Rolling the Dice on Complex Calculations

As fast as modern computers are, calculations still take time. That's where probability and randomness can lend a helping hand.

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Every time a gambler places a bet, there’s a certain probability of winning. But roll the dice again and again, and a new situation emerges where there are possibilities to either net win or lose money in the long term.

The odds are always stacked a bit against players in favour of casinos, but the study of randomness has consequences for simulating outcomes in all kinds of scenarios, says Jeffrey Rosenthal, professor of statistics at the University of Toronto.

“Probability theory is the mathematical approach to randomness and uncertainty,” says Rosenthal. “We try to study how things that are random proceed, often proceeding in time, and how randomness gets more and more random over time.”

Rosenthal studies Monte Carlo computer algorithms, where a sequence of instructions given to a computer to solve a problem or perform a calculation involves randomness as an essential step.

“It’s a little bit like when you take a public opinion poll and you can’t ask everybody questions, so you choose a random sample and phone a random sample of people,” explains Rosenthal.

“Computers do things like that but on a more complicated scale, but they involve actual randomness as the computer program runs to try to learn things.”

As fast as modern computers are, calculations still take time. Given the vast data sets that we generate every day, combing through them to do a calculation exactly can be a challenge. That’s why working with probability still matters.

“Just like you can’t phone everybody in the country and ask them what their opinion is, you can’t run computers long enough and fast enough and strong enough to be able to compute all the complicated statistical models that come up in everything from medical studies, and the finance world, and populations, and all sort of things,” adds Rosenthal.

Monte Carlo algorithms use randomness to help estimate these quantities when it would take too long to calculate them exactly. In other words, they help scientists power through complex calculations by working smarter, not harder.

“There’s more and more data that’s coming to us, and there’s bigger and bigger computational problems, and computers are getting faster, which is good, but that only takes you so far,” says Rosenthal.

“Computers also have to get smarter, which means we need better computer algorithms.”

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Jeffrey Rosenthal is a professor of Statistics at the University of Toronto. Born in Scarborough, Ontario, Canada in 1967, he received his BSc in Mathematics, Physics, and Computer Science from the University of Toronto at the age of 20, his PhD in Mathematics from Harvard University at the age of 24, and tenure in the Department of Statistics at the University of Toronto at the age of 29.

For his research, Rosenthal was awarded the 2006 CRM-SSC Prize, and the 2007 COPSS Presidents’ Award, the most prestigious honour bestowed by the Committee of Presidents of Statistical Societies. For his teaching, he received a Harvard University Teaching Award in 1991, and a University of Toronto Outstanding Teaching Award in 1998. He was elected to Fellowship of the Institute of Mathematical Statistics in 2005, and to the Royal Society of Canada in 2012, and was awarded the SSC Gold Medal in 2013, and a President’s Impact Award in 2019.

Rosenthal’s book for the general public, Struck by Lightning: The Curious World of Probabilities, was published in sixteen editions and ten languages, and was a bestseller in Canada. It led to numerous media and public appearances, to his work exposing the Ontario lottery retailer scandal, and to a President’s Impact Award. It was followed by a second book for the general public, Knock On Wood: Luck, Chance, and the Meaning of Everything.

Rosenthal has also published two textbooks about probability theory, and well over one hundred refereed research papers, many related to the field of Markov chain Monte Carlo randomised computer algorithms and to interdisciplinary applications of statistics. He has dabbled as a computer game programmer, musical performer, and improvisational comedy performer, and is fluent in French.

His web site is, and on Twitter he is @ProbabilityProf.

Despite being born on Friday the thirteenth, Rosenthal has been a very fortunate person.

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