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# Lottery odds .Maths Boffs only!

Right

was having a discussion with a co-worker about winning the lottery(14,000,000 tickets)

If someone buys 2 tickets does this make the odds 7,000,000 to 1 ?.

Surely each ticket has an equal 14,000,000 to 1 chance of winning independantly?

was having a discussion with a co-worker about winning the lottery(14,000,000 tickets)

If someone buys 2 tickets does this make the odds 7,000,000 to 1 ?.

Surely each ticket has an equal 14,000,000 to 1 chance of winning independantly?

2 out of 14,000,000

Original Poster

what you said.

(it's late at night....)

Im sure camelot would like you to think that if 1 = 14,000,000 : 1

then,

2 = 7,000,000

3 = 3,500,000

4 = 1,750,000

all the way to appox 20 tickets giving you a 27 : 1 chance.

Remember all those permitations, 6 numbers plus 1 from 49 and all.

mind blowing convo material

With regards to that link, its half good. if 2 people share 12 million thats 6 each, but if you have 2 tickets to their 1, thats 8 million for you. same as 20 million with 10 people means 2 million each or 3.6 for you(if you bought 2).

Not exatley doubling as some people are claiming, and its certainly not doubling your chances, as they are the same numbers, lol. But worth a pound if 6 million is not enough, for e.g.

JACKPOT (matching all six numbers): 1 in 14 million

FIVE PLUS THE BONUS: 1 in 2.3 million

FIVE: 1 in 55,000

FOUR: 1 in 1,000

THREE: 1 in 57

And just for interest, here are some other chances:

The chance of winning ANY prize: 1 in 54 (about 2%)

The chance of only matching 2 numbers: 1 in 7.5 (about 13%)

The chance of only matching 1 number: 1 in 2.4 (about 41%)

The chance of not matching ANY numbers: 1 in 2.3 (about 44%)

If you're getting a ticket for the Saturday draw, be sure to buy it on the Friday or the Saturday. That's because if you buy it on Sunday, Monday, Tuesday, Wednesday or Thursday you are actually more likely to have died by Saturday evening than you are to win the jackpot!

buying 20 tickets gives you a 1 in 700000 chance, you always divide the number of possible outcomes by number of tickets.

6 numbers drawn from 1 - 49 meaning chance is (use nCr to work out probablitly) 49! / (6! * (43!) which equals 13,983,816. So you have a 1 in 14,000,000 chance of the numbers you have coming up.

So if you buy 2 tickets you have 2 different 1 in 14,000,000 chances of getting the right unique combination. AND SINCE its done on combinations (Not fractions or percent) You can't factor down (all the combinations are different and cannot be ignored) meaning you now have a 2/14,000,000 chance of winning NOT 1/7,000,000.

Hope that helps. Being doing this in stats recently.

I agree.

You have worded it wrong, because both of those fractions are exactly the same.

The way you have to look at it is that both tickets are independently exclusive and do not affect one another. Therefore your odds of winning are 1:14000000 & 1:14000000

Therefore

it cannot be simply divided as lottery does not work like that

If theres a 1 in14million chance then you should only play (statistically speaking) if the jackpot is this or above (which it never usually is).

And even then you should only play if you were the only one, as anyone else winning will effectively reduce the amount you win.

imho you prob get more money (less loss) by playing roulette or something.

But obv i see the appeal of possibility of winning loads from not much in a lottery

I think you are the one that needs to go back to school. ( That's assuming you have left already. )

The real odds of winning the lottery are 50:50.

You either win, or you don't.

Simples.

No, odds dont work like that.

1 ticket = 1 in 14mil

2 tickets = 1 in 7mil

3 tickets = 1 in 4.6mil

4 tickets = 1 in 3.5mil

5 tickets = 1 in 2.8mil

10 tickets = 1 in 1.4mil

20 tickets = 1 in 700k

40 tickets = 1 in 350k

100 tickets = 1 in 140k

1000 tickets = 1 in 14k

10000 tickets = 1 in 1.4k

100000 tickets = 1 in 140

1mil tickets = 1 in 14

14mil tickets = 1 in 1 chance (i.e. you have all the possible combitions now if it is indeed 1/14mil).

Bearing in mind half of your 14 million goes back into the prize fund.

Apart from the driving glove to remember which side of the road to drive on when abroad, yours is possibly the worst idea I've ever heard.

You would get:

about 250,000 lots of 3 balls (£10 each, so £2.5 million)

about 14,000 lots of 4 balls (typically £65, so ~£900,000)

about 250 lots of 5 balls (typically £1500, so ~£400,000)

6 lots of 5+bonus ball (typically £100k, so £600,000)

and the jackpot (typically £2 million).

So you would typically 'win' about £6.4 million as prizes (or in other words, you would typically lose just under £8 million!)

Please tell me you are joking with your calculations.

