2014 Anja S. Greer Conference on Mathematics, Science and Technology

Gambling takes on many forms. A fascinating part of American gambling history is the Punchboard. Though now illegal for gambling, punchboards can be brought into math class to enhance an introduction to probability. A typical punchboard is made of pressed cardboard, anywhere from 3 by 5 inches up to 11 by 17 inches and about an inch thick. It has lots of small holes drilled in it, perhaps as many as 2000. Each hole contains a tiny piece of folded paper with a number on it and each hole would be covered with paper or foil. The rules for each board would be printed on the board along with a colorful theme/story about something that was popular in America at the time. Between 1910 and 1960, in states where they were legal, punchboards were commonly found in stores and bars. A customer would pay money for the opportunity to punch out one of the papers hidden in the holes. If the number on the hidden paper matched a winning number as described on the board, the patron wins. Winnings often were money, candy, or cigarettes. Because the winning numbers and their payouts are stated on the board, probabilities and expected values are relatively easy to calculate. This makes punchboards an excellent way to introduce probability to our students. It's hard to get students excited when we use contrived data out of a textbook. But when I take my colorful punchboards out of the cupboard and let them punch out a few of the hidden papers, all my students are motivated, curious, and attentive.