Statistics
Break even price of a gamble
A game is fair when the price equals the expected payout, leaving a net of zero.
The Formula
fair price = expected payout, so net expected value = expected payout - price
A game is fair when the price equals the expected payout, leaving a net of zero.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| price | Price to play | same as outcome | What you pay to enter the game. |
| payout | Expected payout | same as outcome | The expected value of the prizes alone. |
| net | Net expected value | same as outcome | Expected payout minus the price. |
What Each Symbol Means
pricesame as outcome
Price to play
What you pay to enter the game.
payoutsame as outcome
Expected payout
The expected value of the prizes alone.
netsame as outcome
Net expected value
Expected payout minus the price.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate expected value page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Expected Value, filed under Math. Every number the guide produces comes from substituting into this one line.