# Engel, '13, Merges Interests for Research Project

Jacob Engel didn’t come to Albion College thinking his interests in mathematics and computer science would lead to an honors thesis about how he developed a variation of the game of Craps.

Engel’s only experience with gambling came from working on a high school production of Guys & Dolls. That changed when mathematics and computer science professor Mark Bollman presented his interest in probability during a 2010 fall semester honors course about the eight big ideas that shaped science.

A native of Warren, Engel stayed on campus last summer with funding from the College’s Foundation for Undergraduate Research, Scholarship and Creative Activity to write the computer code and compile the probability for Craps using eight-sided dice as opposed to the usual six-sided dice familiar in the gaming industry.

Engel’s variation, named “Spider Craps”, offers similar odds and payoffs to that of the original game.

“I needed to learn Craps completely and I did that by reading Wikipedia,” Engel said. “Movies like 21 and Rounders helped explain the concept of house advantage.”

While some of the mathematics involved in the project translated easily – automatic winning rolls of seven and 11 in standard Craps correspond to nine and 15 in the spider game – Bollman credited Engel for having the patience to refine the computer code he wrote to perfect the balance for the game where the house would be pleased with its advantage while not driving players away.

After writing the rules, Engel waited for the computer to crunch simulations of 50,000 rolls of the dice and frustration mounted from wondering if the numbers would ever come out just right. Engel estimated his program simulated 2.7 million rolls during the project.

“At several points during the course of the summer we found the simulation was not going to work,” Bollman recalled. “There was one situation where we were directly mimicking the rules and the player had an advantage which would keep it from ever being placed on a casino floor. We went back and changed the rules which involved changing the code and running more simulations. That part of it was some fairly involved programming and a certain amount of mathematical maturity to understand the life cycle of the model where we cycled through the model until we’ve got something where it does what we want it to do.

“We were able to put together a complete game,” Bollman added. “That was the goal when we started the project, but as is so often the case, it was not clear at the beginning if we would be able to get that far.”

Engel presented his research at the College’s Elkin Isaac Student Research Symposium in April and he has a couple of options as he begins writing his thesis. He can try to market the game for casinos or move on to graduate school.

“I really enjoyed this project because it allowed me to mix my interests of mathematics and computer science while developing relationships with professors,” Engel said. “I don’t know of anyone who has done a project like this so I believe I’m one of the few that has developed his one working casino game.”