The lotto - are the odds of getting a sequence of numbers the same as random numbers?

AARRRGH

Hello

I understand the concept of probability, and that the chance of getting 1, 7, 8, 15, 21, 22 is the same as getting 1, 2, 3, 4, 5, 6.

But because there is a relationship between a sequence of numbers (i.e. the next number drawn must be within a certain range) does this affect the odds, or at least, add an extra variable?

Thank

enda1

They have the same probability of course. Its just numbers written on balls. The balls don't know what the numbers are so sequence is only something we notice because of how we view numbers.

AARRRGH

OK, let's say there was a defined relationship between things.

For example -

100 people were lined up in front of me
I have to pick 5 of the people
I happen to know 5 of the people are related, but I don't let that influence my selection
When I pick the 5 people... it turns out I picked the 5 people who are related.

Are the odds of picking those 5 people still the exact same? Or is there an extra variable (affecting the odds) at work because I knew there were related people in the crowd, and I happened to pick them?

IrishKnight

Well if you pick the five people based on the fact you know they are related then the results are scuded.

The lotto is random. To help you a bit this is how to work out the prob of winning the lotto.

There are 45 numbers, you have to choose 6.

45C6 = 8,145,060 possible 6 number combos

The prob of getting the winning 6 is;

P(winning 6 numbers)=1/8145060

or 1.227e-7

or 0.0000001227

Yakuza

If you can pick the 5 related folks at random from the 100 I suggest you go and buy several lotto tickets, as if you're able to predict a 1 in 75,287,520 event, then a 1 in 8,145,060 event should be no bother to you

(In other words, if you claim to be able to truly pick the people at random, then there would be no correlation to the fact that they were related and you picked them. It's just a very unlikely event).

Some (silly) folks try to improve their odds of winning the lotto by assuming that there is always a gap of at least 6 or 7 between lotto balls drawn (and hence reduce the number of tickets they'd have to buy), but it's almost never the case.

IrishKnight

Well a this point, one could buy all the possible combos and is guaranteed to win! Having said that you'll need about €12 million....

Sir Digby Chicken Caesar

that's a six million profit!

Yakuza

Unless someone else wins it too, then you're f**ked
Not to mention that entering around a million lotto slips in 2 or 3 days would be a fair effort in logistics itself

Tar.Aldarion

To go back to OP, in case you are not sure: NO.


It is only if you choose one first and then calulate odds that it could be affected.

seamus

I think the confusion arises because when people see the numbers 123456, they imagine that it must be impossible for them to come out like that.

But what about 634521? Or 412635? These look "more random", but they're not really.

Of course, the odds of 123456 being drawn in that sequence, are much less than them being drawn in any sequence.

subway

seamus wrote: »

Of course, the odds of 123456 being drawn in that sequence, are much less than them being drawn in any sequence.

why?

Tar.Aldarion

Because after you draw one the next number has to be two and so on, also one wouls have to be drawn first. If it was in any sequence there are much more permutations to get the 6 numbers.

seamus

subway wrote: »

why?

There are 720 possible ways that 123456 could be drawn, if you could draw them in any order.

If they must be drawn in sequence, there is only one way that they can be drawn.

Look at it this way - the table below sets out the odds at each draw, of getting the ball that you need on the next go:
Draw No.| In Any Sequence | In Sequence
1 | 5/35 (1/7) | 1/35
2 | 4/34 (2/17) | 1/34
3 | 3/33 (1/11) | 1/33
4 | 2/32 (1/16) | 1/32
5 | 1/31 | 1/31


So After the first draw, say you pull out a 1. If you're happy to get any sequence, then the odds of pulling out a valid ball on the next go is 5/35 (you could pull out 2,3,4,5 or 6 and you'd be happy). If it must be in sequence, then you only have one chance in 35 of getting the right ball, i.e. 2

opr

Surely as the nation of leprechauns and superstitious nonsense many people playing the lotto have what they deem their numbers.

