Probability - lotto & syndicates

rimshott

Any mod's feel free to move this thread if it does not belong here.


Quick question. The Irish lotto.
Is it a waste of time joining a company lotto syndicate.

I work it out at an odd's of 8,145,060 / 1 chance of winning
with one line (45 numbers in the lotto)
So if i join a syndicate in work that consists of 4 people (including me) doing 8 lines every draw (twice a week) for 1 month.
This only gives me a better chance of
8,145,060/1
8,145,059/1
8,145,058/1
8,145,057/1
8,145,056/1
8,145,055/1
8,145,054/1
8,145,053/1
but then i have to split the winnings by 4 :eek:

Am I right?
Can somebody shed some light on this for me?
Is it a complete waste of time(not the lotto - the syndicate:))?

Pherekydes

Joining a syndicate increases your chances of winning (slightly), but when you win (inevitably ), you have to split the winnings.

Put it like this, your chances of winning the lotto are close enough to zero to make no difference. Joining a syndicate multiplies this probabilility (near zero) and makes it equal to, well, near zero (anything times zero is zero, right?).

You can email the Statistics Dept of any University and ask them how many of their staff do the lotto or are in syndicates. Be prepared for much sniggering...

eve

Slow coach wrote: »

You can email the Statistics Dept of any University and ask them how many of their staff do the lotto or are in syndicates. Be prepared for much sniggering...

Maybe not as much sniggering as you may expect. Read here: http://www.mailonsunday.co.uk/pages/live/articles/news/news.html?in_article_id=412386&in_page_id=1770

As previous winners will no doubt testify the key to winning the lottery is, by its very nature, purely down to luck of the draw.

But a syndicate of university professors and tutors relied less on chance to conquer mathematical probability to scoop the jackpot.

Using two boxes, 49 pieces of paper and a bunch of clever mathematicians they won £5.3 million on Saturday night after matching all six numbers.

Having failed to win for the first eight years they decided it was time for a change and devised a plan to beat the odds.

Instead of each member randomly choosing numbers or relying on birthdays and significant dates as they had done this time they came up with an unbeatable formulae.

All 49 numbers were written on pieces of paper and placed in one box. Each syndicate member in turn then picked out six numbers, until eight lines were filled, using 48 of the 49 numbers.

The remaining number was then used to start a new line by the next syndicate member, who picked from a second box where the pieces of paper already drawn had been placed.

As a result each number appeared at least twice in the syndicate's 17 lines, with four numbers appearing three times.

The syndicate, from Bradford University and College in West Yorkshire, then set up a computer programme to check the numbers each and every Saturday night.

It would check their numbers against the winning line in a bid to find a match. But, like all methods, it has taken some time to perfect.

In fact, it took four years - but after matching the winning numbers 15, 18, 23, 31, 37, 49 and the bonus ball 38 they finally hit the jackpot and won £5,299,849.

They have since worked out that it will net them £311,755.82p each.

Syndicate leader Barry Waterhouse, 41, who works at the design and printing section of the university, said they had been playing the lottery ever since it began in 1994 with each member picking their own line.

"But we just weren't winning with the numbers being picked that way, so we thought of a different method which would mean all 49 numbers would be used," said Mr Waterhouse.

"We just thought that if all the numbers are in use we must have a good chance of winning and it has proved so, though you never really think it will happen to you.

"We just had to stick with the numbers and we knew we would win eventually."

Fellow syndicate member, David Firth, 63, said: "We have won tenners and the odd £70 in the past, but now this is the big one."

Mr Firth, who now plans to retire from his job as a printer, said he learnt of the win by text from a fellow syndicate member on Saturday evening.

"He had inputted all 17 lines into a computer programme and so all he had to do was type in the winning six numbers, plus bonus ball, to see if we'd won," he added.

"We're so pleased we decided to rehash the way we drew the numbers and were confident that it would get us a win."

Youngest syndicate winner Ben Watson, a 30-year-old graphic designer, intends to spend his winnings on a season ticket for Bradford City.

A fourth syndicate member was named as Jackie Nichol, 59, who was due to retire from the printing offices at the university to set up a business selling soap.

