Misère Connect Four is Solved

Connect Four is a two-player game where each player attempts to be the first to create a sequence of four of their pieces, arranged horizontally, vertically, or diagonally, by dropping pieces into the columns of a grid of width seven and height six, in alternating turns. Misère Connect Four is played by the same rules, but with the opposite objective: do not connect four. This article announces that Misère Connect Four is solved: perfect play by both sides leads to a second-player win. More generally, this article also announces that Misère Connect <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>k</mml:mi> </mml:math> played on a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>w</mml:mi> <mml:mo>×</mml:mo> <mml:mi>h</mml:mi> </mml:math> board is also solved, but the outcome depends on the game’s parameters <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>k</mml:mi> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>w</mml:mi> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>h</mml:mi> </mml:math> , and may be a first-player win, a second-player win, or a draw. These results are constructive, meaning that we provide explicit strategies, thus enabling readers to impress their friends and foes alike with provably optimal play in the misère form of a table-top game for children.