6 from 42 lottery odds calculator
A 6 from 42 draw has 5,245,786 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
- 5 245 786
- Chance of winning
- 0.000 019 062 9 %
- Expected value of the ticket
- -0.59
- Jackpot at which the bet breaks even
- 13 114 465.00
- Annual cost of playing every draw
- 260.89
- Chance of a jackpot in a year
- 0.000 019 893 3
- Years for an even chance
- 34 842.9
- Your share in a syndicate
- 1 000 000.00
- Syndicate odds: one in
- 524 579
Show the working
- Tickets bought = 1
- Ticket price = 2.5
- Jackpot = 10 000 000
- Draws per week = 2
- Syndicate members = 10
- Possible draws = comb(42, 6) = 5 245 790
- probability = 5 245 790 > 0 ? 1 / 5 245 790 : 0 = 0.000 000 190 629
- Odds: one in = 0.000 000 190 629 > 0 ? 1 / 0.000 000 190 629 : 0 = 5 245 790
- Chance of winning = 0.000 000 190 629 * 100 = 0.000 019 062 9
- Expected value of the ticket = 0.000 000 190 629 * 10 000 000 - 1 * 2.5 = -0.593 708
- Jackpot at which the bet breaks even = 0.000 000 190 629 > 0 ? 1 * 2.5 / 0.000 000 190 629 : 0 = 13 114 500
- Annual cost of playing every draw = 1 * 2.5 * 2 * 52.17857142857143 = 260.893
- Chance of a jackpot in a year = 1 - (1 - 0.000 000 190 629)^(2 * 52.17857142857143) = 0.000 019 893 3
- Years for an even chance = 0.000 000 190 629 > 0 ? ln(0.5) / ln(1 - 0.000 000 190 629) / (2 * 52.17857142857143) : 0 = 34 842.9
- Your share in a syndicate = 10 > 0 ? 10 000 000 / 10 : 0 = 1 000 000
- Syndicate odds: one in = 5 245 790 > 0 ? 5 245 790 / (1 * 10) : 0 = 524 579
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(42, 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 42 odds at a glance
| Tickets | Odds of the jackpot |
|---|---|
| 1 | 1 in 5,245,786 |
| 10 | 1 in 524,579 |
| 100 | 1 in 52,458 |
| 1,000 | 1 in 5,246 |
| 10,000 | 1 in 525 |
Frequently asked
What are the odds of winning 6 from 42?
One in 5,245,786 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.