was supervised by Dr. Catherine Stenson. While at Juniata, he was a member of the cross-country and track and field teams. He is currently attending the University of Rochester to pursue his Ph. D. in Optics.