I am sure that these numbers represent something significant and as such loads of other people have the same numbers. People also play numbers as they are generally deemed lucky numbers the same way in which other numbers are deemed unlucky.

If you were bothered to actually research this in more detail i am sure certain numbers are played regularly by a large % of people doing the lotto, the same way in which certain numbers have a lowish % playing them regularly.

As such given the ramdom event choosing the relevant numbers would mean when you eventually win the lotto thier is less chance of you having to share the jackpot thus giving you an edge.

E=MC²

Opr

subway

ahh, yes, i took your statement up the wrong way.
for some reason i thought you were saying there were better odds of drawing sequential numbers in a predetermined non sequential pattern than in numerical sequence.
ie, "you've more chance of 431256 being drawn than 123456"

but, i now understand you were saying that there are 720 chances of drawing 1 to 6 in any sequence, as opposed to just 1 chance of drawing 1 to 6 in that sequence


so, is anyone going to pick 123456?

stereo_steve

Even though a combination of 123456 has the same odds of occurring as a combination of 6 other numbers , you should never pick 123456 or 654321.

Why? Because you are far more likely to be sharing your winnings with someone picking those numbers as opposed to "random" ones.

hivizman

There's an interesting article on the UK National Lottery here. This claims that, at one time, over 10,000 tickets each week were sold with the numbers {1 2 3 4 5 6}. On one occasion, 133 tickets with the numbers {7 17 23 32 38 42} shared the jackpot.

Assuming that the selection of balls is truly random, the probability of any given combination of six numbers appearing is the same as the probability of any other combination. But humans tend to look for patterns in numbers that are not necessarily there.

Julez

I was woking out odds etc. for the lotto the other day and I'm no matamatical genius or anything but this is what I got

Chances of matching first 45/1,
Chances of matching second 44/1,
Chances of matching third 43/1...etc

So odds are 45x44x43x42x41x40 = 5,864,443,200/1.

Firstly I'm wondering if this is correct and also what would the bonus number do to these odds?

Michael Collins

Julez wrote: »

I was woking out odds etc. for the lotto the other day and I'm no matamatical genius or anything but this is what I got

Chances of matching first 45/1,
Chances of matching second 44/1,
Chances of matching third 43/1...etc

So odds are 45x44x43x42x41x40 = 5,864,443,200/1.

Firstly I'm wondering if this is correct and also what would the bonus number do to these odds?

No that is not quite right. But you're half way there. As was said above, that is the case of matching the lotto numbers in the correct order i.e. it is a permutation. But the lotto works on combinations, so you have to multiply your probability by 6! i.e. 6 factorial = 720. This gives: 6!/5,864,443,200 = 1.2277E-7, as per IrishKnight above.

IrishKnight

Bonus ball can be seen as just another ball. As for the odds, you need to work out the total number of possbile 6 number combos of 45 numbers.

That would be;
45c6=8145060 possbile combos

If you have one line of numbers that would be 1/8145060
two numbers 2/8145060 etc

Michael Collins

Of course don't forget if you're trying to go for the jackpot by buying all the tickets and you're worried someone else might win it and you'll have to share, chances are that you'll get quite a few match 5,4,3 and the bonus, and 3 as well. Probably won't get you that much extra but it's a nice addition...

hivizman

Julez wrote: »

So odds are 45x44x43x42x41x40 = 5,864,443,200/1.

Firstly I'm wondering if this is correct and also what would the bonus number do to these odds?

You haven't taken into account the fact that it doesn't matter what order the balls come out - once the six balls have been chosen, they are sorted into ascending numerical order. The numbers on your lottery ticket are also in ascending numerical order. So you have to divide your figure of 5,864,443,200 by the number of ways of ordering 6 different items, which is 6x5x4x3x2x1 = 720. This gives a total number of possible sets of six lottery numbers (in a 45-ball lottery) as 8,145,060, as Michael Collins notes. By the way, conventionally this would be expressed as odds of 8,145,059/1.

