What's your Game?

Happy lady

All the games you can find here have one thing in common: there is no rolling of dice or flipping of coins. In other words, there's no luck involved. This means they are all about strategy. The cleverer you are at playing them, the bigger your chance of winning.

Another thing the games have in common is that players don't have their own colour (as for example in chess) or their own hand of cards (as for example in Poker). The only thing that sets the players apart is who goes first and who goes second. Games like these are called impartial games.

One interesting thing about impartial games is that, right from the start of the game, one of the two players has a winning strategy. If they play correctly, they can be sure to win, no matter what moves the other player makes. In some games it's the player to go first who has the winning strategy. But in others it's the player to go second. (In theory it's also possible for a game to go on forever, in which case there'd be no winner. But we'll ignore these games here.)

Finding the winning strategy, however, isn't always easy! Have a go playing the games in this pathway and see if you can figure it out!

Most of the games on this pathway are related to the ancient game of Nim. Nim is played with a number of counters arranged in heaps: the number of counters and heaps is up to you. There are two players. When it's a player's move he or she can take any number of counters from a single heap. They have to take at least one counter, and they can't take coins from more than one heap. The winner is the player who makes the last move, so there are no counters left after that move. There is a game of Nim on this pathway, but we have given it a different name. Can you find it?

Mathematicians have completely analysed the game of Nim. They know exactly how to find out which of the two players has the winning strategy and what moves they should make. You can find out more here (though the article is a bit more advanced). If you are brave, then try to see how the Nim strategy relates to the games on this pathway!