Connect Four and Spider Solitaire

Every man dog and millipede on the planet has heard of Connect Four, a well-known two-player game by Milton Bradley. The objective is to line up four pieces of your colour horizontally diagonally or vertically. Unfortunately it is not played in serious competition these days, mainly because the game has been solved. With perfect play by both sides the first player wins.

The solution was found independently by James Dow Allen and Victor Allis (independently) in October 1988. The first player must start in the middle column. If she plays adjacent to the middle column then it’s a draw. Playing anywhere else even loses. Furthermore, the first player requires all 21 discs to force a win if a perfect opponent puts up maximum resistance. For a detailed analysis of the game please check out this excellent video  by Numberphile.

However, I believe Connect Four has not been solved after all, because everybody has been playing it the wrong way.

Consider the board state below. Before reading on, can you predict where the next two discs should be played?

connect4

A cursory examination shows that Yellow threatens to win on the left-most column. Moreover, Yellow has played 8 pieces but Red has only 7. Therefore it is Red to play. Clearly Red must block the threat of vertical Connect-Four. This in turn threatens a diagonal Connect-Four so Yellow’s next move is also forced.

But if you examine the board carefully, you will notice each column is labelled with one of the seven days of the week. Moreover, only 30 cells are marked with numbers but the others are empty. Not surprisingly, the board represents the calendar month for September 2019, which is further corroborated by the text above the board.

It is not hard to guess that Spider GM is going to play a game of Four-Suit Spider Solitaire on every day of this month. Every yellow disc represents a victory, and every red represents a defeat. Spider GM is only concerned with winning the game regardless of the number of moves or time taken to complete it. Of course Spider GM will play without undo. Four in a row still wins the game (but Spider GM can continue to play the remaining days just to fill up the board and see what it looks like). The current position shows a hypothetical game state after the 15th of September.

This completely changes the dynamics of Connect Four. For instance, odd and even threats still exist but here they refer to whether the cell contains an odd or even number (instead of what row the cell lies in). Going back to the example, Spider GM has an even threat on Sunday the 22nd. Unfortunately the next game will be played on Monday the 16th. Therefore the next move will either be a Red or Yellow disc on the cell numbered 16. In other words Spider GM has to wait for a whole week before his threat of winning on the Sunday column comes into play. Of course if Spider GM does win the battle on the 22nd of September then he also wins the war, unless Daily Challenges manages to build an unlikely winning horizontal Connect Four before that date.

Well done if you correctly predicted the next two moves to be “cells 16 and 17, either red or yellow”.

It is easy to see that Connect Four is now an unsolved game again, since the colour of each cell depends on the result of a single game of Spider Solitaire, and not even the Spider GM knows the perfect strategy for the latter. This I believe is the way Connect Four should have been played all along. So if you have enough spare time on your hands to play one game of Spider Solitaire per day and wish to make Connect Four great again then you know what to do 😊 Good luck.

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