The other university employees who won a share of the jackpot have opted for anonymity.

A spokesperson for Bradford University and College said: "We are delighted for all our lucky winners. They work hard and deserve this success.

"Let's hope lightning strikes twice and some of the other college syndicates scoop another jackpot."

A spokeswoman for Camelot said they were aware of the system employed by the university syndicate.

She said: "We are not overly concerned by it as everybody has a method of trying to win. However, we would say that being in a syndicate does increase your chance of a win as one in four jackpots goes to a syndicate."

Mailman

rimshott wrote: »

Any mod's feel free to move this thread if it does not belong here.


Quick question. The Irish lotto.
Is it a waste of time joining a company lotto syndicate.

I work it out at an odd's of 8,145,060 / 1 chance of winning
with one line (45 numbers in the lotto)
So if i join a syndicate in work that consists of 4 people (including me) doing 8 lines every draw (twice a week) for 1 month.
This only gives me a better chance of
8,145,060/1
8,145,059/1
8,145,058/1
8,145,057/1
8,145,056/1
8,145,055/1
8,145,054/1
8,145,053/1
but then i have to split the winnings by 4 :eek:

Am I right?
Can somebody shed some light on this for me?
Is it a complete waste of time(not the lotto - the syndicate:))?

the more lines you play you'll start seeing a consistent return of something like 12 or 13% on the 100% you input meaning you are loosing less. Pooling your stake through a syndicate will allow you to cover more numbers and avoid duplication. You can also identify numbers which are due to come up and select them to increase your chances although really every number has an equal chance of being drawn on each draw.
The best way to maximise the return is to only participate in draws which have rolled over.
Syndicates are there to maximise return and allow particpants an opportunity to win a life-altering pot of money, not to win millions of euro for each player.10 people dividing 3 million would alter each of their lives dramatically even though they only get 300K each.

Fremen

rimshott wrote: »

Any mod's feel free to move this thread if it does not belong here.


Quick question. The Irish lotto.
Is it a waste of time joining a company lotto syndicate.

I work it out at an odd's of 8,145,060 / 1 chance of winning
with one line (45 numbers in the lotto)
So if i join a syndicate in work that consists of 4 people (including me) doing 8 lines every draw (twice a week) for 1 month.
This only gives me a better chance of
8,145,060/1
8,145,059/1
8,145,058/1
8,145,057/1
8,145,056/1
8,145,055/1
8,145,054/1
8,145,053/1
but then i have to split the winnings by 4 :eek:

Am I right?
Can somebody shed some light on this for me?
Is it a complete waste of time(not the lotto - the syndicate:))?

You're a bit off here. Your syndicate will do far better than 8,145,053/1.
It's 8,145,060/8 or about one in a million. (assuming your figure of 8,145,060/1 is correct )

Joining a syndicate means you have a greater chance of winning a smaller prize. It's important to realise that you're still not beating the odds. If there was some way to beat the lotto, someone would have done it by now, and lotteries would be out of business.

It's also worth noting that, in the US, lottery wins are paid out over the course of a lifetime, typically at about 100K a year. Winners can settle for an immediate cash payout of about half the jackpot if they want. I'm not sure what the situation is in Ireland.

I would be a touch cynical about the college stats department winning the jackpot in eve's post. Just because they won doesn't mean the win didn't come from luck. In fact, writing a paper which describes a way foolproof to profit from the lottery would be worth a whole lot more than a jackpot to a statistician.

Edit: re-reading the article, it looks as if the syndicate was actually a group of design and printing staff, not the stats department.

Pherekydes

Foolproof? Hah! It there was a foolproof method of winning any lotto, then every lotto would be won on every draw. By everybody who bothered to employ this foolproof method.

Interesting calculations to ponder:

2 draws for 52 weeks for 100 years = exactly 10400 total combinations drawn. Even if all of these combinations was different, it only amounts to 0.13% of the total combinations possible.

All you can do is buy up as many different combinations as possible/affordable in each draw, choosing less favoured combinations, to increase the likelihood of not sharing a win.

Imagine you jump out of a plane without a parachute. Spread your arms and legs to increase your drag and slow you down. You increase your chances of a soft landing by doing this, but by how much?

