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Law of Large Numbers, Shown with Keno
In keno, a single draw can end almost any way. Over many draws, the average return gets close to the exact value set by the paytable.
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Chance to be ahead
| Length of play (as in the calculator) | Chance to finish ahead |
|---|---|
| A single draw | 3.2% |
| The calculator's short session | 5.3% |
| The calculator's long run | 3.7% |
The rows use the calculator's lengths of play and its keno bet; the values apply to that bet only. Finishing ahead is unlikely at every length shown.
Average return per dollar
average return = total prizes ÷ total wagered
Example: For example, on ten numbers the average return settles near 59.7%. About that share of every dollar wagered comes back as prizes.
Where the return settles
| Numbers picked | Long-run return per dollar | At the largest wager |
|---|---|---|
| One number | 50.0% | 50.0% |
| Two numbers | 60.1% | 60.1% |
| Three numbers | 55.5% | 55.5% |
| Four numbers | 58.2% | 58.2% |
| Five numbers | 60.7% | 60.7% |
| Six numbers | 62.1% | 62.1% |
| Seven numbers | 60.4% | 60.4% |
| Eight numbers | 57.2% | 57.2% |
| Nine numbers | 60.5% | 59.5% |
| Ten numbers | 59.7% | 58.6% |
Exact values from the WCLC keno paytable. For nine and ten numbers, the per-ticket prize cap lowers the return at bigger wagers.
What the law says and does not
What it says
- Over many draws, the average return gets close to the paytable value.
- The more draws, the less the average swings.
- The operator's share shows up in the long run.
What it does not say
- It does not say a win is due after losses.
- It says nothing about the next single draw.
- It does not change the odds of any combination.
- It does not cap losses. The total lost keeps growing.
Words on this page
- Paytable
- The official list of prizes for each count of matched numbers, per dollar wagered.
- Return per dollar
- The share of the money wagered that comes back as prizes on average.
- Long run
- A very large number of draws of the same bet, where the average stops moving much.
Related pages
Why results swing
Short sessions can look very different from the long-run average. See how big the swings are.
Try the keno simulator
Run many draws with real Canadian payouts and watch the average return settle.
Expected value
How the paytable value is calculated from the odds and the prizes, in plain words.
Sources
- WCLC – KENO page · checked Oct 29, 2026
- WCLC – KENO Game Conditions and Prize Structure Statement (2016) · checked Oct 29, 2026
Questions
What is the law of large numbers?
If the same random event is repeated many times, the average result gets close to the expected value. In keno, the return per dollar moves toward the paytable value, for example 60.7% on five numbers.
Why do keno players lose money in the long run?
Every WCLC keno paytable (used in Alberta, Manitoba, Saskatchewan and the territories) returns less than the wager on average: between 50.0% and 62.1% of each dollar. Over many draws the average settles there, so the missing share becomes a real loss.
Does the law of large numbers mean a win is coming?
No. Draws do not remember earlier results. The law describes the average over many draws, not what happens next. After a losing streak, the chance in the next draw is exactly the same.
What does the law of large numbers mean in gambling?
Short results are unpredictable, but long results are not. Over many draws, the average return moves toward the game's fixed return, and that return is below the wager. In a short session the result can be far from the average return.