Consider a simple coin-flip game, which Peters uses to illustrate his point.
Starting with $100, your bankroll increases 50% every time you flip heads. But if the coin lands on tails, you lose 40% of your total. Since you’re just as likely to flip heads as tails, it would appear that you should, on average, come out ahead if you played enough times because your potential payoff each time is greater than your potential loss. In economics jargon, the expected utility is positive, so one might assume that taking the bet is a no-brainer.
Yet in real life, people routinely decline the bet. Paradoxes like these are often used to highlight irrationality or human bias in decision making. But to Peters, it’s simply because people understand it’s a bad deal.
Here’s why. Suppose in the same game, heads came up half the time. Instead of getting fatter, your $100 bankroll would actually be down to $59 after 10 coin flips. It doesn’t matter whether you land on heads the first five times, the last five times or any other combination in between.
The “likeliest” outcome of the 50-50 proposition would still leave you with $41 less in your pocket.
Now, say 10,000 people played 100 times each, without assuming all players land on heads exactly 50% of the time. (This mimics what happens in real life, where outcomes often diverge dramatically from the mean.)
Well, in that case, one lucky gambler would end up with $117 million and accrue more than 70% of the group’s wealth, according to a natural simulation run by Jason Collins, the former head of behavioral economics for PwC in Australia who has written extensively about Peters’ research. The average expected payout, pulled up by a lucky few, would still be a hefty $16,000.
But tellingly, over half the players wind up with less than a dollar.
“For most people, the series of bets is a disaster,” Collins wrote. “It looks good only on average, propped up by the extreme good luck” of a just a handful of players.
While Peters employs plenty of high-level math to make his case, an experiment by a group of neuroscientists in Copenhagen also put his theory to the test. And in the lab, people changed their willingness to take risks when the circumstances changed, in ways his equations anticipated, even when classical economic theory suggested that doing so would be considered irrational.