Calculators
Is a Lottery Ticket Worth It? Expected Value
The average prize money one play returns, minus its price, is the expected value. The calculator above adds up every prize tier, lets you set the jackpot and compares the total with the price.
You pay $6 for a play worth about $1.22 on average, so each play loses about $4.78 in the long run, whichever numbers you choose.
Model: every other play is a random selection; pool prizes split the prize fund left after the fixed prizes between the winners of the tier; a free play is worth one more play. MAXPLUS and MAXMILLIONS prizes are not counted. Not advice.
How it is calculated
Source: OLG game conditions checked Oct 29, 2026 · OLG page checked Oct 29, 2026
Lotto Max value by jackpot →Chance of sharing a jackpot →Odds of every Canadian lottery →
Where a Lotto Max play's price goes
| Part of a Lotto Max play | Amount | What it means |
|---|---|---|
| Price of one play | $6 | What you pay per play per draw |
| Set aside for prizes | $2.88 | Split between the Draw Fund and the prize pools |
| Return to player | 48.0% | Share of the price paid back as prizes |
| Not allocated to prizes | The rest of the price | The part of the price that does not go to prize funds |
The Draw Fund pays, among other things, the Main Jackpot, MAXPLUS and MAXMILLIONS. Source: Lotto Max game conditions.
Expected value in one line
EV = sum over all tiers of (chance of the tier × prize of the tier) − price
Example: For example, Lotto Max with a $30,000,000 jackpot: average prize money is $1.97 per play. Minus the $6 price, the average result is a loss.
What goes into the sum
Jackpot part
Jackpot ÷ jackpot odds. It changes from draw to draw because the organiser sets the jackpot before each draw.
Pool prizes
Middle tiers get a share of the Pools Fund. More winners in a tier means a smaller prize for each of them.
Fixed prizes
The lowest tiers pay a set prize, no matter how many people win them.
Shared jackpot
If other tickets match the same numbers, the jackpot is split equally between them.
Big jackpot vs many winners
Bigger jackpot
- The jackpot part of the value grows with the jackpot
- The chance of the jackpot stays exactly the same
- The organiser sets the jackpot before the draw
More tickets sold
- More tickets mean more people who may match the same numbers
- A shared jackpot is split equally among the winning tickets
- A jackpot winner expects to keep 86.4% of the jackpot on average
- Example: a $30,000,000 jackpot with 10,000,000 tickets sold
Related calculations
Sources
- 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
Questions
Is a lottery ticket ever worth more than it costs?
For Lotto Max with a $30,000,000 jackpot, no: the average prize money is $1.97 per play, against a price of $6. A bigger jackpot raises the value, but a shared jackpot lowers it again.
What is the expected value of a lottery ticket?
Add up the chance of each prize tier times its prize: that is the average prize money per play. Subtract the price and you get the expected value. For Lotto Max at a $30,000,000 jackpot, that is $1.97 minus $6.
Does a bigger jackpot change the expected value?
Yes. The jackpot part grows with the jackpot, the chance of winning it stays the same, and sharing lowers the value. For example, at a $30,000,000 jackpot one Lotto Max play returns $1.97 in prizes on average, against $6.
Does a lottery ticket make money on average?
No. A play has a negative expected value: its average prize money is less than its price. For Lotto Max, 48.0% of the price goes to prizes. Whether the fun is worth the cost is your choice. The spending calculator shows the yearly cost.