Expected value, usually written EV, multiplies each possible outcome by its probability and adds them up. A bet paying 4:1 that wins one time in six has an EV of (1/6 × 4) − (5/6 × 1) = −1/6, or −16.67%.
That example is the any seven bet in craps, and it is the worst wager on the table. The arithmetic is the whole of casino mathematics: compare what a bet pays against how often it wins, and the gap is the house's.
EV is also the right frame for decisions inside a game. Blackjack basic strategy is nothing more than taking the highest-EV action at every choice, and video poker strategy is choosing the hold with the highest EV among 32 options. In both cases the correct play is often the one that feels worse.
What EV does not describe is any particular session. A negative-EV bet wins often; a positive-EV decision loses often. Expected value is a statement about the average of a very large number of repetitions and nothing else.
Where the numbers come from
Related terms in odds & money
- House edge — The average share of each bet the casino expects to keep over the long run.
- RTP — Return to player: the mirror of house edge, quoted as what comes back rather than what is kept.
- Variance — How widely results scatter around their expected value.
- Standard deviation — A measure of how far results typically stray from the average.
- Bankroll — The money set aside for gambling, kept separate from money needed for anything else.
- Unit — One standard bet, used as the yardstick for measuring results and bankroll.
Where an entry quotes a number, that figure comes from the computed sections of this site rather than from another glossary, so the definition and the derivation cannot drift apart. Each entry links to the page where the number is worked out.