Fremen

Slow coach wrote: »

Foolproof? Hah! It there was a foolproof method of winning any lotto, then every lotto would be won on every draw. By everybody who bothered to employ this foolproof method.

Well, I meant foolproof in that anyone using such a method would have non-negative expected value, rather than a guaranteed win.

Pherekydes

Fremen wrote: »

Well, I meant foolproof in that anyone using such a method would have non-negative expected value, rather than a guaranteed win.

Of course, I wasn't aiming my sarcasm at you. More this:

they came up with an unbeatable formulae [sic].

If it's unbeatable why don't they win all the time? :rolleyes:

rimshott

Fremen wrote: »

You're a bit off here. Your syndicate will do far better than 8,145,053/1.
It's 8,145,060/8 or about one in a million. (assuming your figure of 8,145,060/1 is correct )

.

This has to be wrong. Your saying if i do one line my chance is 8,145,060/1 but if I do 8 lines my chances are 8,145,060/8 :eek: Where did you go to school? How in god's name does that give me 1,018,132.5/1 chances of winning?

My question is this are small syndicates a complete waste of time?
By me joining a 4 person syndicate in work, my odds of winning remain the same approx 8 million/1 each line.
But if we win i split it in 4. So if I only done 1 line on my own every week the odds are approx the same as if i joined the syndicate?

Fremen

rimshott wrote: »

This has to be wrong. Your saying if i do one line my chance is 8,145,060/1 but if I do 8 lines my chances are 8,145,060/8 :eek: Where did you go to school? How in god's name does that give me 1,018,132.5/1 chances of winning?

I went to school in dublin. I also did a maths degree and I'm now doing a graduate course in applied probability (well, financial maths. The two are closely related.) Not meaning to sound arrogant, but I honestly do know what I'm talking about.

Ok, look at it this way. Suppose you bought 8,145,058 lottery tickets. There are only two numbers which could be drawn which would result in you not winning. In other words, it's very, very likely that you'll win. My method says the chances of winning when you do this are 8,145,058 in 8,145,060 which is very close to a certainty. Your method puts it at 2/1, which is far from certain.

Another example: suppose I roll a die, and you try to guess what number I roll. If you guess one number, you'll be right one time in six. If you guess two numbers, you'll be right two times in six, or one time in three. The same applies to the lotto.

Pherekydes

Fremen wrote: »

I went to school in dublin.

He's right, rimshott. I went to school in Dublin, too, and I get the same results, therefore we must be right.

Again, put it like this: There are 8 million tickets in a barrel, and you can pick one, or you can pick eight. Which gives the best chance of winning? What are the probabilities? The first gives 1 in 8 million; the second gives 8 in 8 million, or 1 in 1 million.

Xavi6

Lol I read this thread yesterday and knew Nolan would make an appearance. I'm not disappointed!

MathsManiac

...and of course we all know that the physics of the spinning drum is such as to allow the organisers to arrange for the right six balls to emerge. This is the well known 45-body problem that evryone encounters and solves easily in mechanics 101.
:rolleyes:

Pherekydes

But it's not really part of this discussion.

Hagar

To answer the OPs question, joining a syndicate will increase your chances of winning something in the Lotto simply because you are participating in more chances to win. I doesn't matter how insignificant your increased chance of winning is, it's still an increased chance and that is what you asked. Yes, you will have to share any winnings but these winnings may well come from a winning line selected by a colleague that you otherwise would not have had. Any shared win, even a small one, is likely to exceed the amount of money contributed to the syndicate so you are still ahead.

redspider

I dont subscribe to Brian Nolan's 'conspiracy theory'. Rollovers are bigger I understand due to the larger probability 6/49 and the volume of plays per draw.

Here' a question though: are QuickPick's really random, or do they come from a list and are quasi-random? Has anyone done a study on this, including KPMG or Brian Nolan or a uni stats/maths dept? There is anecdotal evidence that QP's are not completely random as very often two lines have similar numbers.

In terms of the OP's question, being in a syndicate gives you a greater chance of winning a smaller/shared prize. ie: you benefit by using others people money to put in more bets/plays, but you lose some benefit by having to share and prizes won.

