6 from 45 lottery odds calculator
A 6 from 45 draw has 8,145,060 equally likely outcomes, so a single ticket wins the jackpot with probability one in that number. The combinatorics are computed as exact integers.
- Possible draws
- 8 145 060
- Chance of winning
- 0.000 012 277 4 %
- Expected value of the ticket
- -1.27
- Jackpot at which the bet breaks even
- 20 362 650.00
- Annual cost of playing every draw
- 260.89
- Chance of a jackpot in a year
- 0.000 012 812 2
- Years for an even chance
- 54 100
- Your share in a syndicate
- 1 000 000.00
- Syndicate odds: one in
- 814 506
Show the working
- Tickets bought = 1
- Ticket price = 2.5
- Jackpot = 10 000 000
- Draws per week = 2
- Syndicate members = 10
- Possible draws = comb(45, 6) = 8 145 060
- probability = 8 145 060 > 0 ? 1 / 8 145 060 : 0 = 0.000 000 122 774
- Odds: one in = 0.000 000 122 774 > 0 ? 1 / 0.000 000 122 774 : 0 = 8 145 060
- Chance of winning = 0.000 000 122 774 * 100 = 0.000 012 277 4
- Expected value of the ticket = 0.000 000 122 774 * 10 000 000 - 1 * 2.5 = -1.272 26
- Jackpot at which the bet breaks even = 0.000 000 122 774 > 0 ? 1 * 2.5 / 0.000 000 122 774 : 0 = 20 362 700
- Annual cost of playing every draw = 1 * 2.5 * 2 * 52.17857142857143 = 260.893
- Chance of a jackpot in a year = 1 - (1 - 0.000 000 122 774)^(2 * 52.17857142857143) = 0.000 012 812 2
- Years for an even chance = 0.000 000 122 774 > 0 ? ln(0.5) / ln(1 - 0.000 000 122 774) / (2 * 52.17857142857143) : 0 = 54 100
- Your share in a syndicate = 10 > 0 ? 10 000 000 / 10 : 0 = 1 000 000
- Syndicate odds: one in = 8 145 060 > 0 ? 8 145 060 / (1 * 10) : 0 = 814 506
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(45, 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.
6 from 45 odds at a glance
| Tickets | Odds of the jackpot |
|---|---|
| 1 | 1 in 8,145,060 |
| 10 | 1 in 814,506 |
| 100 | 1 in 81,451 |
| 1,000 | 1 in 8,145 |
| 10,000 | 1 in 815 |
Frequently asked
What are the odds of winning 6 from 45?
One in 8,145,060 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.