5 from 69 plus 1 from 26 lottery odds calculator
A 5 from 69 plus 1 from 26 draw has 292,201,338 equally likely outcomes, so a single ticket wins the jackpot with probability one in that number. The combinatorics are computed as exact integers. The US Powerball format.
- Possible draws
- 292 201 338
- Chance of winning
- 0.000 000 342 23 %
- Expected value of the ticket
- -2.47
- Jackpot at which the bet breaks even
- 730 503 345.00
- Annual cost of playing every draw
- 260.89
- Chance of a jackpot in a year
- 0.000 000 357 141
- Years for an even chance
- 1 940 820
- Your share in a syndicate
- 1 000 000.00
- Syndicate odds: one in
- 29 220 134
Show the working
- Tickets bought = 1
- Ticket price = 2.5
- Jackpot = 10 000 000
- Draws per week = 2
- Syndicate members = 10
- Possible draws = comb(69, 5) * comb(26, 1) = 292 201 000
- probability = 292 201 000 > 0 ? 1 / 292 201 000 : 0 = 3.4223e-9
- Odds: one in = 3.4223e-9 > 0 ? 1 / 3.4223e-9 : 0 = 292 201 000
- Chance of winning = 3.4223e-9 * 100 = 0.000 000 342 23
- Expected value of the ticket = 3.4223e-9 * 10 000 000 - 1 * 2.5 = -2.465 78
- Jackpot at which the bet breaks even = 3.4223e-9 > 0 ? 1 * 2.5 / 3.4223e-9 : 0 = 730 503 000
- Annual cost of playing every draw = 1 * 2.5 * 2 * 52.17857142857143 = 260.893
- Chance of a jackpot in a year = 1 - (1 - 3.4223e-9)^(2 * 52.17857142857143) = 0.000 000 357 141
- Years for an even chance = 3.4223e-9 > 0 ? ln(0.5) / ln(1 - 3.4223e-9) / (2 * 52.17857142857143) : 0 = 1 940 820
- Your share in a syndicate = 10 > 0 ? 10 000 000 / 10 : 0 = 1 000 000
- Syndicate odds: one in = 292 201 000 > 0 ? 292 201 000 / (1 * 10) : 0 = 29 220 100
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- combinations = C(69, 5) x C(26, 1)
- probability with n tickets = n / combinations
- expected value = probability x prize - cost
Expected value ignores the smaller prize tiers and any rollover sharing. A positive expected value does not make a lottery a good investment, because the variance is enormous.
Buying more tickets multiplies your chance linearly, but so does the cost. Nothing about the odds improves per pound spent.
These are exact integer combinations, not rounded figures.
The US Powerball format.
5 from 69 plus 1 from 26 odds at a glance
| Tickets | Odds of the jackpot |
|---|---|
| 1 | 1 in 292,201,338 |
| 10 | 1 in 29,220,134 |
| 100 | 1 in 2,922,013 |
| 1,000 | 1 in 292,201 |
| 10,000 | 1 in 29,220 |
Frequently asked
What are the odds of winning 5 from 69 plus 1 from 26?
One in 292,201,338 per ticket.
Do quick picks have better odds?
No. Every combination is equally likely. Choosing unusual numbers only changes how many people you would share a jackpot with.