Basics of Strategy From a Third Grade Class

11 10 2009
Last week my students and I were reviewing the strategy of the game of Nim in my third grade class.

Nim is a very simple game that can introduce big ideas of strategy.

The object of the game is to force your opponent to take the last marker. That is, the loser removes the last marker. Of course, the game could be played that the winner is the one who takes the last marker.

Construct three rows of markers: the top row has three markers, the center row has five markers and the bottom row has seven markers. The number of markers for each row and the number of rows is open to options. But, 3-5-7 Nim provides for a short game and yet complex enough for variety and analysis.

Players take turns removing as many markers as they like in one row only. Each player must remove at least one marker per turn. The word Nim probably comes from the Shakespearean word meaning “to take away” or “steal”.

This game can be played anywhere because one can use toothpicks, little rocks or play animals,marks on a chalkboard, or on a foggy window.

Nim is a game that has been played, in various forms, on at least four continents for at least four centuries. Like tic tac toe, it is a challenging game until one realizes that there is a correct way to play. In the case of tic tac toe, there is a correct way for both players and, if both players make the correct moves, the game must always end in a tie.

In the case of Nim, when one player makes the correct moves, he will always win. (Whether this is the player who goes first or the player who goes second depends on the variation of nim being played.)

Where the perfect strategy for Tic Tac Toe is discoverable by a bright child, discovery of the correct nim strategy takes a mathematical intuition of the highest order for one without mathematical experience.

After two months of playing one of my third grade students studied with his parents for a week to discover a winning strategy. He came to class and confidently won me in a game. He has now become a partner teacher in strategy for the class.

For some websites on Nim try:

This gave a good introduction to the basics of strategy. Here I laid the foundation to three basic ways students approach games:

1. Superstitious Plans
According to the writer Raymond Lamont Brown: “Superstition is a belief, or system of beliefs, by which almost religious veneration is attached to things mostly secular; a parody of religious faith in which there is belief in an occult or magic connection.”

Another way to put it is that superstition is an irrational or nonscientific belief in the existence of certain powers operant in the world, with positive or ill (usually ill) effects. These are rituals or patterns of behavior that are believed to have some power to influence the outcome of the game.
What are some examples you have seen as we played the game?

2. Psychological Ploys
The art or practice of using tactical maneuvers to further one’s aims or better one’s position. The use in a sport or game of aggressive, often dubious tactics, such as psychological intimidation or disruption of concentration, to gain an advantage over one’s opponent. Here the concepts of Gamesmanship versus sportsmanship are introduced. Also mentioned are ways players try to psych-out your opponent. Psychological Ploys are the use of dubious (although not technically illegal) methods to win a game
What are some examples you have seen as we played the game?

3. Strategic Play
Strategy is a careful plan or method. Victory is completely dependent on your reasoning and pattern recognition skills, and completely independent of luck
What are some examples you have seen as we played the game?

But it is amazing how such a simple game can introduce the ways people approach life.



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