Lotto Quickpick = Lower probability of winning? - Help end a dispute!

fabbydabby

Hi Lads,

Anyone here good at probability / stats?

i am a first time poster here, long time lurker and though I am quite average at maths compared to some on here, I do find it interesting and as such I was hoping if you would hep me solve an arguement.

I believe that the lotto quickpick system is RIGGED!

A three euro game is the cheapest option in the national lotto, whereby one picks two sets of six numbers out of a possible 45 to try to predict the winning six jackpot numbers. These can be selected by ticking boxes, however some people choose a "quickpick" option since, as its name suggests, it is a quick way to pick the numbers.

The quick pick option uses the lotto machine to "randomly" select six numbers on each line for you. The chances of any six numbers coming up are the same, so it should not make a difference if one picks the numbers themselves or allows the machine to do it for them.
Right?

OR DOES IT????

My problem with the system as it stands can be summarised thusly:

If one were to purchase a three euro quick pick one will regularly see numbers duplicated on both lines. For example, a cursory examination of a ticket purchased by my mother only yesterday revealed the numbers 17, 31 and 40 on both lines!

Here are the numbers that were on her quick pick ticket:

10 17 31 34 38 40
11 15 17 21 31 40

I proposed to my mother yesterday that this duplication significantly adversly affected her chances of winning, and that she should have picked out her numbers like I did, ensuring that different numbers were picked on both lines. She did not agree, citing the random nature of the quickpick selection process as evidence of fairness of the system.

But I believe the quickpick system is unfair and I need you to confirm this for me because NOBODY WILL BELIEVE ME!

I need to know if I am a nutjob and should start wearing tinfoil hats and living in the basement or whether I am right and the lotto people have been fleecing us all for years.

Is there a way that this disadvantage can be expressed numerically like?

Thanking y'all in advance.....

GerardKeating

This weeks winner was a quickpick?

Princess Consuela Bananahammock

fabbydabby wrote: »

Hi Lads,

Anyone here good at probability / stats?

i am a first time poster here, long time lurker and though I am quite average at maths compared to some on here, I do find it interesting and as such I was hoping if you would hep me solve an arguement.

I believe that the lotto quickpick system is RIGGED!

A three euro game is the cheapest option in the national lotto, whereby one picks two sets of six numbers out of a possible 45 to try to predict the winning six jackpot numbers. These can be selected by ticking boxes, however some people choose a "quickpick" option since, as its name suggests, it is a quick way to pick the numbers.

The quick pick option uses the lotto machine to "randomly" select six numbers on each line for you. The chances of any six numbers coming up are the same, so it should not make a difference if one picks the numbers themselves or allows the machine to do it for them.
Right?

OR DOES IT????

My problem with the system as it stands can be summarised thusly:

If one were to purchase a three euro quick pick one will regularly see numbers duplicated on both lines. For example, a cursory examination of a ticket purchased by my mother only yesterday revealed the numbers 17, 31 and 40 on both lines!

Here are the numbers that were on her quick pick ticket:

10 17 31 34 38 40
11 15 17 21 31 40

I proposed to my mother yesterday that this duplication significantly adversly affected her chances of winning, and that she should have picked out her numbers like I did, ensuring that different numbers were picked on both lines. She did not agree, citing the random nature of the quickpick selection process as evidence of fairness of the system.

But I believe the quickpick system is unfair and I need you to confirm this for me because NOBODY WILL BELIEVE ME!

I need to know if I am a nutjob and should start wearing tinfoil hats and living in the basement or whether I am right and the lotto people have been fleecing us all for years.

Is there a way that this disadvantage can be expressed numerically like?

Thanking y'all in advance.....

Nope. Any set of six numbers has the same chance as any other set. The numbers on each line bear no relation to each other - they could have been on three spereate tickets - the chances are still the same. The only thing affecting her chances of winning is if the duplicted numbers come out of the drum first.

ball

Remember, you've the same chances of winning if you pick 1 2 3 4 5 and 6 as with any other combination

fabbydabby

ball wrote: »

Remember, you've the same chances of winning if you pick 1 2 3 4 5 and 6 as with any other combination

OK I know that.