If there's only one combination of six numbers that can match the lottery selection, there must be six possible combinations that match five numbers and the bonus ball - you can drop any of the six numbers in the lottery selection and replace it with the bonus ball.

The various combinations, both winning and non-winning, are as follows:

All six balls____________________1
Five balls plus bonus____________6
Five balls without bonus_______228
Four balls plus bonus__________570
Four balls without bonus____10,545
Three balls plus bonus______14,060
Three balls without bonus__168,720
Two balls plus bonus______126,540
Two balls without bonus__1,107,225
One ball plus bonus_______442,890
One ball without bonus___3,011,652
Bonus ball only___________501,942
No matches at all_______2,760,681

Total_________________8,145,060

I note that the Irish Lottery website is pushing some suggestions for filling in your ticket: choosing three odd numbers and three even numbers; choosing winning numbers from previous draws; and choosing numbers in sequence (at least two sequential numbers). None of these will change your chance of winning, if the lottery is truly random. A random lottery has no memory, so the fact that a particular number was or was not drawn last time has no effect whatsoever on the probability that it will be drawn next time. Similarly, the lottery doesn't know what numbers are odd and what ones are even, so there is no reason to expect there to be any form of balance in the choice of numbers. As there are 23 odd numbers and 22 even numbers, there are 2,727,340 possible combinations with three odd and three even numbers, so the probability of getting a "balanced" set of numbers is roughly one in three.

makl

and presumably you divide 8,145,060 this by 2 if you're playing 2 lines... and so on. 8 lines still over 1 in a million chance.

does it make a difference if you play 8 lines 1 week, then wait 4 weeks before doin the same again, or playing 2 lines every week?

legs11

the chances of any of the previous posters in winning tonight are 18,000,0000,000/1 in other words tbh.

lotto is just a scam anyways.

that be all.

the_syco

legs11 wrote: »

lotto is just a scam anyways.

A scam that benefits charities, and allows people to win money from...:rolleyes:

getthegarglein

legs11 wrote: »

the chances of any of the previous posters in winning tonight are 18,000,0000,000/1 in other words tbh.

lotto is just a scam anyways.

that be all.

A scam that has just netted someone somewhere over 18 million smackeroonies... now theres a scam i want to be involved in

IrishKnight

makl wrote: »

and presumably you divide 8,145,060 this by 2 if you're playing 2 lines... and so on. 8 lines still over 1 in a million chance.

NO no no no.

8,145,060 is the possible number of combos. It doesn't matter how many lines you play this will always stay the same.

If you play two lines then the odds are 2/8,145,060 or 1/4072530

If you play three lines then the odds are 3/8,145,060 or 1/2715020

And so on.

does it make a difference if you play 8 lines 1 week, then wait 4 weeks before doin the same again, or playing 2 lines every week?

Yes and no, the odds for any lotto draw are always the same, no matter what you do. However, if you want to do as much as you can to win, do as many lines for every draw you can.

hivizman

legs11 wrote: »

lotto is just a scam anyways.

All the probabilities for the lottery are public knowledge, and the fact that only about half of the money raised by selling tickets goes into the prize fund is also public knowledge. So anyone buying a ticket knows that the odds are stacked against them. But I suspect that most people feel that the cost of a ticket is trivial against the possibility of winning a large jackpot (and the smaller prizes are nice to get as well). And of course there are the charity benefits.

Although traditional economists consider buying a lottery ticket to be irrational, because you are giving up the cost of the ticket for an expected return of about half of what you pay, behavioural economists can justify playing lotteries. The marginal utility you sacrifice in buying a ticket may be less than the marginal utility you gain by having the chance of a big win. Lotteries play on human behaviour to get people to carry on playing. For example, in a 45-ball lottery with six balls plus a bonus being drawn, about two tickets out of every three will include at least one of the seven balls drawn, thus giving the impression that you're not entirely hopeless at picking the numbers. Many people buy a ticket with their "numbers" each time because they want to avoid the dreadful feeling they anticipate if they don't buy a ticket one time and their numbers happen to come up. For a small number of people, lotteries can be a bit like a drug, but for most of us it's a little harmless fun, a bonding experience if you are in a pool, and an occasional spirit-lifter when you win. If it's a scam, then the con merchants are ourselves, not the lottery.

