Want to improve your HORSE play? Stats expert breaks down the popular basketball game’s odds

Daniel and Jeffrey Rosenthal at Willcocks Common (photo by Margaret Fulford) - For NBA stars and driveway basketball enthusiasts alike, the game HORSE conjures up memories of intense schoolyard competitions and boisterous neighbourhood hangouts. Now, a professor at the University of Toronto has delved into the statistical probabilities of the game - and discovered that simplicity is often the way to go (even though it's not as fun to watch.) "When I was growing up, I would play with my dad, and I remember that he would attempt these really easy shots," recalls Jeffrey Rosenthal , a professor in the department of statistical sciences in the Faculty of Arts & Science. "That goes against what most of us would think to do, which is to make a difficult shot in hopes that your opponent won't be able to match it." When shooting hoops together at the Willcocks Common just south of Sidney Smith Hall last summer, Rosenthal and his half-brother Daniel, a University of Toronto alumnus who studied advanced mathematics as well as philosophy and psychology, wondered if they could mathematically determine the effect of shot difficulty on the probability of winning points. "It may not be the deepest mathematical analysis we've ever done," Rosenthal says. "But trying to justify the rules of HORSE presented us with an interesting question about the probabilities: What is the optimal shot to take to increase your chances of winning?" The co-authors published their results in the June/July 2022 issue of the journal  Notices of the American Mathematical Society.