The New Math

Visit to a Classroom

What are the odds?: Arif Sundrani challenges a classmate in math class.
Kay Hinton

Course title

Freshman seminar Mathematics in Games, Sports, and Gambling (closes within fifteen minutes of registration each time it’s offered).

Professor’s CV

Goodrich C. White Professor of Mathematics Ronald Gould’s research focuses on extremal graph theory. He’s perhaps best known for his work on path and cycle problems. His books include Graph Theory (1988) and Mathematics in Games, Sports, and Gambling—The Games People Play (American Library Association Choice Award, Outstanding Academic Titles 2010). “This is a look at math from a whole different point of view,” Gould says. “I remember the time an administrator walked in and students were all on the floor shooting craps.”

Today’s lecture

Figuring out a “stone-cold strategy” to play NIM, a combinatory game with finite possibilities played by two people with anything that can be stacked (in this case, red, white, and blue poker chips); invented by C. L. Boulton of Harvard in 1902.

Quotes to note

“If you have two equal piles, that’s always end position. The present player is in big trouble, the next player controls the game. The smart move is to mimic what the first player does, so you’re back to two equal piles again. That would always be the way the proper strategy would lead.”

“What we want to do is develop a strategy. The ultimate n-position is an empty board, which is zero position. The next player is going to lose because they can’t move. That’s easy when you have two equal piles, not so easy when you have five unequal piles.”

“Why do we use the base ten system? Because these were the original calculators [holds up fingers]. There’s no other reason base ten would be fundamental to us.”

Students say

“This seminar is interesting and a lot of fun,” says Arif Sundrani 15C. “It makes me think more about every move I make. I’d go to Vegas if I had more money. Actually, I take that back, this class makes me want to keep my money and not go to Vegas at all, since I know the odds. I’m thinking of becoming a math major now.”

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