Bridg-It

Bridg-It (also called Gale), by David Gale, around 1960

First published in Martin Gardner’s “Mathematical Recreations” column in Scientific American (where Gardner gave it the name “Gale” after its author), this game was published (as a boxed game) in the early 1960s under the name Bridg-It. It is a simple connection game, and what looks like another version, called “Connections,” came out in 1992.

The game is played on a board like the diagram shown above. The players alternately connect two orthogonally adjacent dots of their own color with a bridge -- either a length of plastic or (if playing on paper) simply a line of their color. A line may not cross another line already played. The object is to connect the opposite edges of the board that are your color.

Bridg-It thus bears a superficial resemblance to TwixT. (Does anyone know whether one game inspired the other? They seem to have originated about the same time.) But Bridg-It is not nearly so deep a game: it was solved completely by Oliver Gross in the 1960s. His solution appears at the bottom of the page.

Although Bridg-It in the original form is solved, it might be salvaged by making some variations on the rules. One possibility is Double-Move Bridg-It, in which the first player plays one bridge on his first move, and all later moves consist of playing two bridges. Since the board is then filling up twice as fast, I would propose playing Double-Move Bridg-It on a larger board, say 7x8 for each color as shown below.

Another possibility is Whimsical Bridg-It: a play consists of either playing both a red and a black bridge onto the board (connecting pairs of like-colored spots, of course), or declaring yourself either Red or Black. The latter type of move is called the Whim move (I get the name, and the whole idea, from a game by British mathematician John H. Conway), and it can be played only once in a game. The player who declares color plays no bridge that move, but thenceforth each player places one bridge of his color per move and tries to connect his pair of opposite edges.


	In a discussion of solved games like Bridg-It on Richard’s PBeM Server, Scott Huddleston proposed a much simpler way to redeem the game from the winning strategy below: simply allow the second player to swap sides if he wants to use the first player’s move. This rule is often used in connection games like Hex, Twixt, and Star where the first move can give too much advantage, but I suspect that in Bridg-It, pairing strategies like the one below could be devised that would work with any possible first move. And yet I don’t know how. Can any of my readers find a way?


	A winning strategy for the first player in Bridg-It was published in one of Gardner’s later Scientific American columns, now collected in New Mathematical Diversions. The first player simply makes the first move shown in the lower left corner, and then whenever the second player makes a move that touches the end of a dotted line, the first player makes a move that touches the other end.


	Questions, corrections, comments: Send me e-mail at markthom@flash.net


	[Math Education] [Math Recreations] [Abstract Games] [Great Thoughts]