5 from 50 plus 2 from 10 lottery odds calculator
A 5 from 50 plus 2 from 10 draw has 95,344,200 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
- 95 344 200
- Chance of winning
- 0.000 001 048 83 %
- Expected value of the ticket
- -2.40
- Jackpot at which the bet breaks even
- 238 360 500.00
- Annual cost of playing every draw
- 260.89
- Chance of a jackpot in a year
- 0.000 001 094 53
- Years for an even chance
- 633 283
- Your share in a syndicate
- 1 000 000.00
- Syndicate odds: one in
- 9 534 420
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(10, 2) = 95 344 200
- probability = 95 344 200 > 0 ? 1 / 95 344 200 : 0 = 1.04883e-8
- Odds: one in = 1.04883e-8 > 0 ? 1 / 1.04883e-8 : 0 = 95 344 200
- Chance of winning = 1.04883e-8 * 100 = 0.000 001 048 83
- Expected value of the ticket = 1.04883e-8 * 10 000 000 - 1 * 2.5 = -2.395 12
- Jackpot at which the bet breaks even = 1.04883e-8 > 0 ? 1 * 2.5 / 1.04883e-8 : 0 = 238 361 000
- Annual cost of playing every draw = 1 * 2.5 * 2 * 52.17857142857143 = 260.893
- Chance of a jackpot in a year = 1 - (1 - 1.04883e-8)^(2 * 52.17857142857143) = 0.000 001 094 53
- Years for an even chance = 1.04883e-8 > 0 ? ln(0.5) / ln(1 - 1.04883e-8) / (2 * 52.17857142857143) : 0 = 633 283
- Your share in a syndicate = 10 > 0 ? 10 000 000 / 10 : 0 = 1 000 000
- Syndicate odds: one in = 95 344 200 > 0 ? 95 344 200 / (1 * 10) : 0 = 9 534 420
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(10, 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.
5 from 50 plus 2 from 10 odds at a glance
| Tickets | Odds of the jackpot |
|---|---|
| 1 | 1 in 95,344,200 |
| 10 | 1 in 9,534,420 |
| 100 | 1 in 953,442 |
| 1,000 | 1 in 95,344 |
| 10,000 | 1 in 9,534 |
Frequently asked
What are the odds of winning 5 from 50 plus 2 from 10?
One in 95,344,200 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.