Not understanding expected value.

How often a bet wins only tells you part of the story. What it pays when it wins matters too.

Expected value is the average net result of a bet, taking into account every possible outcome and how likely each is. It can be negative even when winning is much more likely than losing.

For the bet on the previous page, an 80% chance of making $1 and a 20% chance of losing $10 gives an average loss of $1.20 per bet.

It isn’t a prediction of your next result.

You can’t lose exactly $1.20 on that bet. You either make $1 or lose $10. The average describes the deal, not what must happen to you today.

A bet with a positive expected value can still lose. It can also be a bad decision if the money at risk is money you need.