Lottery odds

[Sparx]

Thats a bit much dontchathink

 

[old.Tohtori]

Yeah, it' as easy to say no to the wrong question, as it is to say yes and be wrong to another.

Some people just act faster, with initial response, or by thinking that logical answer must be wrong and they're being fooled.

 

[Lamp]

What makes me laugh are the people who actually pay money to those "We'll Tell You How to Win the Lottery - Guaranteed" websites

There's only one way of guaranteeing a win. Buy every ticket combination. And even then you're not guaranteed a single payout of the jackpot. Any number of people could have picked the winning combo which means only a share in the jackpot

 

[Killswitch]

One of my favourite pub subjects for a while was trying to maximise how much you would win, were your numbers to come up. It's pretty simple to prove that, if you're buying one ticket, any analysis of previous draws, ball frequency or anything else will be of no use, right?

So...my strategy is (whenever I buy a ticket) this;

"2 sets of three sequential numbers, all above 31".

An example would be "33,34,35,38,39,40". The thinking is that any single combination of numbers is as likely as any other. Obviously 6 sequential numbers are far less likely than 6 non-sequential numbers, but a *specific* sequential set (say 7,8,9,10,11,12) has the same exact probability as any other draw.

BUT people are idiots...so they wouldn't pick 6 sequential numbers as they are "less likely". Also, many people use birthdays or other dates, so stay above 31 for that. Then, because other people in the UK are smartarses like me, use 2 sets of three sequentials instead of 1 set of six!

It doesn't help my chance to win, but if I DO win, it reduces the odds I'll have to share!

And in answer to the poll, the answer is "yes". In general, doubling the number of tickets you purchase also doubles the probability of a win. This is just simple maths;

1 in 14,000,000
2 in 14,000,000 = 1 in 7,000,000
4 in 14,000,000 = 2 in 7,000,000 = 1 in 3,500,000
...
PROFIT!

 

[Thorwyn]

The birthday part is true. Statistically, a lot more people are betting on numbers < 31 because they want to reflect their "lucky" days.

The sequential number thing is plain wrong however. I read a book on statistics a while ago and one chapter was about the lottery and the odds etc. and they came up with exactly that idea. The highest score of sequential numbers were 5 in a row, scored by the austrian lottery (iirc). And more than 100 people had that sequence right. Even if just a tiny fraction of people is thinking like you, it´s still a pretty large ammount in the end. Any kind of system, shape, sequence other than plain random WILL get you to shared wins.

 

[old.Tohtori]

Not to mention, it would be one of the least things on your mind if you won a 2 share 3 million pot

Yeah, boohoo, feel your pain about a shared win when you win 500k

 

[JingleBells]

If the numbers 1-7 (or is it 1-6, not sure on number of balls in our lottery) came up then the jackpot would be shared with hundreds (if not thousands) of statisticians and professors eager to prove that it has every chance as every other set of numbers

 

[old.Tohtori]

That's true, it almsot makes putting those numbers in ridicilously useless, but it also makes thousands and thousands to the lottery

I personally have a system too, but it's just a "i'll be damned if i stop putting these numbers now" system.

It's an 8 number thing, with 7 lottery balls(3 extra), which basically makes all the possible 7 number lines from 8 numbers. It doesn't cost too much, below 7 euro, and even with 4 correct you get well over 50e usually since you win the 4 correct 4-5 times

With 7 correct, you'd get 7, 6(2 times even), 5(couple of those), 4(a few) etc.

Ofcourse one added number isn't gonna do much for the odds, but hey, it's more fun.

 

[ST^]

Not to mention, it would be one of the least things on your mind if you won a 2 share 3 million pot

Yeah, boohoo, feel your pain about a shared win when you win 500k

I could retire on a million, probably not 500k. Massive difference.

 

[old.Tohtori]

I could retire on a million, probably not 500k. Massive difference.

Sure, there's a difference, but still, come on, you can't deny that it's still nothing worth complaining about when you get, basically, 10 years of very nicely paid job for free

 

[ST^]

If you just went from 0 to 500k, that's great. But when you win and you know the jackpot is £6m, you're going from 0 to expecting £6m to getting 500k. I would be disappointed and happy at the same time

 

[old.Tohtori]

True, from 6mil to 500k would be a bit of a wtf moment, i was more thinking of a 2 split pot of 1mil.

