Expected Value

Expected value is each possible payoff multiplied by its probability, all summed. It is the most useful yardstick for comparing bets under uncertainty.

Don't just picture the best case or dread the worst. Multiply what each outcome is worth by how likely it is, and add them up. That total is what the choice is worth on average.

It prices possibilities you would otherwise judge by vividness. A large prize at long odds can be worth less than a modest, near-sure one. Only the weighted sum shows which.

It prevents being ruled by the extremes — chasing jackpots because they glitter, or refusing good bets because one branch looks frightening.

Write out the weighted sum

#02

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.

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