An alternative approach for you would be to play as much as the syndicate would, and then you can keep all the winnings, including the partials. Also, you will avoid problems that sometimes crop up with syndicates, and there have been a few well published examples:

- someone running off with the ticket and all the winnings

- the placer not actually placing the money at all over the N years but pocketing the bets/plays instead (this is a sneaky one as they are running the book, and as most partial wins are put in to place the bets, they cant lose, unless the jackpot is won)

Maybe you will run your syndicate after reading this ! ;-)

Redspider

i71jskz5xu42pb

Slow coach wrote: »

Joining a syndicate increases your chances of winning (slightly)

Slightly?

If you buy two lines a week you have a set probability of winning.
You and a mate form a syndicate where you buy 4 lines you have doubled your chances of winning. Doubling your odds could not be considered a slight increase.
You and your work mates form a syndicate where you buy 20 lines you have a ten times better chance of winning.
(it goes on like this)

I think your confusing the size of the odds (still high even with 20 lines) with the increased chances of winning.

seamus

redspider wrote: »

There is anecdotal evidence that QP's are not completely random as very often two lines have similar numbers.

In this case, anecdotal evidence is completely useless. People will often spot patterns and similaries in completely random draws, even where patterns don't exist. It's a quite a natural thing to do.

While in other situations anecdotal evidence can sometimes point to something which requires investigation, in the case of random draws, anecdotal evidence only serves to confuse the matter.

That said, there's no reason why the quickpick setup shouldn't be independently audited. From a programming POV, it's a ridiculously simple thing to choose 6 random numbers from 48(?). Examining the results of past draws in order to choose the least likely combination would be a more complicated task and would easily be spotted by even an amateur auditor.

My own personal anecdotal evidence (;)) of listening to the winners of draws, suggests to me that there are just as many quickpick as non-quickpick winners.

Brian Nolan of course completely proves my point re: anecdotal evidence. Without a full listing of all of the wins for a given year, his list is meaningless and attempts to fabricate a pattern where one may not exist at all. It could very well be that the average rollover for a jackpot is 4 draws (i.e. 2 weeks). Therefore, if the lotto started at the beginning of a year, you're likely to see a rollover jackpot won at the middle and end of each month - coincidentally "around" when most holidays take place.

Fremen

redspider wrote: »

Here' a question though: are QuickPick's really random, or do they come from a list and are quasi-random?

I'd bet quite a lot of money they're pseudo-random. Otherwise the quickpick machines would need a radioactive source inside them to generate the random numbers

Pseudo-random number generation had become so good that it's essentially impossible to distinguish from genuine random number generation. All pseudo random number generators eventually repeat themselves, but if you use one like the Mersenne twister it'll take longer than the age of the universe to repeat the pattern, if you churn out one lottery ticket a second.

cavedave

seamus

In this case, anecdotal evidence is completely useless

correct if you want to find if draws are not random fron a chi squared test. Read about it here

All you can do is buy up as many different combinations as possible/affordable in each draw, choosing less favoured combinations, to increase the likelihood of not sharing a win.

Correct. There is an explanation of how to do this here.

Mailman
You can also identify numbers which are due to come up and select them to increase your chances although really every number has an equal chance of being drawn on each draw.

Numbers are never due to come up. Each draw is independent and thinking otherwise is on a par with believing in fairies.

bren2002

Fremen wrote: »

I'd bet quite a lot of money they're pseudo-random. Otherwise the quickpick machines would need a radioactive source inside them to generate the random numbers

Pseudo-random number generation had become so good that it's essentially impossible to distinguish from genuine random number generation. All pseudo random number generators eventually repeat themselves, but if you use one like the Mersenne twister it'll take longer than the age of the universe to repeat the pattern, if you churn out one lottery ticket a second.

Explain this to me, surely any normal vanilla computer can come up 6 non repeating numbers between 1 and 49 (or whatever the top number is), can't be that difficult.

cavedave

bren2002
.
Explain this to me, surely any normal vanilla computer can come up 6 non repeating numbers between 1 and 49 (or whatever the top number is), can't be that difficult.