I guess it depends, winning a pot of 1mil with 5 people would be bit of meh, even if it's still free 200k.

 

[Bugz]

Yes is the short hand answer.

The long hand answer seems to shout no to me. More specifically the instances where you have x of the same numbers on each ticket. Of course, this probability won't be realised until the balls are drawn so it's not really a solid argument.

 

[georgie]

I suppose the best way to think about it is not to think about a ticket with 6 different numbers on it but to think of each different permutation as a single ticket. So if you have one number from the range 1-14 million what's the likelihood that your number will be drawn (1 in 14 mill, I think most people would agree). If you are allowed to pick two numbers instead, it becomes 2 in 14 mill (or 1 in 7 mill).

I think the confusion comes when people start thinking in terms of conditional probability which are contingent on a previous result i.e. once you've checked your ticket and seen that it's not a winning one it is discarded and the probability becomes 1 in 13999999 for the second ticket instead. Pre-draw I would assume there is no conditional probability and every ticket has an equal chance to win. You double your tickets and you double your chance of winning.

Anywho... On to the official answer from Camelot:

The probability of having 1 ticket to win the jackpot in the Lotto game is approx 1: 13,983,816

The chance of having 2 tickets is 2: 13,983,815 (which is not 1:6,991,908)

The chance of having 13,983,816 tickets is 1:1 obviously.

The chance of having 6,991,908 tickets is 1:2

I hope this is clear to realise that buying two tickets instead of one does not double your chances of winning!

Best of luck with your draws!

Which just confuses me tbh.

So they were contacted again stating that the previous reply made bog all sense, and:

As stated the odds of matching all six numbers are 1 in 13,983,816. These odds apply for each individual ticket purchased.

Should you purchase two tickets with different sets of numbers, this does not halve your chances of winning the lottery, it reduces the probability by 1. The number of tickets you purchase does not act as a denominator against the total odds, it reduces the total probability by that amount.

For example, if you purchased 100 tickets, the odds of one of those tickets winning would not become 1 in 139,838 it becomes 1:13,983,716.

With a dice role, any particular number can be rolled again. With the Lotto, there is a maximum number of combinations of 13,983,816 and once one combination is removed by buying a ticket, that combination cannot be produced again therefore it is minus 1.

Therefore odds of one ticket = 1:13,983,816
" odds of two tickets= 1:13,983,815

By purchasing two tickets you do of course have two chances of winning although i hope you can see the odds are not halved.

I've got a sneaky suspicion that they're getting odds, probabilities and ratios all kurfuddled.

Btw the thread I referenced before, where this all started, is here and then moved to here. Also this made me giggle a bit.

 

[Bugz]

Use a simple binomial expansion:

1 - 10C0(1 in 14 mill)^0(13,999,999/14 mill)^10

=> 7.14 x 10^-7

aka 1.4 mill

10 tickets = roughly 10 times as likely to win.

They are using the fact that the probability of any one ticket winning at any one time is independent on the incidences of all other tickets. But this does not mean increasing tickets does not increase your chances of winning.

Consider a dice. It has 20 sides all numbered one to twenty. You want a one. The probability of getting a one is 1/20. Throw 20 dices. Your expected occurrences of one is modeled by a binomial distribution with mean np. N = 20, p = 1/20, E(getting a one) = 1

Apply to lottery: np, 10 x 1 in 14 mill = 1 in 1.4 mill.

What is fantastically ironic about all this is they are basically saying 'having more than one ticket does not increase your chances of winning' if we take this sentence:

For example, if you purchased 100 tickets, the odds of one of those tickets winning would not become 1 in 139,838 it becomes 1:13,983,716.

They fail to see the difference between P(win) and P(ticket 1 = win) or P(ticket 2 = win) and that the summation of P(ticket 1,2...n = win) gives us P(win).

P.S Please keep emailing them georgie - I'd love to see how this pans out.

edit - The be all and end all for this discussion is: 14 mill combinations. If you buy 14 mill lottery tickets containing all the permutations you satisfy the E(win) = 1.

 

[Ctuchik]

i doubt it would double the chances but it would increase it.

shite at math tho so i can't tell just how much

 

[georgie]

Please keep emailing them georgie - I'd love to see how this pans out.

It's not actually me doing the emailing, and I think the guy who did has decided that they suck and cba any more.

