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.
"Towards Bidding Connect Four,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 13
, Article 1.
Available at: http://scholar.rose-hulman.edu/rhumj/vol13/iss1/1