Larger Grid:

Use a larger grid for a longer and more-difficult-to-predict game. Start with 5 horizontal and 6 vertical lines, or even more. Or try drawing the grid of dots without first drawing lines.

Smaller Grid:

Use a smaller grid for younger players. Draw 3 horizontal and 4 vertical lines. The youngest math beasts might enjoy playing on a grid drawn from 2 horizontal and 3 vertical lines.

Hex:

This classic math game is normally played on a grid of hexagons, but a diamond drawn with coins works just as well. Players label opposite sides of the diamond in their color. Then they take turns filling in circles in their color. The player who is able to make a path that connects their opposite sides wins.

Alternatively, one player places dimes and the other player places pennies on the circles, rather than coloring. This has the added benefit that you won't need to redraw the grid each time.

Game Theory:

After playing a few rounds of Circuit Breaker, try a variation. Play the game as described above, but instead of trying to win, both players try to work together so that the game ends in a tie. Before long, you'll notice that ties are impossible in Circuit Breaker. Now let your child try on their own to draw any game board that ends in a tie. Even when you allow there to be more of one color than the other, this is impossible.

Why can't a tie occur? One way to visualize this is to imagine that one player is cutting a piece of paper (rather than drawing, say, red lines), while the other player draws blue lines that cannot be cut through. The cutter's goal is to split the piece of paper in half (dividing the two circuits of the other player), while the drawer is trying to prevent the paper from being entirely divided. Thinking of the game this way, we can see that it wouldn't make sense for a game to end with the paper cut in half and not cut in half at the same time. By the end of the game, the paper is either still one piece, or it isn't.

Strategy:

What is the best strategy for Circuit Breaker? To improve your play, try different things and see what works. Play a game focusing only on offense, for example, then a game focusing only on defense. Or try playing from the center outward, then from the outside inward.

Another way to understand the basics of the game is to start with a smaller grid (see Variations). Even a 2x3 grid can help you understand why the game can never be tied.

Trying things to see what works, starting with a simpler version: these are some of the same problem-solving strategies we want young math beasts to use when confronting a new math problem!

Math History:

Circuit Breaker is also called Gale, after mathematician David Gale who invented it, and is related to Hex, a classic math game invented independently by mathematicians Piet Hein and John Nash. Mathematician Claude Shannon made a mechanical version of Hex that used actual changes of voltage within a circuit so an early computer could beat a human player!