Expected Value

“The long-run average can be a number that never occurs in any single play.”

01 / PLAINLY

What it means, plainly

Expected value is a weighted average: multiply each outcome by its probability and add the results. It describes many theoretical repetitions, not what happens next.

02 / CONTEXT

A little more

Expected value multiplies each outcome by its probability and adds the products. It summarizes the theoretical average over many repetitions, not a promise about the next one.

03 / WHY IT MATTERS

Why it matters

It compares options by combining consequences with probabilities, provided you also examine how the possible outcomes are distributed.

04 / EXAMPLE

A familiar example

A game pays 10 with probability 0.1 and 0 otherwise: its gross expected value is 1, even though it never pays exactly 1.

05 / LIMIT

What it does not mean

Two options with equal expected value may have very different risks, distributions, and consequences.

06 / NOTICE

Notice it in your day

Calculate the expected value of the game that pays 10 with probability 0.1 and 0 otherwise. Then list the only payouts it can actually produce.

FINAL NOTE

The idea worth keeping

Combine probabilities with consequences, then inspect spread and time horizon too.

QUESTIONS / 02

Questions people still have

How is expected value calculated?

Multiply each outcome by its probability and add the products.

Does expected value predict the next play?

No. It summarizes a theoretical average over many repetitions.