Expected Value
Expected value is the payoff of each possible result multiplied by its probability, all summed. It is the single most useful yardstick for comparing bets under uncertainty.
To weigh a decision, don't just picture the best case or dread the worst. Take each outcome, multiply what it's worth by how likely it is, and add the results up. That number — the expected value — is what the choice is worth on average across all the futures it could produce.
It sharpens decisions by pricing possibilities you'd otherwise judge by vividness. A large prize at long odds can be worth less than a modest, near-sure one; a small chance of a huge loss can sink an otherwise attractive bet. Only the weighted sum reveals which is which.
The failure it prevents is being ruled by the extremes — chasing jackpots because they glitter, or refusing good bets because one branch looks frightening. Expected value forces every branch onto the same scale, so the whole picture decides, not the loudest part of it.
Write out the weighted sum
Lay the outcomes on a line
For the option in front of you, list the distinct results and estimate the odds and payoff of each — in money, time, or whatever you actually care about. Rough figures beat none.
Multiply, then add
Weight each payoff by its probability and total them. Do the same for your alternatives. The option with the higher expected value is, on average, the better bet — not the one with the prettiest best case.
- Odds times payoff, for every branch
- Compare the totals, not the highlights
Then check you can survive the downside
Expected value quietly assumes you get to keep playing. Before acting on it, confirm no single branch is fatal — a positive average is worthless if one outcome ends the game for good.
Don't ask which outcome you hope for. Ask what the whole spread is worth once you weigh it by the odds.