5 from 35 plus 1 from 15 lottery odds calculator

A 5 from 35 plus 1 from 15 draw has 4,869,480 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

4 869 480

≈ Rounded 5 from 35 plus 1 from 15 odds

Possible draws: 4 869 480
Chance of winning: 0.000 020 536 1 %
Expected value of the ticket: -0.45
Jackpot at which the bet breaks even: 12 173 700.00
Annual cost of playing every draw: 260.89
Chance of a jackpot in a year: 0.000 021 430 6
Years for an even chance: 32 343.4
Your share in a syndicate: 1 000 000.00
Syndicate odds: one in: 486 948

Show the working

Tickets bought = 1
Ticket price = 2.5
Jackpot = 10 000 000
Draws per week = 2
Syndicate members = 10
Possible draws = comb(35, 5) * comb(15, 1) = 4 869 480
probability = 4 869 480 > 0 ? 1 / 4 869 480 : 0 = 0.000 000 205 361
Odds: one in = 0.000 000 205 361 > 0 ? 1 / 0.000 000 205 361 : 0 = 4 869 480
Chance of winning = 0.000 000 205 361 * 100 = 0.000 020 536 1
Expected value of the ticket = 0.000 000 205 361 * 10 000 000 - 1 * 2.5 = -0.446 393
Jackpot at which the bet breaks even = 0.000 000 205 361 > 0 ? 1 * 2.5 / 0.000 000 205 361 : 0 = 12 173 700
Annual cost of playing every draw = 1 * 2.5 * 2 * 52.17857142857143 = 260.893
Chance of a jackpot in a year = 1 - (1 - 0.000 000 205 361)^(2 * 52.17857142857143) = 0.000 021 430 6
Years for an even chance = 0.000 000 205 361 > 0 ? ln(0.5) / ln(1 - 0.000 000 205 361) / (2 * 52.17857142857143) : 0 = 32 343.4
Your share in a syndicate = 10 > 0 ? 10 000 000 / 10 : 0 = 1 000 000
Syndicate odds: one in = 4 869 480 > 0 ? 4 869 480 / (1 * 10) : 0 = 486 948

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(35, 5) x C(15, 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 35 plus 1 from 15 odds at a glance

Tickets	Odds of the jackpot
1	1 in 4,869,480
10	1 in 486,948
100	1 in 48,695
1,000	1 in 4,869
10,000	1 in 487

Frequently asked

What are the odds of winning 5 from 35 plus 1 from 15?

One in 4,869,480 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.