100 Game Theory

This is a great game to introduce game theory at a young age while simultaneously assessing place value and addition concepts.

Race to 100

How to Play:

Two players start from 0 and alternatively add a number from 1 to 10 to the sum. The player who reaches 100 wins.

I usually give students a hundreds chart to help keep track of where they are, as well as a “Race to 100” handout with tables to record what number each person said. Also once they discover that saying “89” guarantees they will be able to say 100, I have them star that number. I ask them to think if there are any other numbers that guarantee a win.

A 3rd grader shows the winning strategy visually on a hundreds chart. He put an X on the numbers he wants to say, and then shaded in the numbers his opponent "him" would be able to say.

A 3rd grader illustrates the winning strategy visually on a hundreds chart. He put an X on the numbers he wants to say, and then shaded in the numbers his opponent “him” would be able to say.

Extensions:

How would the strategy change if it were a race to 99?

How about if we change the numbers that you can add?

This is part of the family of games commonly known as Nim, NRICH has a thorough article and resources for these games called “Meet the Nim Family.”

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Filed under Elementary, Games

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