Games of Chance

It’s a snowy Friday night in February, and wind lashes at the clusters of young professionals on their way to the Irish pubs and Greek restaurants of Toronto’s trendy Danforth strip. But inside studio two of the Bad Dog Theatre – a three-year-old, hole-in-the-wall comedy joint – the heat is making the audience flush harder than an off-colour Andrew Dice Clay routine.

The ratcheting temperature can be blamed on the tiny quarters: the 400-square-foot windowless studio holds 25 spectators and four maniacal comedians, who are performing improv for the pay-what-you-can crowd. A comedic version of rapier sword-fighting, improv is an intellectual sport in which each strike of an ad lib helps build a scene. The troupe members play off one-liners (or “offers”) that they throw each other, parrying and jostling their way to laughter or careening downward to a thud of silence.

Perhaps the most boisterous troupe member is U of T statistics professor Jeffrey Rosenthal – a six-foot-three, scruffy fellow with broad shoulders, a head of curly brown hair and a thunderous voice. (“He is Little John from Robin Hood,” says improv buddy Mike Ranieri. “A big, burly, lovable guy.”) Rosenthal ricochets from playing a son yearning for the acceptance of his housepainter father to a jilted housewife. Then – channeling a bellowing, frenzied version of Mel Gibson in Braveheart and adding the most diabolical Scottish accent outside Glasgow’s Barlinnie prison – he turns to a familiar role. He roars: “Alright then little boys and girls. It’s me first day teaching so I don’t want anybody giving me a hard time. That includes yew.” [looking at a cast member in a chair]

Student [cast member]: “Yes, Mr. Angus.”

Rosenthal: “Now look – I was told that you’re a difficult class. So here’s what I want you to do. I want you to just cower in fear and repeat after me: “I’m a miserable NOBODY.”

Students [cast members], en masse: “I’m a miserable nobody.”

Rosenthal: “You’re really not a bad class after all.”

Two weeks earlier, in his U of T office, Rosenthal wisecracks about what I will write if the performance flops: “He said he did improv but I went to the show and he’s actually an idiot. All his other work must be fraudulent, too.'” And comedy is a crapshoot, requiring a steely self-confidence and high-spirited sociability. Rosenthal, 38, started improv classes in 1995 at Theatresports in Toronto and began performing gigs after almost three years of training. “There’s a lot of randomness in how it goes, but when it goes well, and I actually make people laugh and enjoy themselves it’s exciting. And it also made me start thinking about other things differently…” He speaks of learning to “go with the moment” both on the stage and in the classroom. “Improv applies pretty much to your whole life – you’re always being confronted by things that you didn’t expect, or you couldn’t anticipate. And are you going to let it throw you off? Or are you going to embrace it and go with it?”

Embracing randomness – and being aware of its dangers and delights – is Rosenthal’s specialty. His latest book, Struck by Lightning: The Curious World of Probabilities (HarperCollins Canada 2005), shows readers how to use simple mathematical concepts – most notably, probability theory – to assess the odds of random events happening to them. In other words, how likely are you to actually get walloped by one of those rare occurrences that obsess you on a sleepless Sunday night? If, for example, you worry excessively about being the victim of a homicide, there is a chapter on how to assess crime statistics correctly. (According to Rosenthal, if we look at the difference between counts [total number of homicides] and rates [homicides per 100,000 people], we can see that the risk of being murdered in Canada has been on a slight decline since the mid-1970s – indicating it may be our fear of violent crime that is on the rise.) And during those raging late-summer electrical storms, it might be useful to know that only three Canadians died after being struck by lightning (as compared to, say, 74,824 of cardiovascular diseases) in 2001.

If, on the other hand, you hanker to beat the house at craps or 21 or blackjack, Struck by Lightning might help you calculate your odds. (Hint: rein in your inner Ben Affleck, and step away from the table – you’re not going to get rich quick. Casinos guarantee that games are weighted in their favour by employing probability theorists to calculate the average net payouts.) The book also includes chapters on understanding the margin of error in polling; interpreting medical studies; and – for those who vacillate over decisions large and small – utility functions (numerical ratings), which can help you decide whether to buy house insurance, ask out an attractive colleague or try a new medical treatment.

The book has clearly hit a public nerve: last year, it reached number seven on the Maclean’s bestseller list, and is now slated for release in the U.S., Germany, Australia, New Zealand, Japan and Italy. Struck by Lightning is an example of a publishing industry trend: books that merge an academic specialty with the concerns of a general audience. “The book shows how we can understand and interpret the events of our lives using simple math. If nothing else, it makes probability and statistics interesting and accessible for the layman,” says Radu Craiu, an assistant professor of statistics at U of T.

