Betting on Low-Probability Outcomes

Why Error Management Theory Matters in Decision Making

A previous version of this post was published on Psychology Today.

Image by Pete Linforth from Pixabay

Betting often brings to mind activities like poker, slot machines, or lotteries—contexts where probabilities take center stage. But in reality, every decision we make involves a bet of some kind. For instance, ordering a pizza from your favorite restaurant is a bet: you’re wagering that (1) the costs you incur (e.g., price, waiting time) will (2) lead to an outcome (the pizza arriving), from which (3) you will derive a benefit (satisfaction and satiation) that (4) outweighs the costs.

We often learn that the key to good decision making involves mastering probabilities. The bets we make are generally safer placed on high-probability outcomes—those outcomes we believe are very likely to occur, such as such as the pizza we ordered arriving as expected (see Figure 1)¹. Yet, there are times when it makes sense to base decisions on the potential consequences of a low-probability outcome. Error Management Theory explains why it’s sometimes reasonable to hedge our bets and act as though the low-probability outcome will occur, especially when the stakes are significant.

Figure 1. The Way Good Decision Making Is Often Conceptualized.

Error Management Theory

Error management theory (EMT) was described by David Buss and Martie Haselton to explain what are often described as decision-making errors—instances where our decisions deviate from what we might expect if solely considering the probability of an outcome. EMT posits that human decision making evolved to hedge against specific errors, particularly when the stakes are high. In cases where a low-probability outcome poses significantly greater potential consequences than a higher-probability outcome, it can be reasonable to act as though the low-probability outcome will occur.

EMT helps us navigate the trade-offs between two different types of errors, prioritizing the one with greater consequences in a given context. Type I errors (false positives) involve deciding based on the assumption that an event will occur when it doesn’t. Type II errors (false negatives) involve deciding based on the assumption that an event will not occur when it actually does.

For example, smoke detectors are generally designed to be more accepting of Type I errors than Type II errors. They are calibrated to be overly sensitive, sounding an alarm even when there is no fire present (Type I error). The greater acceptance of Type I errors makes sense in this context because the consequences of failing to detect a real fire (Type II error) are far more catastrophic than the inconvenience of a false alarm. Alternatively, in criminal justice, the principle of innocent until proven guilty with proof being based on a standard of beyond a reasonable doubt implies that the system is more accepting of Type II errors (letting a guilty person go free) than Type I errors (convicting an innocent person). This approach reflects a fundamental value judgment that the justice system places on protecting individual rights over ensuring every guilty person is punished.

While in an ideal world we might strive to eliminate both error types, real-world decision making is rarely so clean. Probabilities are often unknown, consequences subjective, and trade-offs complex. EMT provides a framework for prioritizing errors effectively, helping humans make rational choices even in uncertain or high-stakes scenarios. This aligns with the concept of bounded rationality, where decision making is shaped by the limitations of knowledge, cognitive resources, and time².

Although betting on low-probability outcomes may sound counterintuitive, EMT demonstrates how it can be a rational choice when the stakes are high. Consider the decision to wear a seat belt during a car trip. The probability of being in a car accident on a 1,000-mile journey is approximately 0.3%, or 1 in 366. At first glance, this low likelihood might suggest that wearing a seat belt is unnecessary. However, in the event of an accident, wearing a seat belt increases the chance of survival by roughly 45%. In this case, the potential consequences of a Type II error—failing to prepare for the possibility of an accident—vastly outweigh the minor inconvenience of a Type I error (wearing a seat belt during an uneventful trip; see also Figure 2).

Figure 2. Deciding Whether or Not to Wear a Seat Belt

EMT also applies to decisions where the low-probability outcome carries significantly positive consequences. Lotteries are a prime example. Winning any lottery is an extremely low-probability event, yet people frequently buy tickets. Why? Many perceive the life-changing benefits of winning to outweigh the relatively minor costs of playing (Figure 3). In this context, players act as though the low-probability outcome might occur, valuing the potential reward over the small, predictable loss³. This tendency is amplified as jackpots increase, with the larger reward making the bet feel even more worthwhile (Stetzka & Winter, 2021)⁴.

Figure 3. Deciding Whether or Not to Play the Lottery.

