Expected Value Betting
Expected value weights each possible outcome by its probability and adds the results. A decision with a high chance of failure can still have positive expected value if the possible gain is large enough relative to the losses.
THE IDEA
Expected Value Betting
Expected value betting is a decision-making framework that calculates the average outcome of a decision by multiplying the probability of each possible outcome by the value of that outcome and summing across all outcomes. It encourages taking risks when the expected positive return exceeds the expected cost, especially when the same type of bet can be made repeatedly.
Musk's Thinking About the Tesla and SpaceX Bets
| Probability | Value |
|---|---|
| 10% chance of success | The company makes a big dent in one of the most pressing problems facing humanity (sustainability, space travel). |
| 90% chance of failure | Musk loses his investment, but isn’t personally ruined. The company probably makes a bit of progress on the problem. |
Overall, both Tesla and SpaceX seemed like good bets to him—even though the most likely outcome for each was failure.
Another way to think about whether a bet is positive expected value is to imagine taking it many times. Would the value of the expected successes outweigh the value of the expected failures? Over the course of a lifetime, someone like Elon Musk probably has the time and money to attempt at least ten companies like Tesla and SpaceX. If his best guess is that nine of those ten companies will be failures, then the key question is: Would it be worth failing nine times in exchange for one big success?
In reality, you almost never get to repeat the exact same bet many times. But you’ll have the opportunity to make many different bets over the course of your life. You’ll face bets at your company and in your career more broadly; bets on investment opportunities; chances to bet on trusting another person, or making a difficult ask, or pushing your comfort zone. And the more positive expected value bets you make, the more confident you can be that you’ll end up ahead overall, even if each individual bet is far from a sure thing.
When to use it
Assessing investment opportunities where the potential upside is large but the probability of success is low.
Deciding whether to launch a new product or business venture that has high potential payoff but high risk of failure.
Choosing career moves that involve short-term risks for long-term gains, such as switching industries or taking on a challenging role.
Evaluating personal decisions like social risk-taking (making a difficult ask) or pushing comfort zones, where the cost of failure is small but the reward is significant.
FROM THEORY TO EVERYDAY LIFE
In practice
Elon Musk's Bet on Tesla and SpaceX
In Galef’s account of Musk’s reasoning, he considered a 90% chance of failure compatible with a worthwhile investment because of the possible contribution to sustainability or space travel. This describes how he valued the gamble; it does not independently establish its probabilities or returns.
Career Risk-Taking Example
Consider a hypothetical career gamble with a 20% chance of a gain valued at 10x a baseline unit and an 80% chance of a loss valued at 2 of those units. Expected value: (0.2 * 10) + (0.8 * -2) = 2 - 1.6 = +0.4 units. The arithmetic depends on the assumed probabilities and a common value scale. Whether to take the risk also depends on whether the loss is affordable.
A MOMENT TO REFLECT
Put it to work.
Think of a major decision you're facing. What are the probabilities and values of each possible outcome? Calculate the expected value.
How would you apply expected value thinking to a recurring decision that you make many times, like choosing which projects to invest your time in?
What biases might prevent you from accurately estimating probabilities or values in your own expected value calculations?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- The Scout Mindset (Julia Galef)