It is very difficult. It is like codes (very like infact) it seems easy but is not.


“Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin.” ~ John von Neumann

Fremen

Explain this to me, surely any normal vanilla computer can come up 6 non repeating numbers between 1 and 49 (or whatever the top number is), can't be that difficult.

The problem is to do with the way computers work. Computers use algorithms to solve problems. An algorithm is a kind of recipie for solving a problem: it breaks the problem up into steps, then runs through each step in sequence. The problem is, for a given input into an algorithm, you always know what the output will be. In other words, algorithms work deterministically.

The whole point of random numbers is that they can not be predicted: they work non-deterministically. How can you make a machine which works deterministically spit out a non-deterministic output? The answer is, you can't.

A pseudo-random number generator works by transforming inputs into outputs. A good generator will take two slightly different numbers as input, and turn them into completely different numbers as output. Mathematically, this is really difficult to do reliably.

While it's not difficult to generate six lotto numbers, it could be quite tough to generate six million different draws without creating obvious patterns. I'd imagine quick-pick customers would get pretty pissed off if they found out that their draw had already been sold to ten other customers.

Pherekydes

Jeremiah Orange Poison wrote: »

Slightly?

If you buy two lines a week you have a set probability of winning.
You and a mate form a syndicate where you buy 4 lines you have doubled your chances of winning. Doubling your odds could not be considered a slight increase.

I think your confusing the size of the odds (still high even with 20 lines) with the increased chances of winning.

If you buy two lines a week your probability of winning is 0.00000025 approx

If you buy twenty lines a week your probability is 0.0000025 approx

The difference is 0.0000022 approx

I think you're confusing the size of the odds (insignificant) with the increased chances of winning.

seamus

Fremen wrote: »

A pseudo-random number generator works by transforming inputs into outputs. A good generator will take two slightly different numbers as input, and turn them into completely different numbers as output. Mathematically, this is really difficult to do reliably.

Indeed. One big problem with pseudorandom generators is that no matter what, if you know what the inputs are going to be, you can always determine the output, which negates the "randomness" of it.

To clarify when I said above, "From a programming POV, it's a ridiculously simple thing to choose 6 random numbers from 48(?).", most (if not all) programming languages come with a simple library to generate random numbers. So while the actual underlying process of generating a seemingly random number is a topic worthy of years of study, to a programmer it's a easy as calling getRandom(48).

I think you're confusing the size of the odds (insignificant) with the increased chances of winning.

The assertion though that your chances of winning have increase tenfold is still correct. The beauty of statistics - you can paint anything as good as you want. Even if you buy 100 tickets, your odds are still ~ 1 in 50,000, but you've increased your chance of winning one-hundredfold.
This is how headlines like "Gun crime up 10%" sell papers. If you have ten gun crimes this year and 11 next year, that's a ten percent increase, but it's not remotely significant.

Pherekydes

seamus wrote: »

This is how headlines like "Gun crime up 10%" sell papers. If you have ten gun crimes this year and 11 next year, that's a ten percent increase, but it's not remotely significant.

Yep, this was exactly my point.

buckfast4me

I think it's very annoying the way they added 3 numbers (42->45) making the odds increase from 1/5,000,000 (roughly) to 1/8,000,000 causing these huge €12 million jackpots. In my opinion it's better if 12 people win €1 million each than 1 person winning €12 million. Stupid lotto! Who did the extra numbers benefit exactly?

cavedave

In my opinion it's better if 12 people win €1 million each than 1 person winning €12 million. Stupid lotto!

True it is better for overall happiness for 12 people to win 1 million then one person to win 12 million

Who did the extra numbers benefit exactly?

It benefits the lottery. People are more likely to buy tickets when these big jackpots are present.

Fremen

cavedave wrote: »

True it is better for overall happiness for 12 people to win 1 million then one person to win 12

Continuing this argument to its logical conclusion, it's better for 12 million people to win one euro than one person to win 12 million. Therefore people would be happier keeping their money.

Lotto creates nothing but misery!

i71jskz5xu42pb

Raynard wrote: »

They must think that such fraud is going un-noticed!

Your years of selfless, dedicated study of various documents on the internet has uncovered this plot by the National Lottery. It's all part of an introduction of the new world order.