But are you saying that if you gave me 3 euro to go into a shop and buy two lines of a lotto ticket for you and I came out with the following numbers

Line 1: 1, 2, 3, 4, 5, 6
Line 2: 1, 2, 3, 4, 5, 7


you would be ok with it because the numbers have no relation to each other?

Surely it would be better to have totally different numbers on each of the two lines of the game, maximising your spread of numbers chosen for your money?

Would this not be better:
Line 1: 1, 2, 3, 4, 5, 6
Line 2: 7, 8, 9, 10, 11, 12

allthedoyles

But if , as tthe op suggests , that the numbers are been duplicated on a quickpick - could this be challenged ?

I am gonna keep an eye on my own QP's from now on .

fabbydabby

I am gonna keep an eye on my own QP's from now on .

The duplication thing happens constantly on them, which is why I never do them

ball

fabbydabby wrote: »

OK I know that.

But are you saying that if you gave me 3 euro to go into a shop and buy two lines of a lotto ticket for you and I came out with the following numbers

Line 1: 1, 2, 3, 4, 5, 6
Line 2: 1, 2, 3, 4, 5, 7


you would be ok with it because the numbers have no relation to each other? Surely it would be better to have totally different numbers on each of the two lines of the game, maximising your spread of numbers chosen for your money.

Well obviously if you have the exact same combination twice, it cuts your odds of winning in half.

If you have 1 or 2 of the same numbers on both lines it means there are less numbers that will win it for you,
But, if the 1 or 2 are drawn, they are more likely to get you a winner than any other number

Edit: I didn't realise you changed the last number on both lines

spoonface

fabbydabby wrote: »

Surely it would be better to have totally different numbers on each of the two lines of the game, maximising your spread of numbers chosen for your money?

You're lacking a basic grasp in probabilities when you say this. Even if there is some link between the numbers on the two quickpicks chosen, this has zero effect on the probability of you winning the Lotto (holding the assumption that the picking of the balls is truly random, I sure hope it is).
Yes, you could pick 1,2,3,4,5,6 and 1,2,3,4,5,7 and it would make no difference. Spread doesn't matter here. Yes everybody would be flabbergasted if 1,2,3,4,5,6 came up as the winning ticket but then again if you win with any set of numbers you should be flabbergasted because the odds were millions to one against that happening to you.

Personally I think the odds are too bad on the Lotto and I play the Dubai Duty Free draws instead which are only 5000 to 1 and represent much better value as I see it - the prize money isn't frittered away on small-wins, National Lottery overhead or charity and every draw guarantees one winner. You'd be better off saving up your Lotto play money and once or twice a year play the Dubai draws instead, that's what I do myself.


.

fabbydabby

But, if the 1 or 2 are drawn, they are more likely to get you a winner than any other number

OK, I see your point here alright.

So you're saying that having duplicated numbers in your lines has absolutely no impact on the expected payout from playing the lottery then?

What about the smaller prizes though. If none of my line 1 numbers are drawn would it not be better to have 6 totally different numbers on line two?

ball

fabbydabby wrote: »

OK, I see your point here alright.

So you're saying that having duplicated numbers in your lines has absolutely no impact on the expected payout from playing the lottery then?

Pretty much

red_fox

For the small prizes, say your two sets of numbers differ by one number only, then you have 6c4 + 5c3 ( = 25) combinations of four numbers, any combination of four from line one, and any combination of four from line 2 that includes the different number (i.e. a combination of 3 from remaining 5 repeated numbers). So in a particular draw you'd have a smaller chance of winning something.

