Lottery Calculator
Enter the pool size, how many numbers are drawn, and how many you match. The calculator outputs exact probabilities and insights for single and multiple tickets.
Used to estimate expected jackpot value.
P(Matching 6)
0.00000715%
Single ticket probability
Chance with 1 Tickets
0.00000715%
At least one ticket hits exactly m matches
Expected Jackpot Value
$0.14
Assuming jackpot requires all 6 matches
How to Use This Calculator
- Enter the size of the number pool and how many numbers are drawn in the lottery.
- Specify the number of matches you are interested in (e.g., full jackpot or secondary prizes).
- Provide how many tickets you plan to purchase to see the chance of success at least once.
- Add an optional jackpot amount to estimate expected value based solely on the top prize.
Formula
P(match exactly m) = [C(k, m) · C(n − k, k − m)] / C(n, k)
P(at least one success) = 1 − (1 − P(match))tickets
The formula counts how many ways you can pick m winning numbers and fill the rest with losing numbers, divided by the total number of possible tickets. Independence between tickets is assumed.
Full Description
Lotteries combine combinations mathematics with astronomical odds. This calculator reveals just how rare a jackpot is and quantifies the marginal benefit of buying additional tickets. It focuses on classic “n choose k” lotteries where order does not matter and numbers cannot repeat.
Use it to compare different lottery formats, evaluate syndicate strategies, or illustrate the law of large numbers in classrooms. Extend the analysis by adding secondary prize tiers or ticket costs to compute net expected value.
Frequently Asked Questions
Does buying more tickets help?
More tickets increase the probability of success linearly for small probabilities, but the odds remain tiny. The calculator shows diminishing returns clearly.
Can I model bonus balls?
This version assumes a simple draw without bonus balls. For games with extras, compute each prize tier separately and sum the results.
Does order matter?
No. The formula uses combinations, so it applies to lotteries where numbers can appear in any order. For ordered draws, multiply by k! accordingly.
How do taxes or ticket prices factor in?
Adjust the expected value by subtracting ticket cost per entry and applying any tax rate to the jackpot. The current calculation shows gross expected value for the top prize only.