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Expected Value Explained in Plain Words
Expected value is the average amount a ticket pays back over many draws. Build one in the bar above from outcomes and chances. Then see how keno and lottery tiers add up.
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The one formula
Expected value = sum over every outcome of (chance of that outcome × prize for that outcome)
Example: For example, adding chance × prize over every Lotto Max tier at one jackpot size gives about $1.97 per play – less than a play costs.
How to calculate it
- List every outcomeWrite down each prize tier. Include the outcome where the ticket pays nothing.
- Find each chanceTake the odds for each tier from the official game conditions and turn them into a chance.
- Multiply chance by prizeFor each tier, chance × prize gives that tier's share of the average.
- Add and compareAdd all the shares to get the expected value. Subtract the ticket price to see the average loss per ticket.
Built from tiers: a keno example
| Numbers picked | Paying matches | Average paid back per bet |
|---|---|---|
| Two numbers | 2 of 2 | 55.1% |
| Three numbers | 3 of 3 | 52.1% |
| Four numbers | 4 of 4 | 52.8% |
| Five numbers | 4 of 5, 5 of 5 | 42.0% |
| Six numbers | 5 of 6, 6 of 6 | 44.3% |
| Seven numbers | 5 of 7 to 7 of 7 | 48.3% |
| Eight numbers | 6 of 8 to 8 of 8 | 46.6% |
| Nine numbers | 6 of 9 to 9 of 9 | 43.0% |
| Ten numbers | 0 of 10, 7 of 10 to 10 of 10 | 44.8% |
OLG Daily Keno, official prize table. Each row: sum of chance × prize over its tiers, divided by the bet. The rest of the bet is the expected loss.
Long run vs one ticket
Expected value
- Average payback per ticket over a very large number of draws
- Same for every combination of numbers
- Below the price in lottery and keno games
- Does not change with past draws
One ticket
- Usually pays nothing
- Sometimes pays one prize tier
- Can land far above or below the average
- Says almost nothing about the average
Words used on this page
- Outcome
- One possible result of a ticket, such as a prize tier or no prize.
- Chance
- How likely an outcome is, written as a share of all possible results.
- Expected value
- Sum of chance × prize over every outcome: the average payback per ticket.
- Return to player
- Expected value divided by the bet, shown as a percentage.
- Expected loss
- Ticket price minus expected value: the average amount lost per ticket.
- Spread
- How far single results usually land from the average. See variance.
Expected value in real games
Sources
- OLG – Daily Keno past results and odds · checked Oct 29, 2026
- WCLC – KENO page · checked Oct 29, 2026
- OLG – Lotto Max Game Conditions · checked Oct 29, 2026
- WCLC – Lotto Max Game Conditions, in effect 2026-04-10 · checked Oct 29, 2026
- OLG – Conditions de jeu du Lotto Max · checked Oct 29, 2026
- Loto-Québec – Conditions de jeu du Lotto Max, en vigueur le 2026-04-10 · checked Oct 29, 2026
- OLG – Daily Keno Game Conditions · checked Oct 29, 2026
- OLG – About Daily Keno · checked Oct 29, 2026
- WCLC – KENO Game Conditions and Prize Structure Statement (2016) · checked Oct 29, 2026
Questions
What is expected value in simple terms?
It is the average amount one ticket pays back if the same bet is repeated a very large number of times. Multiply each prize by its chance and add the results.
What is the expected value formula?
Expected value = sum over every outcome of chance × prize. Subtract the ticket price to get the average gain or loss per ticket.
Can expected value be negative?
The net expected value is negative when the average payback is below the price. In OLG Daily Keno the average payback is between 42.0% and 55.1% of the bet, so the net value is negative.
How is expected value used for lottery tickets?
It compares the average payback with the price. For example, one Lotto Max calculation gives about $1.97 per play, below its price. See Lotto Max expected value.
Does expected value tell me what one ticket will pay?
No. It is a long-run average. One ticket usually pays nothing or a single prize. Variance shows how far results swing.