5 from 50 plus 2 from 12 lottery odds calculator
A 5 from 50 plus 2 from 12 draw has 139,838,160 equally likely outcomes, so a single ticket wins the jackpot with probability one in that number. The combinatorics are computed as exact integers. The EuroMillions format.
- Possible draws
- 139 838 160
- Chance of winning
- 0.000 000 715 112 %
- Expected value of the ticket
- -2.43
- Jackpot at which the bet breaks even
- 349 595 400.00
- Annual cost of playing every draw
- 260.89
- Chance of a jackpot in a year
- 0.000 000 746 271
- Years for an even chance
- 928 814
- Your share in a syndicate
- 1 000 000.00
- Syndicate odds: one in
- 13 983 816
Show the working
- Tickets bought = 1
- Ticket price = 2.5
- Jackpot = 10 000 000
- Draws per week = 2
- Syndicate members = 10
- Possible draws = comb(50, 5) * comb(12, 2) = 139 838 000
- probability = 139 838 000 > 0 ? 1 / 139 838 000 : 0 = 7.15112e-9
- Odds: one in = 7.15112e-9 > 0 ? 1 / 7.15112e-9 : 0 = 139 838 000
- Chance of winning = 7.15112e-9 * 100 = 0.000 000 715 112
- Expected value of the ticket = 7.15112e-9 * 10 000 000 - 1 * 2.5 = -2.428 49
- Jackpot at which the bet breaks even = 7.15112e-9 > 0 ? 1 * 2.5 / 7.15112e-9 : 0 = 349 595 000
- Annual cost of playing every draw = 1 * 2.5 * 2 * 52.17857142857143 = 260.893
- Chance of a jackpot in a year = 1 - (1 - 7.15112e-9)^(2 * 52.17857142857143) = 0.000 000 746 271
- Years for an even chance = 7.15112e-9 > 0 ? ln(0.5) / ln(1 - 7.15112e-9) / (2 * 52.17857142857143) : 0 = 928 814
- Your share in a syndicate = 10 > 0 ? 10 000 000 / 10 : 0 = 1 000 000
- Syndicate odds: one in = 139 838 000 > 0 ? 139 838 000 / (1 * 10) : 0 = 13 983 800
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(50, 5) x C(12, 2)
- 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 EuroMillions format.
5 from 50 plus 2 from 12 odds at a glance
| Tickets | Odds of the jackpot |
|---|---|
| 1 | 1 in 139,838,160 |
| 10 | 1 in 13,983,816 |
| 100 | 1 in 1,398,382 |
| 1,000 | 1 in 139,838 |
| 10,000 | 1 in 13,984 |
Frequently asked
What are the odds of winning 5 from 50 plus 2 from 12?
One in 139,838,160 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.