Math, Strategy, and Creativity: Po-Shen Loh explains the mathematics behind dice

By Staff Writers Michael Ren & Kelly Yang

Carnegie Mellon University associate professor Po-Shen Loh, Phd. visited MSJ for a talk on the mathematics behind dice rolling on October 17. The presentation took place after school from 3 p.m. to 4 p.m. in the Flex Room.

In addition to his position at Carnegie Mellon, Loh is also head coach of the US’s International Math Olympiad (IMO) team. The IMO is an annual global mathematics competition among teams of high schoolers representing their respective countries, and in 2015 and 2016, Loh’s team placed first overall for the competition. Loh is also the co-founder of Expii, an online learning platform that aims to personalize and tailor STEM education for the individual. “I started to think about what I would want to do to try to help lift the level of interest in mathematics on the national scale because I happened to be in a position where I was caring about the national scale,” said Loh. Similar to Khan Academy, Expii users can choose the course they want to focus on then progress through a series of lessons that culminates in a quiz on the topic.

Loh opened his talk with a game of chance to discuss the mathematics associated with dice. In this scenario, he asked two volunteers to each roll a die, with scorekeepers adding up the numbers rolled in a total of 10 throws. When the game finished, he passed around his dice and asked if anyone noticed any oddities. An audience member pointed out that unlike conventional die, as in Loh’s set of dice, the one was not opposite the six.

Based off this observation, Loh subsequently introduced more related properties of die and explained how these traits affected probability and games of chance. If even one feature of the die were altered, he explained, then the expected value could be changed and manipulated by an astute player. Loh continued his lecture with an interesting demonstration of how this could be done, exploring the different ways to roll in order to increase a player’s probability of winning. Loh showed the application of these concepts to board games like Monopoly such that the game essentially became a game of dice rolling skill as opposed to a game of luck.

Loh wrapped up his lecture with a final demonstration that was similar to the first, but rather than adding the rolled numbers, he had the scorekeepers multiply them. The two volunteers attempted to utilize newfound die-rolling techniques, ending their match with two vastly different scores. Loh proceeded to explain the statistics associated with the game and finished his presentation with a rigorous mathematical explanation that verified his observations of dice rolling strategy. In conclusion, Loh said “I like to show these very surprising applications of math … what I do is that I use my mathematical experience to think about some real-world things and see if I can find some math that nobody has seen before.”

As the lecture came to an end, Loh thanked students and teachers for coming. Many audience members approached him afterwards to ask him questions, discuss his presentation, and take pictures.

Interview

The Smoke Signal: What is your regular line of work at Carnegie Mellon University?

Po-Shen Loh: I’m officially a math professor at Carnegie Mellon University, but the way that Carnegie Mellon works, it’s a very innovative university where the school is interested in all of their faculty doing as much creative work as possible. The definition of the word creative is very vague, so for example, I create in a couple of ways. One of them is in the research, where I work in the intersection between combinatorics, probability, and algorithms — theoretical computer science. And there I’m thinking about new things that maybe the world hasn’t thought about before. The other way that I often add to creativity is through innovation, like Expii, which is [the company] I run. If you go to www.expii.com you’ll see that we have come up with an unusual new way to make education completely free and personalized, so that’s another creative art. And of course, the art of teaching itself is also creative; one can try to find out new ways to inspire or to communicate insightfully. So basically what I do at Carnegie Mellon is create, and that’s how the university likes to think of what its faculty do.

SS: What inspired you to start Expii?

PL: Around that time — it was right after I became the national coach for the US math olympiad team — and I started to think about what I would want to do to try to help lift the level of interest in mathematics on the national scale in the US, because I happened to be in a position where I was caring about the national scale. And at the time when I was doing this, I didn’t, and I still don’t, have a lot of money, or a lot of connections to try to push policies through. But what I realized is everyone has smartphones in their pockets, so one way to try to change the approach to mathematics nationwide is to go in through smartphones on a free app that then makes access to excellence in math available to everyone. So that was the original principle to Expii.

SS: What advice would you give students who are struggling in math?

PL: I think that [math being interesting] is the most important part. Seeing that math can give you superpowers in how you look at the world and how you discover things that other people might not have noticed before is amazingly powerful. People need to have insight in order to do just about anything, and to see math as a framework to getting that insight is really powerful. But, at the same time there’s another part that can help too. One reason why some people think of math as hard or not fun is because it looks like it involves a lot of memorization. When you’re young, when you’re doing elementary school math or middle school math, it might seem like it’s easier just to memorize all the formulas without understanding what they mean, or why to use them because you might only be using two or three formulas. But if you try to learn everything just by memorizing, by the time you get to high school, there’s just too much to hold in with some chaotic memorization where nothing is connected to each other. It’s a whole lot easier to say, “oh, even if I forget how the quadratic formula looks, I can always complete the square.” and then you’re never stuck, because you’re not relying only on your memorization. And I’ll even say, the reason I love math is because it’s the only subject where you don’t have to remember stuff.

SS: In what ways can math be applied to daily life?

PL: I think that one thing that I also brought towards the end is that you can use the mathematics to help build algorithms that help you calculate things about the world that give you advantages in situations. Like I commented, if people have time, you might be able to build that smartphone app which snaps a shot of the Monopoly board and tells you the optimal strategy. So this is like an application of math towards computers. There are other applications of math like towards physics; again, it depends on whether you’re interests are towards physics, but as soon as you try building anything, the ability to calculate and predict what’s going to happen makes it so you don’t have to build as many things. Somehow everyone says “measure twice, cut once” but it helps to first use the math to know what to even measure. For me, what I like to throw out when I give these talks is I like to show these very surprising applications of math, where it’s like “math applied to dice,” where nobody thought of that before. So what I do is that I use my mathematical experience to think about some real-world things and see if I can find some math that nobody has seen before.

Photo by Staff Writer Kelly Yang