Probability
Lottery Odds Calculator
Count main and bonus outcome spaces, calculate one-ticket and multi-ticket jackpot probability, and compare jackpot-only expected value with spend.
Possible main-number combinations-
Possible bonus combinations-
Distinct jackpot outcomes-
Jackpot probability per ticket-
One-in jackpot odds-
Jackpot probability across entered distinct tickets-
Ticket spend-
Gross jackpot-only expected value-
Jackpot-only EV after ticket spend-
Decision view
Lottery combination lattice and ticket coverage
Lottery combination lattice and ticket coverageMain and bonus choice spaces multiply into the jackpot universe, with purchased tickets shown as a visible sliver of coverage.
Exact scenario comparisonDistinct tickets purchased changes while all other entered assumptions remain constant.
| Distinct tickets purchased | Possible main-number combinations | Possible bonus combinations | Distinct jackpot outcomes | Jackpot probability per ticket | One-in jackpot odds | Jackpot probability across entered distinct tickets | Ticket spend | Gross jackpot-only expected value | Jackpot-only EV after ticket spend |
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How to use Lottery Odds Calculator
- Enter the published pool and pick sizes.
- Include a bonus pool only when the jackpot requires it.
- Use distinct tickets; duplicated lines do not add outcome coverage.
Calculator guide
Understanding Lottery Odds Calculator
Lottery jackpots are counting problems. The order of drawn main numbers normally does not matter, so combinations—not permutations—define the number of distinct tickets.
Detailed calculation process
Detailed lottery outcome-space calculation
The default game selects six unordered numbers from 49 and one bonus number from ten.
General formula: C(n,k)=n!/[k!(n-k)!]N=C(n_m,k_m)C(n_b,k_b)p_1=1/Np_t=1-(1-p_1)^tEV_J=tJp_1-tc Combinations count each unordered selection once. Independent pools multiply; multiple-ticket probability uses the probability that every ticket loses.
What each symbol means
Worked substitution with the default inputs
The default jackpot odds are one in 139,838,160 per ticket; ten distinct tickets still cover only about 0.00000715% of outcomes.
Worked situations
Practical examples
- Choosing six from 49 creates 13,983,816 main-number combinations.
- Adding one of ten bonus numbers produces 139,838,160 jackpot outcomes.
Better inputs
Useful tips
- Use the actual jackpot rule rather than a game name.
- Separate annuity headline value from cash value and tax.
- Include lower-tier prizes only in a complete expected-value analysis.
Before relying on the result
Limitations and common mistakes
- The expected value includes only the entered jackpot.
- Shared prizes, taxes, cash-option discount, lower prizes, and sales-dependent jackpot risk are omitted.
- The multi-ticket expression assumes independently sampled or distinct outcomes.
Reference
Key terms
- Combination
- Unordered selection of k objects from n.
- Outcome space
- Number of distinct jackpot-result combinations.
- Complement rule
- Probability of at least one win equals one minus no wins.
Important note
Lottery play is entertainment, not an investment plan. Verify official rules, prize structure, cash value, taxes, claim terms, and responsible-play guidance.
Frequently asked questions
Do ten tickets make the odds ten times better?
Approximately for extremely small probabilities, but the exact at-least-one formula is 1-(1-p)^10.
Does a larger jackpot improve the probability?
No. It changes value, not the draw mechanism.
Why can jackpot-only EV be negative?
Expected jackpot receipts may remain below ticket spend before taxes and prize sharing.