5 from 56 plus 1 from 46 lottery odds calculator
A 5 from 56 plus 1 from 46 draw has 175,711,536 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
- 175 711 536
- Chance of winning
- 0.000 000 569 115 %
- Expected value of the ticket
- -2.44
- Jackpot at which the bet breaks even
- 439 278 840.00
- Annual cost of playing every draw
- 260.89
- Chance of a jackpot in a year
- 0.000 000 593 912
- Years for an even chance
- 1 167 090
- Your share in a syndicate
- 1 000 000.00
- Syndicate odds: one in
- 17 571 154
Show the working
- Tickets bought = 1
- Ticket price = 2.5
- Jackpot = 10 000 000
- Draws per week = 2
- Syndicate members = 10
- Possible draws = comb(56, 5) * comb(46, 1) = 175 712 000
- probability = 175 712 000 > 0 ? 1 / 175 712 000 : 0 = 5.69115e-9
- Odds: one in = 5.69115e-9 > 0 ? 1 / 5.69115e-9 : 0 = 175 712 000
- Chance of winning = 5.69115e-9 * 100 = 0.000 000 569 115
- Expected value of the ticket = 5.69115e-9 * 10 000 000 - 1 * 2.5 = -2.443 09
- Jackpot at which the bet breaks even = 5.69115e-9 > 0 ? 1 * 2.5 / 5.69115e-9 : 0 = 439 279 000
- Annual cost of playing every draw = 1 * 2.5 * 2 * 52.17857142857143 = 260.893
- Chance of a jackpot in a year = 1 - (1 - 5.69115e-9)^(2 * 52.17857142857143) = 0.000 000 593 912
- Years for an even chance = 5.69115e-9 > 0 ? ln(0.5) / ln(1 - 5.69115e-9) / (2 * 52.17857142857143) : 0 = 1 167 090
- Your share in a syndicate = 10 > 0 ? 10 000 000 / 10 : 0 = 1 000 000
- Syndicate odds: one in = 175 712 000 > 0 ? 175 712 000 / (1 * 10) : 0 = 17 571 200
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(56, 5) x C(46, 1)
- 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 56 plus 1 from 46 odds at a glance
| Tickets | Odds of the jackpot |
|---|---|
| 1 | 1 in 175,711,536 |
| 10 | 1 in 17,571,154 |
| 100 | 1 in 1,757,115 |
| 1,000 | 1 in 175,712 |
| 10,000 | 1 in 17,571 |
Frequently asked
What are the odds of winning 5 from 56 plus 1 from 46?
One in 175,711,536 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.