However the expected value of your winnings will be the same. (you're less likely to win but if you do you're more likely to win more - if both lines were the same then you'd win half as often but when you did you'd win twice as much (for the small prizes, not the jackpot))

Finally if the two lines share two or fewer numbers the probablility of winning some prize in any given draw is the same as if they were all different.

fabbydabby

However the expected value of your winnings will be the same. (you're less likely to win but if you do you're more likely to win more - if both lines were the same then you'd win half as often but when you did you'd win twice as much (for the small prizes, not the jackpot))

Right. That makes sense to me. But does this not beg the question then that if you have (for example) 4 winning numbers on one line and the same 4 numbers on the next you should be entitled to two prizes?

And are you?

Obviously not the case with the jackpot since each winner takes a cut but what about the smaller prizes where (say) 4 numbers gets you 20 quid. Would having these four numbers twice get you 40 quid?

Thanks for the replies everyone by the way!

SteelyDanJalapeno

If you consider the qp ticket as a whole and not as seperate lines, and then compare this to a ticket which you chose the numbers on,

if the qp has 2 lines with 3 numbers coming up twice compared to your own chosen numbers with no duplicates,

then yes i believe the chance of winning with your own chosen ticket is greater, as you have 2 chances, on your own ticket.

red_fox

I'm not certain of the rules, but I think the lines are considered seperate even if they are on the same ticket, but you can only win once per line. So two lines with the same winning four numbers should get two prizes. And two lines with the same winning six numbers should each get an equal share in the jackpot, no extra winnings for you if you're the only person who won, but if you shared the jackpot with one other you should get two thirds instead of one half.

fabbydabby

Well explained. Thanks.

blackbetty69

did anyone do it the derren brown way? dyin to know would that increase chances of winnin.. ya iv only done a few qps in my life and didnt have much confidence in the numbers i was shoveled

JackieChan

Blackbetty,
I think the fundamental flaw of the Derren Brown theory on doing the lottery in some collective form is this: The lottery is random.

The number of balls in a jar, or the weight of an animal are something that can be measured in a precise way, so this is not something random.
For example,you can stare at a glass of balls and break it down in to sections and mentally approximate how many are in each section and in turn give an estimate for the jar.

I (yes, without proof I know) would expect that with more and more estimates, there would be close to a normal distribution, with a mean that would tend towards the actual answer.

Again the difference is that there is a right answer,there is no right number to choose in the lottery.

PS: And yes I have noticed the same issue of 2 or 3 numbers repeated on two line quick picks a lot!

henbane

If quickpicks on the same ticket didn't allow for duplicates then they would definitely not be random. As each 6 numbers in a quickpick is random, then it is entirely conceivable that the same two sets of six could appear on the same ticket. Random does not mean different, it means random. All of this depends on the quality of the National Lottery's RNG but that is independently audited so there is no reason to assume it's bent.

ball

Can you believe, after talking about this yesterday, a friend of mine found out today he won €400k on a syndicate.


Back to the drawing board

MathsManiac

henbane wrote: »

If quickpicks on the same ticket didn't allow for duplicates then they would definitely not be random. As each 6 numbers in a quickpick is random, then it is entirely conceivable that the same two sets of six could appear on the same ticket. Random does not mean different, it means random. All of this depends on the quality of the National Lottery's RNG but that is independently audited so there is no reason to assume it's bent.

Indeed, it would be very surprising if one did NOT regularly see duplicate numbers on the two lines.

In the 42 ball game, the probability that two quickpick panels will be completely distinct is (36C6) / (42C6), which is only 0.37. That is, you expect to see at least one shared number 63% of the time. By a similar calculation, there's a 20% chance that you'll see 2 or more shared numbers.

Eliot Rosewater

An analogy could be drawn with birthdays. If you select a random group of 60 or so people your are nearly guaranteed to find 2 people with the same birthday I believe. Just because the selection pool is large does not mean the chances of picking two the same are small.

In any case, "betting is a tax on idiocy," eh? :pac:

Being serious though. The very fact that bookies exist and continue to be financially stable indicates a net gain in revenue for them which indicates that the average punter loses. Its all very logical.