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# Lottery odds .Maths Boffs only!

6y, 5m agoPosted 6 years, 5 months ago
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?
6y, 5m agoPosted 6 years, 5 months ago
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(41)
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#1
Yeah, odds will still be the same, but you will be 2 of 14 million, each ticket has the same amount of chance
#2
Wouldnt it be 14,000,000/2 then if they bought 2 tickets
#3
Two tickets = twice the chance of winning

2 out of 14,000,000
#4
so is that the same as 1/7,000,000?
#5
i.e. 1 in 7,000,000

what you said.

(it's late at night....)
#6
i say 2 tickets gaves you the odds of 13,999,999 to 1.

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.
#7
careful, he's busy being a badass again.
#8
if you really want a mind blowing conversation at work, check out this thread i made a year and a half ago about a national lottery idea...

mind blowing convo material
#9
acecatcher3
if you really want a mind blowing conversation at work, check out this thread i made a year and a half ago about a national lottery idea...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.
#10
Here are the approximate chances of all the different prizes:

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%)
#11
Also

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!
#12
Geezso

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.

buying 20 tickets gives you a 1 in 700000 chance, you always divide the number of possible outcomes by number of tickets.
#13
You don't have a 1 in 14,000,000 chance of winning from buying a ticket cause thats how many tickets are sold. That number has been calculated from the chances of you having the right numbers

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.
#14
ErrorOperator
You don't have a 1 in 14,000,000 chance of winning from buying a ticket cause thats how many tickets are sold. That number has been calculated from the chances of you having the right numbers

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.
#15
ErrorOperator
You don't have a 1 in 14,000,000 chance of winning from buying a ticket cause thats how many tickets are sold. That number has been calculated from the chances of you having the right numbers

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.

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
#16
^^ agreed

it cannot be simply divided as lottery does not work like that
#17
Lottery is always going to cause people to lose money. (in general)
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
1 Like #18
DarrylJohn
Yeah, odds will still be the same, but you will be 2 of 14 million, each ticket has the same amount of chance
krazykel
Wouldnt it be 14,000,000/2 then if they bought 2 tickets
14,000,000:2is 7,000,000:1 you muppets, go back to school.

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.
#19
Geezso

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.

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).
#20
#21
If you did buy 14 million tickets how much would you win by covering all of the combinations?

Bearing in mind half of your 14 million goes back into the prize fund.
#22
#23
sorry, sold out
#24
acecatcher3
if you really want a mind blowing conversation at work, check out this thread i made a year and a half ago about a national lottery idea...

mind blowing convo material

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.
#25
ok! have you got any nails?
#26
Bobbajob
If you did buy 14 million tickets how much would you win by covering all of the combinations?

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

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!)
#27
Geezso
i say 2 tickets gaves you the odds of 13,999,999 to 1.

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.

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
#28
acecatcher3
if you really want a mind blowing conversation at work, check out this thread i made a year and a half ago about a national lottery idea...mind blowing convo material
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.

explain why mon brave
#29
acecatcher3
acecatcher3
if you really want a mind blowing conversation at work, check out this thread i made a year and a half ago about a national lottery idea...mind blowing convo material
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.

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.
#30
Crompee
Geezso
Im sure camelot would like you to think that if 1 = 14,000,000 : 1then,2 = 7,000,0003 = 3,500,0004 = 1,750,000all the way to appox 20 tickets giving you a 27 : 1 chance.
No, odds dont work like that.1 ticket = 1 in 14mil2 tickets = 1 in 7mil3 tickets = 1 in 4.6mil4 tickets = 1 in 3.5mil5 tickets = 1 in 2.8mil10 tickets = 1 in 1.4mil20 tickets = 1 in 700k40 tickets = 1 in 350k 100 tickets = 1 in 140k1000 tickets = 1 in 14k10000 tickets = 1 in 1.4k100000 tickets = 1 in 1401mil tickets = 1 in 1414mil tickets = 1 in 1 chance (i.e. you have all the possible combitions now if it is indeed 1/14mil).

Yes I know that, i was simply pointing that out.
#31
Geezso
i say 2 tickets gaves you the odds of 13,999,999 to 1.Im sure camelot would like you to think that if 1 = 14,000,000 : 1then,2 = 7,000,0003 = 3,500,0004 = 1,750,000all the way to appox 20 tickets giving you a 27 : 1 chance.Remember all those permitations, 6 numbers plus 1 from 49 and all.
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 lolWhy has nobody clocked onto this sooner? oO

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 :-)
#32
Geezso
i say 2 tickets gaves you the odds of 13,999,999 to 1.

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.

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.
#33
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.

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.
#34
I think the problem is people are getting it wrong and thinking 2 tickets will drop the odds to 1 in 7m chance is because they haven't factored in that you have to get SIX numbers to win the jackpot. So if you have TWO different sets of SIX numbers you will get 2 x 1 in 14m chances and not halve your chances. So if you bought a MILLION tickets you'd reduce the odds to roughly 7 chances in a 100 to win. (i.e. 1,000,000/14,000,000= 0.0714285 out of 100).
#35
so the odds do not drop to 1/7,000,000 for 2 tickets ?

any links to shut him up!
#36
Found this, explains exactly how it cannot be 1 in 7 million for 2 tickets, just 2 in 14 million.

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.
#37

-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.
#38
greg_68
Found this, explains exactly how it cannot be 1 in 7 million for 2 tickets, just 2 in 14 million.

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."

No, for every ticket you buy you don't double your chances of inning, just the 1st 2 tickets:

1 = 1:14 Million
2 = 1:7 Million
3 = 1:4.6 (recurring) Million
4 = 1:3.5 Million

Anyway that is not possible for this application anyway, because the 2 you buy could end up bein exactly the same numbers anyway, so ur screwed
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.
#39
Well your explanation only reflects the fact that you would prefer to spend £1 on a seperate set of numbers, not how spending an extra £1 on the same numbers is the worst idea you've ever heard.

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.
#40
greg_68
Found this, explains exactly how it cannot be 1 in 7 million for 2 tickets, just 2 in 14 million.

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.

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.