More Dots or More Cars:

After playing a simple version of the game, try drawing roads with more dots, or try adding more red cars. Also try out different starting arrangements.

Strategic Thinking:

Play several rounds of Bumper Cars. As you play, ask your child to tell you when they know who will win. Even young players will notice that whoever picks up the last red car in front of the blue car will lose. Let's call such a car the "Bummer Car" since, if you have to pick it up, then, bummer, you'll probably lose. In fact, the only way you wouldn't lose after picking up the Bummer Car is if your opponent were to make a mistake. Of course, in real life, mistakes happen. To understand how a game works, though, we want to plan how to win without relying on our opponent's mistakes, so let's assume, as we think about Bumper Cars, that both players are playing without making any mistakes.

Since picking up the Bummer Car leads to losing, no one will do so until they have to. They'll drive other cars forward if they can. So the Bummer Car only gets picked up when all other cars are moved up as far as they can go, in a "traffic jam." Whoever creates this final traffic jam arrangement will force their opponent to pick up the Bummer Car.

Depending on the starting game board, there is a lot of complexity involved in how to create the traffic jam scenario for your opponent. We encourage you to try out each of the starting game boards shown above in Variations, and any others you think of. For each, can you figure out which player will be able to create the final traffic jam?

Let's think about just one scenario: The Bummer Car in the very front space, followed by some empty spaces, then the blue car with another red right behind.

If the next player, Player 1, moves the blue car all the way up, then Player 2 will move the rear red car all the way up, creating the final traffic jam and therefore winning. So Player 1 doesn't want to do that.

But if Player 1 moves the blue car only part of the way up, Player 2 can still move the rear red car right up behind the blue car, creating the same situation, but with fewer spaces for the blue car to move. Eventually, Player 1 will be forced to move the blue car directly behind the Bummer Car, and Player 2 will be able to follow, creating the final traffic jam. So, Player 2 will tailgate the blue car as closely as possible, eventually creating the final traffic jam and winning. This means that whoever is able to create an arrangement like the one above will be able to win!

Noticing these arrangements and understanding how they will lead to the final traffic jam can help guide choices you make earlier in the game.