Game components?

When I was younger, my dad taught me how to play Nim, a game that uses 15 coins in three piles as its components. I’ve always loved that simple game, and enjoy teaching it to kids now that I’m an adult. I’ll explain how it works below.

It comes from a category of games called Combinatorial Games, which are games that have exactly two players, a completely public game state, and no element of luck. They usually have a very limited selection of moves for each player, but do not restrict player choices. This is known as impartiality; or, at any position in the game each player has the same moves available.

Having knowledge of a few combinatorial games (as well as a ready supply of change) can benefit you in several ways:

• You can use a combinatorial game as an impromptu game aid, perhaps when a character wants to gamble in a tavern or as a test of wits used to gain audience with a guru or to petition a noble lord.
• It’s a great way to pass the time when you’re waiting on something, perhaps at the DMV, or waiting for a movie to start.
• If you have kids, combinatorial games can be a fun way to engage their mind and improve their critical thinking skills…it also teaches them to think like a gamer! Teachers can use combinatorial games as a fun way to engage students and distract them from math lessons for a bit.
• It can be a good way to break the ice at parties where you don’t know anyone. Unless you’re incredibly entertaining, though, this might not apply if you’re intending to meet girls.

So, let’s take a look at a few combinatorial games that you can play with just a few coins.

Nim

Setup: Make three piles of coins, with 3, 5, and 7 coins respectively.

Rules: On your turn, you must take at least one coin, but may take as many coins as you like from a single pile, including the entire pile.

Winner: The person to take the last coin wins.

Alternate: A different version only uses 10 coins in a single pile, and each player can take either one or two coins from the pile each turn. Whoever takes the last coin wins.

Circular Kayles

Setup: Arrange a circle of coins. The circle can have any number of units, which makes it convenient if you don’t have 15 coins available. Between 9 and 15 is a good number.

Rules: Each player on his turn can remove either a single coin or any two coins that were originally adjacent in the circle.

Winner: The person to take the last coin wins.

Grundy’s Game

Setup: Make a pile of coins, any size (although at least 10 is preferable).

Rules: Each player on his turn breaks any pile into two piles with different amounts of coins. So, a pile of 6 coins could be broken into piles of 5 and 1 or 4 and 2, but not 3 and 3.

Winner: The person to make the last move wins.

Of course, any of these games could also be played with small candies like M&Ms or Skittles, dice, or any other small representative objects (coins are just the most common to have around).

Do you have any favorite combinatorial games, or childhood games using simple, readily available components?