 

[Thorwyn]

The probability of having 1 ticket to win the jackpot in the Lotto game is approx 1: 13,983,816

The chance of having 2 tickets is 2: 13,983,815 (which is not 1:6,991,908)

The chance of having 13,983,816 tickets is 1:1 obviously.

The chance of having 6,991,908 tickets is 1:2

The probability of human stupidity being infinite is 1.

 

[Ingafgrinn Macabre]

No... it doesn't double your chances.


Say, other people have in total bought 125 tickets. You buy one
Then you have a 1 in 126 chance to win.
If you buy two, you have a 2 in 127 chance to win. You have to take the extra ticket you buy in account.

So if you buy 1 ticket, you have a 0.7937% chance to win
If you buy 2 tickets, you have a 1.5625% chance to win.
1.5625/0.7938 = 1.96875 so you don't double your chances. Nearly, but not totally since you have to add your n'th ticket to the pool.

 

[Bugz]

That isn't true Ingafgrinn.

When you buy your ticket, the probability of winning is determined by the correspondence between your numbers and the numbers on the night.

When you buy another ticket, they don't add more combination to the balls.

The size of the share of winnings is irrelevant in calculating the probability of having a winning ticket.

 

[Ingafgrinn Macabre]

That isn't true Ingafgrinn.

When you buy your ticket, the probability of winning is determined by the correspondence between your numbers and the numbers on the night.

When you buy another ticket, they don't add more combination to the balls.

The size of the share of winnings is irrelevant in calculating the probability of having a winning ticket.

That depends on the type of lottery. On a standard lottery, you take all the sold ticket numbers, throw 'em in a big'ol'jar, husstle, and take out 1 ticket. In other lotteries, they also draw from the unsold tickets, and that's just plain mean in my book, but you're right then it wouldn't matter how many tickets you bought, it wouldn't change the pool size.

 

[Bugz]

I forget there exists more lotteries than the UK's.

Ignore me!

 

[Marc]

That depends on the type of lottery. On a standard lottery, you take all the sold ticket numbers, throw 'em in a big'ol'jar, husstle, and take out 1 ticket. In other lotteries, they also draw from the unsold tickets, and that's just plain mean in my book, but you're right then it wouldn't matter how many tickets you bought, it wouldn't change the pool size.

Thats a raffle. We are talking about the lottery, if which there are a set number of combinations regardless of how many people buy tickets

 

[DaGaffer]

Yes it doubles your chances, but just to be clear, that doesn't mean it halves the odds.

 

[Helme]

Yes it doubles your chances, but just to be clear, that doesn't mean it halves the odds.

This.

You double your chance to win - but the odds of winning are still the same no matter if you buy 200 tickets or 1.

 

[Killswitch]

This.

You double your chance to win - but the odds of winning are still the same no matter if you buy 200 tickets or 1.

That doesn't seem to make any sense...in fact, this whole thread has me confused. The chance of any individual ticket winning is essentially one divided by the total number of combinations. That doesn't change whether you have one ticket or <Dr_Evil>one million tickets</Dr_Evil>.

Let's try an example...let's pretend that instead of a lottery, we had a national dice roll. If you bought a single ticket, you'd have a one in 6 chance of a win (assuming a fair, unweighted D6). If you had two tickets that were different, surely you'd then have a 2 in 6 chance of a win. If you bought 6 tickets, you'd be guaranteed a win.

I don't see any evidence that this doesn't scale up to the real lottery. Provided your tickets are unique and the lottery is fair, the chance of a win should be <number of tickets> / <number of possible results>. That means that doubling the number of tickets you purchase will double the chances of a win. I can't see how it could work any other way.

 

[Bugz]

This.

You double your chance to win - but the odds of winning are still the same no matter if you buy 200 tickets or 1.

What?

The individual ticket 'odds' are still the same but the P(win), whether you choose to express it as odds, percentages, ratios is increased by increasing the number of combinations via buying more tickets.

The equation for odds is: p/(1-p).

Let's say we have a dice. P(1 six) = 1/6 so using the equation above we get: 1/5 aka 1:5

Let's say we have two dice. P(1 six) = 5/18 so using the equation above we get: 5/13 aka 5:13

5:13 odds are not the same as odds of 1:5.

In fact, ask yourself this. If the odds of winning aren't changed by the number of tickets you have. When I hold 14.7 million tickets that each sum up to correspond with the 14.7 million combinations, what are my odds of winning? According to you, it's still 1 in 14.7 mill?