Why We Can’t Stop Believing Past Luck Shapes What Comes Next todayheadline

A fair coin knows no memory, but our minds insist it does.

In a massive study of more than 12,000 people, researchers at the University of Chicago and Princeton found that individuals adjust their expectations of future coin tosses based on past streaks of lucky or unlucky guesses, even when they fully understand that outcomes are random. Published August 26 in PNAS Nexus, the work shows that success breeds optimism and failure breeds pessimism, patterns that spill over into betting behavior and risk-taking decisions. The results highlight a stubborn cognitive bias: humans simply cannot resist using the past as a guide to the future, even when chance is in control.

From Coins to Consequences

Coin flips may seem trivial, but they are a clean test of randomness. The team, led by Russell Roberts of the University of Chicago, designed five experiments where participants predicted the outcomes of five flips, some with real quarters, others with virtual coins. Because the flips were fair, all results—from five straight wins to five straight losses—emerged naturally without trickery.

The findings were striking. Those who guessed correctly more often rated themselves as better predictors and expected more success on future flips. They were also more willing to make riskier bets. Conversely, participants who missed more flips became discouraged, expecting worse results ahead and betting more conservatively. The effect was asymmetric: failure pushed people further into pessimism than success lifted them into confidence.

Luck, Skill, and Illusion

Even though participants were told the task was random, many attributed streaks to personal skill. When asked whether their results were due to luck or talent, successful guessers leaned toward skill, while those with poor results saw only misfortune.

“People consistently demonstrated the tendency to expect future performance to resemble past performance and acted on those expectations,” the authors write in PNAS Nexus.

The results echo classic cognitive traps like the “hot hand fallacy” and the “illusion of control,” but the authors note that their study stands out because it used actual random devices rather than deceptive setups or fictional scenarios. This makes the bias harder to dismiss as an artifact of poor design.

Why It Matters Beyond Coin Tosses

The study points to broader lessons about how people respond to randomness in everyday life. Whether in sports, investing, or disaster recovery, humans often mistake chance streaks for meaningful signals. For example:

• Basketball coaches change strategy more often after close losses than wins.
• Lottery stores that sell a winning ticket see a surge in sales.
• People spared by natural disasters are less likely to take precautions than neighbors who suffered losses.

These real-world behaviors mirror the same bias revealed in the coin-toss experiments: we update expectations based on outcomes that were random all along. For readers seeking background on how probability works, Khan Academy offers a primer on probability.

Key Findings

• Sample: Over 12,000 participants across five experiments (lab and online).
• Task: Predict outcomes of five fair coin tosses, real and virtual.
• Effect: More successes led to optimism and higher risk-taking; more failures led to pessimism and risk-avoidance.
• Asymmetry: Negative effects of unlucky failures were stronger than positive effects of lucky successes.
• Controls: Effects persisted regardless of probability knowledge, risk attitudes, or reward incentives.
• Location: Experiments conducted at a public lab in the U.S. Midwest and via Amazon Mechanical Turk.
• Safety/Design: Outcomes were transparently random, with no deception.

Takeaway

Even when people know the odds and see randomness unfold before their eyes, they cannot help but let past outcomes shape their beliefs about the future. This ingrained bias toward extrapolating from lucky streaks and unlucky failures may quietly influence how we bet, learn, and make decisions in domains far more consequential than coin flips.

Journal: PNAS Nexus
DOI: 10.1093/pnasnexus/pgaf237