Results
Prize tiers
| Name | Condition | Probability | Odds | Prize (optional) | Include in EV |
|---|
Expected value (EV)
Prizes are treated as fixed values you enter. If a prize is blank, that tier is excluded from EV.
EV breakdown (p × prize)
| Tier | p | Prize | p×prize |
|---|
Simulation (optional)
| Tier | Theory p | Sim p | |error| | Count |
|---|
Main-match histogram (sim)
| Match count | Count | p |
|---|
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If the URL becomes too long (many custom tiers), download CSV instead.
How to interpret the results (with an example)
- Jackpot odds for a simple “pick K from M” game are typically
1 / C(M, K)(when there are no bonus/pool rules). - “1 in X” is just
1/p. It is an intuitive scale, not a promise that you will win once every X tickets. - Multiple tickets: the tool uses
1 − (1 − p)^mfor “at least one win”, assuming independent random tickets. - Expected value (EV) uses the prize values you enter as fixed numbers. Real payouts can vary (jackpot changes, winner splits, taxes, annuities).
Example: 6 from 49 (jackpot)
A single-ticket jackpot probability is 1/C(49,6) = 1/13,983,816 ≈ 0.00000715%. With 10 independent random tickets, 1 − (1 − 1/13,983,816)^10 ≈ 0.0000715%.
Common pitfalls
- Prize tiers can overlap. This tool resolves overlaps using higher-tier priority so total probability stays ≤ 1.
- Simulation is a sanity check for the theory results. Use enough draws to reduce random noise.
References
How to read lottery odds
Enter the game rules first: pool size, picks, bonus rules, ticket price, and prize tiers. The calculator converts those rules into exact combinations, reciprocal odds, at-least-one-win probability, expected value, and return rate.
How it works
Jackpot and tier odds come from combinations such as C(M, K). Buying more independent tickets changes at-least-one probability with 1 - (1 - p)^m, but it does not make any single ticket more likely to win.
When to use
Use this page to compare game formats, explain "1 in X" odds, estimate expected value from prize tables, or show why jackpot size and winner splits matter.
Common mistakes to avoid
- Forgetting bonus-number tiers when a game uses them.
- Treating EV as guaranteed profit instead of a long-run average.
- Ignoring jackpot sharing, taxes, annuity/cash choices, and changing prize pools.
- Assuming multiple tickets are independent when you intentionally avoid duplicate combinations.
See also
FAQ
How do I compute the jackpot probability?
For a lotto-style game (pick K from M), jackpot odds are typically 1 / C(M, K).
How does a bonus number affect the odds?
Bonus tiers depend on both the main-match count t and bonus-match count s. This tool computes P(t,s) exactly from combinations.
What does “1 in X” mean?
It is the inverse probability 1/p, shown as an intuitive approximation (“about one win per X tickets”).
How do I compute “at least one win” when buying m tickets?
Use 1 − (1 − p)^m, where p is the probability of the target event (any win or a specific tier).
What is expected value (EV) / return rate?
EV per ticket is Σ(p_i·prize_i) − price. Return rate is Σ(p_i·prize_i) / price when price > 0.
Can I use this when prizes vary each draw?
Yes, but enter a fixed prize amount for estimation. Real payouts can vary due to jackpot changes and winner splits.
What does the simulation seed do?
A seed makes the simulation reproducible.
How it’s calculated
1 − (1 − p)^m(independent random tickets).m ≥ log(1−target)/log(1−p).