5 from 45 lottery odds calculator

A 5 from 45 draw has 1,221,759 equally likely outcomes, so a single ticket wins the jackpot with probability one in that number. The combinatorics are computed as exact integers.

Tickets bought

Ticket price

Jackpot

Draws per week

Syndicate members

Odds: one in

1 221 759

≈ Rounded 5 from 45 odds

Possible draws: 1 221 759
Chance of winning: 0.000 081 849 2 %
Expected value of the ticket: 5.68
Jackpot at which the bet breaks even: 3 054 397.50
Annual cost of playing every draw: 260.89
Chance of a jackpot in a year: 0.000 085 411 9
Years for an even chance: 8115
Your share in a syndicate: 1 000 000.00
Syndicate odds: one in: 122 176

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, 5) = 1 221 760
probability = 1 221 760 > 0 ? 1 / 1 221 760 : 0 = 0.000 000 818 492
Odds: one in = 0.000 000 818 492 > 0 ? 1 / 0.000 000 818 492 : 0 = 1 221 760
Chance of winning = 0.000 000 818 492 * 100 = 0.000 081 849 2
Expected value of the ticket = 0.000 000 818 492 * 10 000 000 - 1 * 2.5 = 5.684 92
Jackpot at which the bet breaks even = 0.000 000 818 492 > 0 ? 1 * 2.5 / 0.000 000 818 492 : 0 = 3 054 400
Annual cost of playing every draw = 1 * 2.5 * 2 * 52.17857142857143 = 260.893
Chance of a jackpot in a year = 1 - (1 - 0.000 000 818 492)^(2 * 52.17857142857143) = 0.000 085 411 9
Years for an even chance = 0.000 000 818 492 > 0 ? ln(0.5) / ln(1 - 0.000 000 818 492) / (2 * 52.17857142857143) : 0 = 8115
Your share in a syndicate = 10 > 0 ? 10 000 000 / 10 : 0 = 1 000 000
Syndicate odds: one in = 1 221 760 > 0 ? 1 221 760 / (1 * 10) : 0 = 122 176

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, 5)
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 45 odds at a glance

Tickets	Odds of the jackpot
1	1 in 1,221,759
10	1 in 122,176
100	1 in 12,218
1,000	1 in 1,222
10,000	1 in 122

Frequently asked

What are the odds of winning 5 from 45?

One in 1,221,759 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.