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How Lottery Odds Work
Lottery probability is calculated using combinations (not permutations) because the order of drawn numbers does not matter. The probability of matching all drawn numbers equals one divided by the total number of possible combinations.
For a typical 6/49 lottery, you must match 6 numbers from a pool of 49. The number of ways to choose 6 from 49 is C(49,6) = 13,983,816, giving odds of approximately 1 in 14 million. Partial matches use the hypergeometric distribution.
Formula
Common Lotteries
| Lottery | Format | Jackpot Odds |
|---|---|---|
| Powerball | 5/69 + 1/26 | 1 in 292,201,338 |
| Mega Millions | 5/70 + 1/25 | 1 in 302,575,350 |
| EuroMillions | 5/50 + 2/12 | 1 in 139,838,160 |
| 6/49 Lotto | 6/49 | 1 in 13,983,816 |
Frequently Asked Questions
Does buying more tickets improve my odds?
Yes, linearly. If the jackpot odds are 1 in 14 million, buying 10 tickets gives you 10 in 14 million (1 in 1.4 million). However, the expected value is usually still negative since ticket costs exceed expected winnings.
Are some numbers luckier than others?
No. In a fair lottery, every combination has exactly the same probability. However, choosing less popular numbers means you would share the prize with fewer people if you win.
What is the expected value of a lottery ticket?
Expected value = (probability of winning x prize) - ticket cost. For most lotteries, the expected value is negative. A $2 ticket with 1 in 300 million odds at a $100 million jackpot has an expected value of about -$1.67.