It's important to note that individuals often differ in how they evaluate these scenarios. Factors such as personal values, risk tolerance, and subjective perceptions of costs and benefits influence how people weigh high- versus low-probability outcomes. For example, consider two individuals deciding whether to invest in a high-risk start-up. For one, the decision activates values tied to risk aversion, leading to prioritization of financial security and the decision not to invest because it represents a low-probability outcome. For the other, it activates values associated with risk-taking, leading to prioritization of the potential for significant gains and the decision to invest due to the potential benefit if the investment pays off. These differing values highlight how individual decision-making frameworks are shaped by the interplay between risk perception and personal priorities⁵.

Applying Error Management Theory in Decision Making

EMT offers a framework for navigating the trade-offs inherent in decision making, especially when dealing with uncertain or high-stakes scenarios. To effectively apply EMT, we must weigh four critical factors:

1. Impact of Low-Probability Outcomes: Assess whether the potential consequences of the low-probability outcome are substantial enough to justify prioritizing it. For example, if a rare event like a major financial crash would lead to catastrophic loss, it might warrant action despite its low probability. A decision is reasonable if the scale of potential impact justifies the consideration.

2. Likelihood of Occurrence: Even a low-probability event needs to meet a threshold of plausibility. Reasonable application of EMT requires basing this on credible evidence or logical inference. An event so implausible as to border on fantasy (e.g., alien invasion) would not merit action, regardless of potential consequences.

3. Anticipated Benefits: Weigh the tangible and intangible benefits of addressing the low-probability outcome. Benefits should be clear, achievable, and sufficiently significant to justify the decision. Betting on a low-probability outcome that yields negligible gains is rarely reasonable.

4. Cost-Benefit Alignment: Decisions made under EMT should balance the resources required to mitigate a low-probability event against the potential benefits of doing so. If the costs vastly outweigh the gains (e.g., spending millions to prevent an event with negligible personal impact), the decision veers into irrationality.

Yet, decision-making under EMT hinges on our willingness to accept certain costs in pursuit of potential benefits. This willingness is shaped by how we prioritize outcomes, interpret probabilities, and balance the trade-offs unique to each decision.

Take, for instance, decisions related to disaster preparedness. People vary in their willingness to invest in home insurance or emergency supplies. Some may weigh the low-probability risk of a natural disaster and prioritize the financial security provided by preparation. Others might downplay the risk or perceive the costs as outweighing the benefits, leading to minimal preparation. These differences often stem from personal values, risk tolerance, and how individuals frame the potential consequences of such events.

Similarly, in financial planning, one person might invest conservatively, prioritizing long-term stability, while another might take risks, seeking high returns. Both approaches align with EMT principles, reflecting diverse assessments of trade-offs and subjective priorities.

EMT provides a valuable lens through which we can understand the complexities of decision-making under uncertainty. By weighing the potential impact, plausibility, benefits, and cost-benefit alignment of various outcomes, we can make more deliberate and reasonable choices, even in situations where probabilities and stakes are unclear.

However, applying EMT effectively is not without its challenges. Many decisions involving low-probability outcomes occur unconsciously, sometimes leaving us vulnerable to errors. These include over- or underestimating probabilities, misjudging costs and benefits, or failing to recognize critical factors. Faulty assumptions—such as perceiving connections between costs and benefits that do not exist—can further complicate decision making. By bringing these unconscious processes to light and deliberately evaluating the trade-offs involved, we can mitigate errors and enhance the quality of our decisions.

1. Many of these recommendations assume the costs of various options are roughly equivalent.

2. This is a topic that comes up in my posts on a semi-regular basis.

3. Though EMT applies to both positive and negative low-probability outcomes, low-probability negative outcomes are likely to produce more universal application of EMT (as evidenced by the fact more people wear their seat belt than play the lottery).

4. People’s willingness to gamble online using sports betting apps also aligns with the principles of bounded rationality and EMT. Online sports betting apps make it easier for individuals to wager small amounts with reasonable odds of winning modest rewards, creating a sense of accessibility and control. The perception of affordability (small bets) combined with achievable outcomes enhances the appeal, even if the overall odds still favor the house. This is similar to the lottery example, where perceived benefits and ease of participation outweigh strict probabilistic reasoning.

5. Each person’s frame of reference likely influences which values are activated.