MathsManiac

By way of expansion on the above comment about "traditional economists":

Assertions that playing the lottery is irrational operate on the assumption that the value to the individual of any quantity of money is in direct proportion to its face value. This is fine when the amounts gambled and won are of comparable magnitude, but not otherwise. It's hard to be precise about this aspect, because it will differ for each individual.

Most people could not tell you the precise amount of money they have in their pocket or wallet at a given moment, so one might argue that the cost of the minimum play lottery ticket is essentially 0. (That is, if you literally wouldn't notice it disappearing from your pocket.)

Here's a similar interesting question: Suppose you've just one ten million euro on the lottery. Would you risk it all on the toss of a coin to add another 20 million to it? Game theory using face value of money tells you this is a bet you should take, but there's no way I'd take it!

Taking real value as proportional to face value would also lead you you to never take out insurance on anything.

There's an interesting chapter about this stuff in the book "How long is a piece of string?" by Rob Eastaway and Jeremy Windham. Chapter 5: "Should I phone a friend" considers, among other things, how three different people in different financial circumstances might make different rational gambling decisions at different stages in "Who wants to be a millionaire?"

Also, by the way, one can argue that in playing the loot, you're actually buying more than the chance of winning - you're also buying the chance to dream about what you would do if you won!

hivizman

MathsManiac wrote: »

There's an interesting chapter about this stuff in the book "How long is a piece of string?" by Rob Eastaway and Jeremy Windham. Chapter 5: "Should I phone a friend" considers, among other things, how three different people in different financial circumstances might make different rational gambling decisions at different stages in "Who wants to be a millionaire?"

Also, by the way, one can argue that in playing the loot, you're actually buying more than the chance of winning - you're also buying the chance to dream about what you would do if you won!

Thanks for the reference - I'll follow up the book you mention.

Also, I entirely agree about the chance to dream - you can't really dream about winning unless you enter. Isn't there a joke about the guy who prays to God to let him win the jackpot on the lottery. After the draw, he goes back and complains to God that he didn't win. God replies "Help me out here - buy a ticket!"

cavedave

The argument goes that lotteries are stupid because you have a very low chance of winning. So low in fact that you are more likely to die before you win then to win.

This argument is weird because we are encouraged to do more difficult tasks where we are even less likely to affect the outcome. Voting in an election takes more effort and time then buying a lottery but your vote virtually never decides an election.

There has been one case of a single vote deciding the election of an Irish TD. In the 2002 Irish general election, Dan Neville won a seat in the parliament by just one vote. There have been an average of more then 150 td’s in Ireland in its 27 elections. Each TD represents at most 30,000 people but say 25,000. So 27 elections of 25,000 people is one out of 101,250,000 total votes decided an election. You might argue “But if no one voted there would be no point having an election?” Well if no one bought a lottery ticket the lottery would not keep running for long either.

So the chance of your vote being the deciding factor in an election is less then your chance of winning the euromillions lottery.

Pherekydes

cavedave wrote: »

There has been one case of a single vote deciding the election of an Irish TD. In the 2002 Irish general election, Dan Neville won a seat in the parliament by just one vote.

There has never been the case of a single vote deciding an election. Even in the case of an election with 3 voters, the 3 people decide the election, not the one person whose vote makes it 2-1. How do you decide which vote is the winning vote, anyway?

cavedave

Pherekydes

There has been one case of a single vote deciding the election of an Irish TD. In the 2002 Irish general election, Dan Neville won a seat in the parliament by just one vote.
There has never been the case of a single vote deciding an election. Even in the case of an election with 3 voters, the 3 people decide the election, not the one person whose vote makes it 2-1. How do you decide which vote is the winning vote, anyway?

