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
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).