How jackpot probability is calculated
For a single-pool game (e.g., UK Lotto: pick 6 from 59), the total number of legal tickets is the binomial coefficient C(N, M). The jackpot probability is 1 divided by that.
For a two-pool game (e.g., Powerball: 5 from 69 main + 1 from 26 Powerball), the two pools are independent, so combinations multiply:
The "any prize" odds shown here are the probability of winning any tier (lowest tier and above) — typically 1 in 25 for Powerball, 1 in 24 for Mega Millions. Prize-tier odds in the table are computed from the joint hypergeometric distribution across both pools.
Compared across major lotteries
| Game | Format | Jackpot odds | Any-prize odds |
|---|---|---|---|
| Powerball (US) | 5/69 + 1/26 | 1 in 292,201,338 | 1 in 24.87 |
| Mega Millions (US) | 5/70 + 1/24 | 1 in 302,575,350 | 1 in 24.00 |
| EuroMillions | 5/50 + 2/12 | 1 in 139,838,160 | 1 in 13.00 |
| UK Lotto | 6/59 | 1 in 45,057,474 | 1 in 9.32 |
| Lotto Max (Canada) | 7/50 | 1 in 33,294,800 | 1 in 6.60 |
| 6/49 (India / Canada classic) | 6/49 | 1 in 13,983,816 | 1 in 54 |
| Oz Lotto | 7/47 + 3/47 | 1 in 62,891,499 | 1 in 44 |
FAQ
Are these odds before or after annuity / lump-sum?
The probabilities are the odds of winning, period. The amount you actually receive depends on annuity-vs-lump-sum choice, taxes, and other winners (jackpot is shared). For pure expected-value analysis, multiply jackpot by probability and subtract the ticket price + average tax burden — almost always negative.
Why are Powerball odds so much worse than older lotteries?
Lottery operators have steadily increased pool sizes since the 1990s to grow the headline jackpot — bigger jackpots drive ticket sales, more than offsetting the longer odds. Powerball in 2015 expanded the main pool from 59 to 69 numbers; jackpot odds went from 1 in 175M to 1 in 292M.
Is buying multiple tickets a good strategy?
It linearly improves your odds — 100 tickets = 100× the chance of winning. But it also linearly increases your cost. Expected value stays the same (and stays negative). The only reason to buy multiple tickets is enjoyment.