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Lottery Mathematics, Explained Simply
Lottery math is counting, value and chance. Each explainer covers one idea in plain words, with tables built from the published odds of Canadian games.
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Counting
Combinations
How many different tickets a game allows. This count gives the jackpot odds.
Keno math
You pick spots and the draw picks numbers from a pool. Each number of spots has its own odds table.
Odds vs probability
Two ways to write the same chance. Lotteries usually print odds as one chance in a large number.
Odds cheat sheet
Published odds of Canadian lotteries side by side, prize tier by prize tier.
How a chance is calculated
Probability = winning combinations ÷ all possible combinations
Example: For example, if a game allows more combinations, each ticket has a smaller chance of matching all of them.
Value
Expected value
The average a ticket pays back over many draws, minus its price. For lottery tickets it is normally less than the price.
Pari-mutuel prizes
Some prizes are a share of a pool. More winners in a tier means a smaller share for each.
Jackpots
A bigger jackpot changes the prize, not the odds. The chance of matching every number stays the same.
How expected value is calculated
Expected value = sum of (each prize × its probability) − ticket price
Example: For example, a tier with a large prize but a tiny probability adds only a small amount to the sum.
Randomness and myths
Independent draws
Balls have no memory. Results of the last draw do not change the next one.
Hot and cold numbers
A number drawn often lately is not more likely next time. Every number has the same chance in every draw.
Near misses
Missing the jackpot by one number is still a miss. It does not mean a win is getting closer.
Quick pick vs own numbers
A machine choice and your own choice have exactly the same odds.
What changes and what does not
Can change
- The jackpot amount
- How many winners share a pari-mutuel tier
- The size of each shared prize
Never changes the odds
- Past draw results
- Hot or cold numbers
- Quick pick or own numbers
- When or where a ticket is bought
Questions
How is lottery math calculated?
By counting. First count every possible ticket, then count how many tickets win each prize. Dividing gives the odds. Multiplying each prize by its probability and adding them up gives the expected value.
Is the lottery truly random?
The published odds assume every number has the same chance in each draw and draws do not affect each other. Under that assumption, past results tell you nothing about the next draw.
Do I need math to understand the lottery?
No. The explainers use plain words and tables. Knowing what the published odds mean and what expected value is covers most of it.
Does a quick pick have different odds than my own numbers?
No. Every combination has the same chance of being drawn, whether a machine chooses it or you do.