Thats an interesting point. My comparison was more between someone who did/did not go out and buy a lottery ticket and someone who did/did not go out and vote. Winning in each case I would define as winning the lottery or changing the result so it now goes the way you voted. I can find no cases where an election was tied. So no cases where you deciding to vote or not to would make a difference *(except the one election listed where you could have tied the result).

makl

IrishKnight wrote: »

NO no no no.

8,145,060 is the possible number of combos. It doesn't matter how many lines you play this will always stay the same.

If you play two lines then the odds are 2/8,145,060 or 1/4072530

If you play three lines then the odds are 3/8,145,060 or 1/2715020

And so on.

yea, divide 8,145,060 by 2 for 2 lines ("1/4072530" chance).

Pgibson

Princess Innocent Knickers wrote: »

that's a six million profit!

Its been tried here in Ireland!

By a certain Stefan Klincewicz and pals in 1992 !

Read all about it here:

http://findarticles.com/p/articles/mi_qn4158/is_19960104/ai_n9632803

.

Pal

I consider myself to be a Lotto Cynic.
Will never play it.
It doesn't matter what sequence the balls come out.
The balls don't think about it.
No mathematics can change the fact that the Government always wins and the punter always loses.

Now would anybody like to buy a ticket. I'm running my own Lotto.
Somebody's guaranteed to win.
Me !

Pgibson

As long as you regard the Lotto as a "Fun Tax" that you just might win you are ok.

I never play it because the (my) money goes on Sport.

Sport is for life's losers...people who can't do mathematics.

.

Pherekydes

Pgibson wrote: »

Sport is for life's losers...people who can't do mathematics.

.

There's a lot of people who do both.

Wasn't it Plato (or Aristotle) who said "Alegebra and Athletics" or maybe it was "Gymnastics and Geometry" were the ideal preparation for life (meaning Mathematics and Physical Training- a variation on the Roman "Mens sana in corpore sano" ethic)

M.T. Cranium

Actually, there can be a slight non-random effect in the design of the lottery machine, if your numbers are generated that way. In Canada, we have a lottery called 6-49 where six numbers (one to forty-nine) are generated "at random" from balls dropping out of a spinning chamber. However, after 25 years of this, the actual frequency of the balls arriving at the bottom and falling out is not quite random. It shows the different probability of the balls arriving there from the six rows that empty into the chamber, and the numbers in the 40s have tended to come out more frequently than the rest, then same for the 30s relative to the rest. Also there seems to be a slight preference for the higher unit values that come out first into the chamber (like 8,9,10, 18,19,20 etc). This preference has not been so blatant that it would be worth skewing your picks, but it is a non-random factor in the lottery. Of course, if your lottery generates random numbers electronically then this detail means nothing. You should see if they keep the same stats, and study the process and the frequency, see if there's any pattern to it or not.

There is also one good reason not to play consecutive numbers -- a lot of people do, and if you happen to win, you will share the prize with a lot more people than usual. This happened here recently on some lottery, a second place prize (five of six numbers) went to anyone who had 41, 42, 43, 44, 45 and instead of the usual handful, it was like ten thousand splitting the prize pool, and they ended up getting about 2% of the usual value of the prize.

You're far better off to play the sports lottery, even if a person knew nothing about sports and marked the tickets at random, their chances of winning would be greater than these big lotteries. So if you do know something about sports, and can eliminate some obvious non-starters (like Canada winning anything) you're far ahead of random probability going in.

Pgibson

If all the balls were initially "created equal" then any differences might be down to the paint on them.

Is is conceivable that a ball with "44" painted on it weighs a tiny fraction more than a ball with "1" painted on it?

Or, if the numbers are embossed on the balls rather than painted on, there may be a minute difference in the weight of the balls.

Or there may be a difference in the "coefficient of friction" on the balls with more marks engraved on them....ie the balls with the higher numbers.

SOMETHING interesting is happening anyway !

Just a thought.

(P.S. The very first Space Shuttle rose off the ground ever so slightly slower than expected...they traced it to the weight of the paint !)

.