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 use this calculator effectively
This guide helps you use Lottery odds & probability calculator (EV, jackpot, 1 in X) in a repeatable way: define a baseline, change one variable at a time, and explain each output using explicit assumptions before sharing results.
How it works
The calculator applies deterministic formulas to your input values and only rounds at the final display layer. This makes it useful for comparative analysis: keep one scenario as a baseline, then vary assumptions and measure the delta in both absolute terms and percentage terms. If a change appears too large or too small, verify units, period conventions, and sign direction before interpreting the result.
When to use
Use this page when you need a fast planning estimate, a classroom check, or a reproducible scenario that teammates can review. It is most effective at the decision-prep stage, where you need to compare options quickly and decide which assumptions deserve deeper modeling or external validation.
Common mistakes to avoid
- Mixing units such as percent vs decimal, or monthly vs yearly settings.
- Changing multiple fields at once, which hides the real cause of result movement.
- Comparing outputs across tools without aligning constants and default conventions.
- Treating rounded display values as exact inputs for downstream calculations.
Interpretation and worked example
Start with a baseline case and save that output. Next, edit one assumption to reflect your realistic alternative, then compare both the direction and size of change. If the direction matches domain intuition and magnitude is plausible, your setup is likely coherent. If not, check hidden defaults, unit conversions, boundary conditions, and date logic before drawing conclusions.
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).