Rosenthal’s academic field is an exclusive one: he studies Monte Carlo algorithms (his specialty within this branch is an even bigger mouthful: Markov chain Monte Carlo randomized computer algorithms). In simplest terms, Monte Carlo algorithms are a way of using randomness to gauge quantities that are too difficult to compute directly. As Rosenthal explains in his book, they were first used at the Manhattan Project in New Mexico – birthplace of the atomic bomb – during the Second World War. Scientists needed to ensure the bomb contained the correct amount of uranium: too much, and it would explode prematurely, killing those surrounding the project. Using some of the world’s first computers, scientists randomly simulated the motion of neutrons and the atomic-bomb chain reaction over and over again. This allowed them to deduce how the neutrons would behave on average, and what fraction would escape. Monte Carlo algorithms are now used in almost every sphere where randomness exists: from managing investment portfolios to gauging which medicines work during trials. “One neat thing about probability, as opposed to many branches of mathematics, is that it is connected to so many things on a personal level and a professional one,” says Rosenthal.

In an early chapter of Struck by Lightning, Rosenthal explains how mathematicians invented Erdös numbers – a chain-of-connections game in which anyone linked to the gifted Hungarian mathematican Paul Erdös would be assigned a number value, with the most direct link receiving a number one. A Hollywood variation of the pastime, Six Degrees of Kevin Bacon, is now ubiquitous in the pop-culture landscape. And, given the number of U of T family connections Rosenthal has, anyone who has stepped on U of T soil might be able to play a new version of the game: Six Degrees of Jeffrey Rosenthal. His father, Peter, is a professor of mathematics at the university who specializes in operator theory. (For a decade, Rosenthal and his dad worked two floors apart in Sidney Smith Hall.) His mother, Helen, recently retired as a math lecturer at U of T Scarborough. Brother Alan is a computer science lecturer on the St. George campus, while brother Michael is an instructional technology analyst at OISE/UT. Jeffrey’s wife, Margaret Fulford, is the faculty librarian at the Faculty of Dentistry.

While Rosenthal was growing up in Scarborough, Ont., his numerically minded parents introduced him to mathematical concepts at an early age: by the time he was eight, he could prove the classic math idea that the number of prime numbers is infinite. He also had a working knowledge of probability theory, which he used to increase his chances of vanquishing his two brothers at Monopoly: he would compute the probabilities of his brothers rolling certain numbers on the dice and landing on certain squares, to decide whether to buy more real estate on his property. (Unfortunately, they employed the same tactics, making for some cutthroat Monopoly games.) And when he was a teenager studying math, physics and computer science at U of T in the late 1980s, he could envision “mathematician” as a profession in a way other undergraduate students didn’t seem to grasp. “For me, it seemed the natural career choice to work in mathematical sciences,” he says.

After graduating with a bachelor of science from U of T in 1988, Rosenthal attended Harvard University, earning a PhD in mathematics at the tender age of 24. It was at Harvard that he first began applying probability theory to everyday situations. In his second year, Rosenthal was slated to fly to the John F. Kennedy International Airport in New York to visit relatives – but a week before his departure, a plane crashed near the airport, killing 73 people. Rosenthal was skittish about getting on his flight, but found solace in the currency of cold hard numbers: he determined there were about 5,000 flights a week to the airport – and that the chances were probably less than one in 5,000 that, in the following week, there would be another disaster. The odds were low enough to convince him to board the plane. “At first I thought, ‘Oh my God there’s been a plane crash at JFK.’… It was only upon calming myself I thought wait a minute – I should stop and think about this more,” he says. “When you’re doing research work it tends to be so specialized that it’s easy to forget the connections to things around you. You’re working on your subtleties and you don’t look around so much. It was a case of trying to blend what I’m working on with the everyday.'”

Translating difficult concepts for a general audience, and playing to a crowd, are roles that come naturally to Rosenthal. Improv friend Ranieri explains how, a few years back, Rosenthal bought a video camera and solicited his friends to write and act in amateur movies with him. (One of their most recent pieces is the “Night of the Living Dead Christmas Special,” in which Rosenthal sings about “slay rides” and chomps on gifts of “brains” made of cauliflower.) The friends decided to create a movie trailer for Rosenthal’s first academic textbook, A First Look at Rigorous Probability Theory. “At first I thought, ‘What a stupid thing to do a movie on’ – a preview movie for this boring stats book. But we thought ‘That’s why it’s funny, right?’ so we did Rigorous Probability: The Movie,” says Ranieri. Rosenthal now shows the video to his graduate classes.

