To Jeffrey Rosenthal, a Professor in the Department of Statistical Sciences, probability is a key topic among his research interests, and the concept of luck, in particular, is an intriguing idea to be explored. “Being born on Friday the 13th, I’m no stranger to the question of luck,” he likes to joke.
Skills or just luck?
“One way to think about luck is that it comprises random things that happen outside of our control,” Rosenthal explains. “Picture this: you’re out bowling with some friends and have just scored a winning strike. You then proceed to score three more in a row. At the sight of four consecutive strikes in a row, you may be inclined to attribute your winning streak to your bowling skills. On the other hand, you may believe that your lucky shots were outcomes of pure luck. In the end, the question comes down to distinguishing between the two.”
For statistician Jeffrey Rosenthal, exploring the concept of luck versus skill and the probabilities of everyday life have been a fascinating research interest. Alongside three master students, Rosenthal delved deeper into his inquiry by taking a particular interest in how the question of luck versus skill unfolds itself in poker games.
“It’s a much narrower focus, but we think it has implications for the bigger picture,” Rosenthal clarifies, “It’s the question of, if somebody wins at poker, does this mean they got lucky or that they played well? It’s certainly a combination of both because there’s definitely a lot of luck in poker, but it’s undeniable that there’s also a lot of skill. That’s why there are some people who are champion poker players and some people who are not.”
Thousands of computer-simulated poker hands
Through the use of three thousand computer-simulated poker hands each, Rosenthal and his students were able to examine up to 10 different game strategies between each set of players. With their findings, they were able to quantitatively measure how much of a player’s profit was due to luck versus skill.
“We simulated different players and we programmed their individual strategies,” Rosenthal describes, “The idea was that we programmed some of them to play pretty well with strategies that were smart, while programming others to just fold as soon as the other player bets, which is a silly strategy. The logic was that, as far as the skill goes, the better players should win more money, but, as far as luck goes, that should be about the same.”
On the one hand, a poker player’s win may be attributed to their lucky deal of cards – something that they cannot control. On the other hand, the player’s decisions throughout the game—their decision to fold, bet, or raise—may just as well demonstrate their skillful abilities at a game of poker. This is where the question of a good versus bad poker player comes into play.
The impact of luck
Rosenthal and his team of students developed a definition of what they called one’s ‘equity in the middle of a hand,’ the ability to determine how much players could expect to win or lose at any given point in a poker game. At the heart of their definition: the assumption that equity is always changing.
“If you’re holding really good cards and the other player is not doing well, you think that you’re probably going to win a lot of money. But how much you win still depends on how much you bet and what cards come up,” Rosenthal explains. “When something good happens, equity goes up, and when something bad happens it goes down. We looked at both: equity going up as a result of a card being dealt – so, that being luck; as well as equity increasing as a result of the player’s betting – that being skill.”
The idea is that bad poker players can get just as lucky as good ones. The poker game simulations of Rosenthal’s team provide unique insight into the extent of the impact of luck.
The long run
“Whether you’re a good or bad player, the amount of luck will balance out. Whereas, for the skill part, if we wrote a program that plays strong poker, it would win more due to skill and if you had a poor player program, it would lose more due to skill. In the long run, when looking at a good versus a bad poker player, it is evident that the good poker player will win more. However, no matter how good a poker player is, this is not a golden guarantee that they will win every time,” explains Rosenthal. “As much as we would like to believe that our wins may be fully attributed to skill, in a game of poker, luck will always play a significant part.”
The research that Rosenthal and his students conducted, highlights a general principle about statistics and probability—that the more you repeat things, luck tends to balance itself out.
“Even if we’re just flipping a coin and seeing what fraction of the time we get heads, if I just flip a few coins maybe I get all heads or maybe I don’t get any heads. But, if I flip a thousand coins, it gets pretty close to fifty percent heads. We call that the law of large numbers,” explains Rosenthal.
This same way of thinking applies to their simulations. That is to say, simulated once or twice between two players, the result could very well be all luck. The worst player may win it all simply because they got the cards that they needed. In the long run, however, the golden luck of the players tends to fade away as skill comes into the picture as the winning factor.
Probability thinking and decision making
Rosenthal’s interest in luck versus skill has become a significant point of public outreach for him. In his two books, Struck by Lightning: The Curious World of Probabilities (2006), and Knock on Wood: Luck, Chance, and the Meaning of Everything (2018), Rosenthal offers the general public an engaging, informative, and fun way to approach questions around probability and luck. Rosenthal's expertise in the field of statistical probability and around questions of luck versus skill have earned him something of a celebrity status in this field. He is frequently contacted by companies and media organizations requesting his comments and expertise.
Whether it’s debating your chances of whether or not a job interview will go well, or easing fears of flying, Rosenthal’s work offers a unique insight into how luck, both good and bad, is commonly perceived and/or misunderstood.
Rosenthal’s research in the field of probability can have a positive influence in challenging people’s views of everyday life probabilities. As he likes to put it, “It can influence people’s behaviour. They might make different decisions about gambling and lotteries and won’t be as afraid of flying because they realize how unlikely it is to win the lottery or die in a plane crash. I think that public outreach about randomness can have a positive influence, spreading probability thinking to a larger group.”