Tiers (editable)
| Name | Condition | p | Odds | Prize (optional) | EV |
|---|
Summary
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 (Monte Carlo)
| 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), export CSV instead.
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).