In the first episode of the hit TV show “My Name is Earl,” a two-bit thief finds a winning scratch ticket worth $100,000. In sheer revelatory joy, he punches the air, whoops with glee and dances his way out onto the road – where a senior citizen in a Buick slams into him, and sends his ticket casting off into the wind. While Earl is in hospital, his wife visits to hand him divorce papers, inform him she is having an affair with the local bar owner, and that her two children aren’t his. Stunned, drugged and imprisoned in a cast, Earl turns on the TV, and watches an interview with MTV personality Carson Daly – who is talking about how karma changed his life. “Karmaaaa,” says a gobsmacked Earl, who undergoes a spiritual epiphany. Convinced he is being paid back for a lifetime of bad deeds, Earl makes a list of all his wrongdoings – from siphoning gas to rigging a high school football game – and sets out to make amends with the universe. The result? While crossing number 136 (“been a litterbug”) off his list by cleaning up a motel parking lot, he finds the lost winning ticket in the detritus.

Is there karma? Is someone above taking notes and keeping score? When you’re a probability theorist, the idea of fate or the existence of the karma gods of Earl’s universe appear, well, highly improbable. In fact, Rosenthal is a member of the Humanist Association of Canada, a non-theistic group that believes life choices should not be guided by a belief in supernatural deities, but by human reason and compassion. Rosenthal speaks on the discord between fate and probability. “Often people will point to certain statistic examples: Here’s a good guy who almost died and then he didn’t and there must have been some divine intervention or master plan, but that’s what we the probabilitists would call a selection bias… You can just as easily find examples where the opposite happened: the bad guy got away and the good guy got killed. I say, well that’s perfectly consistent with the idea that these things happened randomly and that there is no all-powerful force controlling them,” he says. “To me it seems more useful to understand and deal with the world that we have and try to take actions that will improve the world based on what it is – rather than to ascribe things to it that there’s not evidence of.”

In October 1999, Rosenthal married Margaret Fulford in a humanist ceremony at Hart House: the service took place in the Debates Room, and the reception in the Great Hall. Rosenthal, an amateur musician (he plays everything from the trumpet and keyboard to the saxophone and bongo drums), sang and played guitar for his new bride. “The really romantic part was he sang a song that he had written for me when we had just been dating for six weeks, which was called ‘Margaret, Won’t You Fly to P.E.I. with Me?” says Fulford. “He also sang a Paul Simon song called ‘Kathy’s Song,’ which was the first song that he sung for me when we were first dating. It was very sweet.”

It’s a Wednesday afternoon, week 17 of the first-year seminar class “Probability and Uncertainty” in Sidney Smith Hall on the St. George campus. The room, with its austere windowless surroundings, is oddly reminiscent of the Bad Dog Theatre studio. The crowd is slightly smaller, and the laid-back atmosphere has a Sunday morning sleepiness, with students – in oversized sweatshirts, baggy jeans and caps – slouched low in their seats. Hardcover editions of Struck by Lightning sit on the maroon tabletops.

Rosenthal enters in a green sweater, khakis and beige sneakers. He begins talking at the hotfoot pace that he uses when he is enthused about something – which seems to be most of the time. Today the group is studying the “p-value” (the probability that an observed result occurred by pure chance) that is built into medical studies. Five per cent is the standard p-value, but Rosenthal wants the students to really think about what this means. He wants them to understand that it raises the possibility that one medical study in 20 might be wrong. “If we see something through observation, we always have to wonder if they just got lucky – whether shooting hoops or conducting medical studies,” he says.

He whips out a deck of cards, and his p-value performance begins. He tosses one club, one diamond and one heart to the student next to him and asks him to put the cards face down. “Question: do I have psychic powers?” Rosenthal looks at the back of the card, thinks hard, and guesses “clubs” – it’s a diamond. He misses on all three. “That seems to indicate I don’t have psychic powers.”

The mission extends to the students. With the enthusiasm of entering a game of Texas Hold ’em, they gather in groups of two and three to try it for themselves. They do a series of telepathic “tests” – from staring at a facedown card, to inhaling over it, to running their fingers across it – to see if they can determine the card’s suit. (They must guess right three times in a row – 1/3 times 1/3 times 1/3 – to reach a statistically significant p-value of 3.7 per cent.) The jokers in the crowd make loud snorting noises during the inhaling segment. There are yells of “cheater.”

At the end of the trials, Rosenthal asks, “Who, according to current scientific standards, has psychic powers?” Three of the 17 students raise their hands. The talk parlays into what further experiments could be done to clarify results, and what tricks pharmaceutical companies could employ if they were desperate to get a new drug approved. “There is a flip side,” says one astute student. “Maybe a drug that could have saved lives was lost because there was too rigid a standard.” The students start thinking discriminately.

Before they leave Rosenthal runs over next week’s assignment: publication bias. It’s a loaded topic dealing with the medical-study controversy surrounding Dr. Nancy Olivieri and the pharmaceutical company Apotex. But he also asks them to read anecdotes in the book with names such as “Jumping Frog,” “Happiness Hat” and “Meditation Medical Miracles.” Because even in the curious world of probabilities, there’s always room for a little improvised entertainment.

Stacey Gibson is managing editor of U of T Magazine.