6 from 59 lottery odds calculator
A 6 from 59 draw has 45,057,474 equally likely outcomes, so a single ticket wins the jackpot with probability one in that number. The combinatorics are computed as exact integers. The UK National Lottery main draw.
- Possible draws
- 45 057 474
- Chance of winning
- 0.000 002 219 39 %
- Expected value of the ticket
- -2.28
- Jackpot at which the bet breaks even
- 112 643 685.00
- Annual cost of playing every draw
- 260.89
- Chance of a jackpot in a year
- 0.000 002 316 09
- Years for an even chance
- 299 275
- Your share in a syndicate
- 1 000 000.00
- Syndicate odds: one in
- 4 505 747
Show the working
- Tickets bought = 1
- Ticket price = 2.5
- Jackpot = 10 000 000
- Draws per week = 2
- Syndicate members = 10
- Possible draws = comb(59, 6) = 45 057 500
- probability = 45 057 500 > 0 ? 1 / 45 057 500 : 0 = 2.21939e-8
- Odds: one in = 2.21939e-8 > 0 ? 1 / 2.21939e-8 : 0 = 45 057 500
- Chance of winning = 2.21939e-8 * 100 = 0.000 002 219 39
- Expected value of the ticket = 2.21939e-8 * 10 000 000 - 1 * 2.5 = -2.278 06
- Jackpot at which the bet breaks even = 2.21939e-8 > 0 ? 1 * 2.5 / 2.21939e-8 : 0 = 112 644 000
- Annual cost of playing every draw = 1 * 2.5 * 2 * 52.17857142857143 = 260.893
- Chance of a jackpot in a year = 1 - (1 - 2.21939e-8)^(2 * 52.17857142857143) = 0.000 002 316 09
- Years for an even chance = 2.21939e-8 > 0 ? ln(0.5) / ln(1 - 2.21939e-8) / (2 * 52.17857142857143) : 0 = 299 275
- Your share in a syndicate = 10 > 0 ? 10 000 000 / 10 : 0 = 1 000 000
- Syndicate odds: one in = 45 057 500 > 0 ? 45 057 500 / (1 * 10) : 0 = 4 505 750
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(59, 6)
- 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 UK National Lottery main draw.
6 from 59 odds at a glance
| Tickets | Odds of the jackpot |
|---|---|
| 1 | 1 in 45,057,474 |
| 10 | 1 in 4,505,747 |
| 100 | 1 in 450,575 |
| 1,000 | 1 in 45,057 |
| 10,000 | 1 in 4,506 |
Frequently asked
What are the odds of winning 6 from 59?
One in 45,057,474 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.