Probability
Lottery Probability Calculator
Count possible lottery lines, calculate single-line and multi-line jackpot probability, compare ticket outlay with jackpot-only expected value, and find the after-tax jackpot required for break-even.
Possible unique number combinations-
Jackpot probability per line-
One-in jackpot odds per line-
Jackpot probability across purchased lines-
Total ticket outlay-
Modeled after-tax cash jackpot-
Expected jackpot value-
Expected net value, jackpot only-
After-tax jackpot needed to break even-
Decision view
Combination space and ticket coverage
Combination space and ticket coverageA combination-space grid and logarithmic odds ladder show how few of the possible lines are covered, while cash-value and ticket-cost blocks keep probability separate from payout assumptions.
Exact scenario comparisonIndependent ticket lines purchased changes while all other entered assumptions remain constant.
| Independent ticket lines purchased | Possible unique number combinations | Jackpot probability per line | One-in jackpot odds per line | Jackpot probability across purchased lines | Total ticket outlay | Modeled after-tax cash jackpot | Expected jackpot value | Expected net value, jackpot only | After-tax jackpot needed to break even |
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How to use Lottery Probability Calculator
- Enter the pool size and numbers selected on each line.
- Enter distinct ticket lines and cost per line.
- Convert the advertised jackpot to the modeled after-tax cash amount and compare expected value with outlay.
Calculator guide
Understanding Lottery Probability Calculator
A lottery line is an unordered selection, so jackpot odds come from combinations rather than permutations. This calculator keeps mathematical coverage, ticket spending, cash-value assumptions, and withholding separate.
Detailed calculation process
Detailed lottery combination and value calculation
The default example evaluates ten 6-from-49 lines against a $5,000,000 advertised jackpot.
General formula: M=C(N,K)=N!/[K!(N-K)!]p_1=1/Mp_T=1-(1-p_1)^TJ_a=J(c/100)(1-w/100)EV=J_a*p_T-Tq Combination count determines jackpot odds. Purchased lines change coverage, while payout assumptions change value but not probability.
What each symbol means
Worked substitution with the default inputs
Ten lines cover ten of 13,983,816 combinations; multiplying that exact coverage by $2,356,000 and subtracting $20 reproduces the displayed jackpot-only net value.
Worked situations
Practical examples
- A 6-from-49 lottery has C(49,6)=13,983,816 possible lines.
- Ten distinct lines cover only about 0.0000715% of that combination space while costing $20 at $2 per line.
Better inputs
Useful tips
- Use distinct lines; duplicate lines do not add combination coverage.
- Confirm whether the advertised prize is an annuity or cash option.
- Do not interpret jackpot-only expected value as total game return when lower prizes exist.
Before relying on the result
Limitations and common mistakes
- The model excludes lower prize tiers, jackpot sharing, ticket taxes, and behavioral spending.
- Draws and lines are assumed fair and independent.
- Withholding may differ from final tax liability.
Reference
Key terms
- Combination
- An unordered selection of K numbers from N.
- Cash value
- Lump-sum amount before the modeled withholding.
- Coverage
- Purchased distinct lines divided by all possible lines.
Important note
Lottery participation can create financial harm; treat ticket spending as entertainment expenditure, not an investment plan.
Frequently asked questions
Does buying twice as many lines double my chance?
Approximately when coverage is extremely small, but the exact calculation uses the complement rule.
Why is the expected value negative?
The very small jackpot probability may not offset ticket outlay even for a large prize.
Are lower prizes included?
No. This page deliberately isolates jackpot probability and value.