Rumour has it that the next lotto roll over will be 12 million Ameros

PS - It's you isn't it Jim?

Thomas_S_Hunterson

Raynard wrote: »

Congratulations to the National Lottery for yet another controlled lotto rollover this weekend.

I should have taken my time to send this post to boards and wait to see if the National Lottery would rectify their ways or if the 3rd largest Lottery rollover out of four which is set to be played out this year accomplished a prize fund of €17m or over, or will we have to wait until later in the year to play out that drama!


Surely this has to be one of the biggest cases of fraud in this country. Its past the point of coincidence to the stage where you have to think that someone is tampering somehow with the system, no matter how many adjudicators are present, something is amiss.


I wish to draw your attention to the fact that the National Lottery had no overall jack pot winners during the month of May.

I am fully aware that they allowed about 24 Porsche Cayman Sport cars to be won during the month, no more than a total cost of around €2m or less, again to put out a smoke screen for the general public as if it was totally out of the control of the National Lottery.

The National Lottery maintain that they are fair and honest in everything they do and that they operate to the highest professional standards in all their activities. That all Lottery games including Lotto are operated to the highest standard of integrity and security, that all draws are independently scrutinised by independent auditors from KPMG and that lotto draws are transmitted live as they happen in studio by RTE.

I wonder!

However, they only have to withhold the jackpot for 4 more rollover draws to obtain the biggest ever jackpot prize of €17,000,000 or over and no bank holiday to get in the way so it wont look too obvious.

They must think that such fraud is going un-noticed!

Using that font makes you look like either you're talking crap or a 419er:pac:

Mailman

I'm beginning to suspect something fishy is going on. There are just too many roll overs and not enough of the lotteries are being won on the first go. Either that or the participation rate is very low for them to rollover so often.

Yakuza

I was at a function (Commons) in Trinity where Ray Bates (previous director of the National Lottery) was one of the guests (He graduated from the same course I did). Afterwards, we had a Q and A session with him, and one of the questions asked was why did they increase the numbers from 36 to 39 (as it was then, about 10/11 years ago).

His answer was that they used a metric known to them as "Coverage" - the amount of the possibilities that were covered every draw. As the lottery got more and more popular, more people were entering, and more of the possible subsets of 36C6 (1947792) were getting selected each draw, pushing up the chances of a win each week (and hence a lower prize fund building up, and less publicity for the company). I think that they noticed that over half the above combinations were being selected each week, so there was an even-ish chance of a winner.

To that end, they increased it up to 39C6 (3262623 combinations) which (at the then current level of play) would have brought the level of coverage back down to 1/3 or so.

Roll on to today, and I'm guessing that they used the exact same logic to bump up the number again to 42 (5245786 combinations) and again to today's 45 (8145060 combinations) and they'll continue to do so as long as more and more money is spent on the game).

In 2007, there was €357.7m of lotto sales (source: http://www.lotto.ie/downloads/Lottery_Annual_report_07.pdf)
That's approx €3.4m per draw, or 2.3m entries per draw (assuming €1.50 per draw (I know they changed the price last year but I'm assuming that is an average spend per ticket, whether they used the plus option too).

Of those 2.3m I'd warrant that there were less than 2m (perhaps 1.9m) unique entries (1,2,3,4,5,6 is a very common entry as are the Lost lotto numbers (remember when 5 of them came up and a boatload of folks matched 5 a few years ago !:)), and lots of folks use dates of birth as their chosen numbers, so there'd be lots of entries with all the numbers clustered under 31. So with 1.9m unique numbers out of a total pot of 8.1m, that's a less than 1 in 4 chance of any given prize being won on a given draw.

Even as the pot goes up, and more folks play, the number of unique combinations probably doesn't go up linearly (for the reasons given above) - unless all the new players use quick picks (which are meant to be unique from other quick picks in any given draw) so the fact that more people are playing the game doesn't mean it's that much more likely to be won, only that the prize fund is getting bigger.

No need to break out the tinfoil hats just yet, methinks

Anyhoo, those are my thoughts!