Your calculations mean that I can go and spend £24 on tickets and then I'm pretty much a certainty to win £14mil lol

Why has nobody clocked onto this sooner? oO

explain why mon brave

Would of thought it was pretty obvious but here you go;

Becaues its only worth while if there is a good chance if you win in the first place (which there isnt)

Much better off spending the £1 on different numbers to increase your chances of winning a lesser amount than putting all your faith in one set of numbers which are much less likely to come in.

Yes I know that, i was simply pointing that out.

Yes i was joking. I would have thought the line ''would like YOU to think that'' clarified that. Maybe its my extremely dry sense of humour :-)

Isn't that right for 1 and 2 but you should be going 4,8, 16 etc from then on. You are doubling/halving, not adding one/halving.

If you were asked in your stats class to put 2/14,000,000 in its lowest terms, what would your answer be??

2 tickets gives a 1 in 7m chance, double the chance of 1 ticket (14m to 1). And thats even if 5 of the numbers are the same and the last one is different.

Original Poster

any links to shut him up!

if you bought 2 tickets and the numbers were different you'd have a 2 in 14,000,000 or a 1 in 7,000,000 chance thats right."

That's not right, and to answer kempie.... Using that forumla i.e. 1 ticket 1 in 14 Million, 2 tickets 1 in 7 Million.... so if you keep goin on that assumption it works out in the following way

1 Ticket = 1 in 14 Million

2 Tickets = 1 in 7 Million

3 Tickets = 1 in 3,500,000

4 Tickets = 1 in 1,750,000

5 Tickets = 1 in 875,000

6 Tickets = 1 in 437,500

..

..

17 Tickets = 1 in 106

18 Tickets = 1 in 53

19 Tickets = 1 in 26

20 Tickets = 1 in 13

21 Tickets = 1 in 6

22 Tickets = 1 in 3

23 Tickets = 1 in 1 (1.6689 to be exact)

So using that logical all you need are 23 tickets to win the lottery.

2 Tickets is a 2 in 14000000 chance this is not the same as 1 in 7000000 because there are 14000000 combinations. You can't factor down the number of combinations in this way.

Your applying fraction logic which doesn't apply in this case.

-Take too long

-Cost too much

-Not be able to be done from 1 shop - 1 shop has 1 terminal (or 2) and a set of 7 lines takes 5 seconds to do, that would be

2 million sets of 7 lines

2 million times 5 seconds = 10,000,000 seconds

10,000,000 seconds / 60 = 166,666 minutes

166,666 minutes / 60 = 2,777 hours

2,777 hours / 24 = 115 days to make 14 million tickets.

.

.

.

-You would be an idiot to buy 14 million tickets.

Everyone who plays the lottery is hoping to win th jackpot not 2 x £5.90 prizes....therefore adding £1 to double your possible jackpot winnings really isn't that bad an idea.....just clearly not something you would be interested in doing.

I posted it before, If you buy 2 tickets.. you've doubled your chances, if you buy 3, you triple your chances (than if you had just bought one).. people are going wrong as they're doubling there chances for buying 2 then doubling it again for buying 3.

1 ticket = 1 in 14mil

2 tickets = 1 in 7mil

3 tickets = 1 in 4.6mil

4 tickets = 1 in 3.5mil

5 tickets = 1 in 2.8mil

10 tickets = 1 in 1.4mil

20 tickets = 1 in 700k

40 tickets = 1 in 350k

100 tickets = 1 in 140k

1000 tickets = 1 in 14k

10000 tickets = 1 in 1.4k

100000 tickets = 1 in 140

1mil tickets = 1 in 14

14mil tickets = 1 in 1 chance (i.e. you have all the possible combitions now if it is indeed 1/14mil).

Is the exact odds if it is 1 in 14million chance per ticket.

For example, if you buy 3 tickets, you have a 3/14mil chance of winning as you have 3 different combinations out of 14million combinations. which is 1/4.6mil chance of winning.

You can factor down combinations and use fractions, this is exactly what fractions were designed for. Its astonishing how people are taught to the test in schools now instead of taught how to actually work the stuff out and how to apply it.

If i bought 14million tickets, each with a different combination.. i would have a 1:1 in chance of winning, as ive got every combination. If i bought 7million tickets, i would have a 2/1 chance of winning as ive got half the combinations.. theres a 50% chance that the winning combination will be in my 7million half and a 50% chance that the winning combination will be in the 7million i didnt buy.

People seem to be getting confused as its a high number, so lets say.. theres only one number and its 1-6.

I buy 1 ticket, with the number 1 on it. I have a 1/6 chance of winning that lottery, as ive got 1 combination out of the possible 6.

I buy 2 tickets with the numbers 1 and 2 on it. I now have a 2/6 chance which is 1/3 chance of winning that lottery, as ive got 2 combinations out of the possible 6 (I have 1/3'd of the possible combinations).

I buy 3 tickets with the numbers 1, 2 and 3 on it. I now have 3/6 chance which is 1/2 chance of winning that lottery, as ive got half the possible outcomes. I dont have 3x 1/6 chance, i have 1/2 chance.