Tar.Aldarion

I wouldn't waste your money on this, put it in a high interest account heh. It is called idiot tax for a reason. :-)

Mailman

lotto plus 2 on saturday had nearly all numbers above 31 but the winings were similiar to other draws. If people were actually chosing numbers lower than 31 for birthdays, house numbers, etc.... I would have expected it to be a much smaller number of winners compared to the weeks before.
I know that the draw drum is transparent but I still feel the process itself isn't transparent.
Also who gave the Lottery the permission to increase the number of balls. I'm not greedy. I just want to win a million or two to hand in my notice, not 14 million which wouldn't make me feel any wealthier than if I had won 2 million.

Thomas_S_Hunterson

Yakuza wrote: »

I was at a function (Commons) in Trinity where Ray Bates (previous director of the National Lottery) was one of the guests (He graduated from the same course I did). Afterwards, we had a Q and A session with him, and one of the questions asked was why did they increase the numbers from 36 to 39 (as it was then, about 10/11 years ago).

His answer was that they used a metric known to them as "Coverage" - the amount of the possibilities that were covered every draw. As the lottery got more and more popular, more people were entering, and more of the possible subsets of 36C6 (1947792) were getting selected each draw, pushing up the chances of a win each week (and hence a lower prize fund building up, and less publicity for the company). I think that they noticed that over half the above combinations were being selected each week, so there was an even-ish chance of a winner.

To that end, they increased it up to 39C6 (3262623 combinations) which (at the then current level of play) would have brought the level of coverage back down to 1/3 or so.

Roll on to today, and I'm guessing that they used the exact same logic to bump up the number again to 42 (5245786 combinations) and again to today's 45 (8145060 combinations) and they'll continue to do so as long as more and more money is spent on the game).

In 2007, there was €357.7m of lotto sales (source: http://www.lotto.ie/downloads/Lottery_Annual_report_07.pdf)
That's approx €3.4m per draw, or 2.3m entries per draw (assuming €1.50 per draw (I know they changed the price last year but I'm assuming that is an average spend per ticket, whether they used the plus option too).

Of those 2.3m I'd warrant that there were less than 2m (perhaps 1.9m) unique entries (1,2,3,4,5,6 is a very common entry as are the Lost lotto numbers (remember when 5 of them came up and a boatload of folks matched 5 a few years ago !:)), and lots of folks use dates of birth as their chosen numbers, so there'd be lots of entries with all the numbers clustered under 31. So with 1.9m unique numbers out of a total pot of 8.1m, that's a less than 1 in 4 chance of any given prize being won on a given draw.

Even as the pot goes up, and more folks play, the number of unique combinations probably doesn't go up linearly (for the reasons given above) - unless all the new players use quick picks (which are meant to be unique from other quick picks in any given draw) so the fact that more people are playing the game doesn't mean it's that much more likely to be won, only that the prize fund is getting bigger.

No need to break out the tinfoil hats just yet, methinks

Anyhoo, those are my thoughts!

At least one managed to rape it good and proper a few times back when there was 36 numbers and it only cost something like 50/75 pence per box. They were able to buy every possible combination for less than the jackpot.

Obviously they were taking a risk that someone else would win and they would have to split the pot, but from what i heard, it paid off.

/edit more info on this wiki page: http://en.wikipedia.org/wiki/Lottery#Probability_of_winning (end of section)

Yakuza

Sean_K wrote: »

At least one managed to rape it good and proper a few times back when there was 36 numbers and it only cost something like 50/75 pence per box. They were able to buy every possible combination for less than the jackpot.

Obviously they were taking a risk that someone else would win and they would have to split the pot, but from what i heard, it paid off.

/edit more info on this wiki page: http://en.wikipedia.org/wiki/Lottery#Probability_of_winning (end of section)

Ah yes, the Scruffy Murphy syndicate. If I recall correctly, even though they split the top prize with 2 others, the guaranteed £100 for a match 4 made it profitable (but if they'd had to split it with more, they'd have lost money). Pretty soon after that, the Lotto went to a bi-weekly draw, to reduce the window of being able to cover all the combinations in a draw in the time between draws, and I'm not sure if they ever offered a (relatively) large prize for match 4 since then.