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What are the odds...


coldel

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...bought two lucky dips for Euro Millions online - the numbers I got for the two lines are identical except the last one which is one number different.

 

I sent a mail to the national lottery, they replied saying that it was just chance and that their software is effectively infallible. I haven't taken the time to work it out but to select 5 random numbers from 1-50 and 2 random numbers from 1-11....then, to repeat that and get the same four numbers (which are the lowest four of the five) and the fifth one is one number higher, followed by the same two numbers randomly from 1-11....well they are pretty long odds.

 

I replied saying I am not happy with their response :thumbdown:

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It a little annoying as I put in that I wanted to play the numbers Tues and Fri for a few weeks, so its cost twenty quid to effectively play the same numbers twice. But yeah, its more to the point that they check it out, which I dont think they have, I didnt send them my login name or anything so they cant have actually checked the transaction to make sure it was working ok - I guess its more me just wanting them to properly do their job instead of fobbing me off with some stock answer out the library :surrender:

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It a little annoying as I put in that I wanted to play the numbers Tues and Fri for a few weeks, so its cost twenty quid to effectively play the same numbers twice. But yeah, its more to the point that they check it out, which I dont think they have, I didnt send them my login name or anything so they cant have actually checked the transaction to make sure it was working ok - I guess its more me just wanting them to properly do their job instead of fobbing me off with some stock answer out the library :surrender:

 

Yeh, fair one. Its perfectly feasible that this is a genuine software error.

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...bought two lucky dips for Euro Millions online - the numbers I got for the two lines are identical except the last one which is one number different.

 

I sent a mail to the national lottery, they replied saying that it was just chance and that their software is effectively infallible. I haven't taken the time to work it out but to select 5 random numbers from 1-50 and 2 random numbers from 1-11....then, to repeat that and get the same four numbers (which are the lowest four of the five) and the fifth one is one number higher, followed by the same two numbers randomly from 1-11....well they are pretty long odds.

 

I replied saying I am not happy with their response :thumbdown:

 

Million to one chances crop up nine times out of ten.

 

Douglas Adams.

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You do understand how a lottery works, right? There is an equal chance of all numbers being drawn, so it really doesn't make much difference if you have two almost identical tickets. If anything you've got a better chance of winning decent money as whatever you do win has a good chance of being doubled up now.

 

If it does bother you that much then I'd probably not use their Lucky Dip next time, and just make your own numbers up.

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Dan, yes I do understand how the lottery works, but you are missing the point completely, the odds of the system drawing those numbers are astronomical, I was just concerned something seriously had gone wrong.

 

Just to clarify, your statement is incorrect, there is not an equal chance of the numbers being drawn, in fact it is almost impossible to make a truly random number generator.

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I guess having done a stats degree, numbers bother me when they do not make sense. I put it through on the system and I got two lines of seven numbers that were identical apart from one number which was one digit higher ie line one it was 32, line two it was 33. The odds of this occuring i would guess are something like 15,000,000-1.

 

Naturally I thought something was up, so I emailed the lottery to say I think there may have been an error. They didnt check my transaction they just stated it wasnt, without checking anything. That is what I am narked about. Being fobbed off.

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Naturally I thought something was up, so I emailed the lottery to say I think there may have been an error. They didnt check my transaction they just stated it wasnt, without checking anything. That is what I am narked about. Being fobbed off.

Thats the problem these days - the customer service team are so far removed from any kind of real "do-er" (coder, designer, etc) of the systems that they dont even know where to start asking the questions, let alone get answers. Far easier for them to just say "computer is right" and hang up on you :thumbdown:

 

That does sound very odd, epescially as the only different digit is the last one and its only one higher than the previous line. However I guess (and I havent done stats/probabilities for a long time) the actual probability of both numbers coming up is the same (they are both just a randomly generated number and just as likely to come up as each other or any other number combination), but having them one after the other is a very very long shot. OK so thats not quite true if you know how computers and random number generators really work, but when they designed the random number generator they wont have coded it as just doing +1 :lol:

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Naturally I thought something was up, so I emailed the lottery to say I think there may have been an error. They didnt check my transaction they just stated it wasnt, without checking anything. That is what I am narked about. Being fobbed off.

Thats the problem these days - the customer service team are so far removed from any kind of real "do-er" (coder, designer, etc) of the systems that they dont even know where to start asking the questions, let alone get answers. Far easier for them to just say "computer is right" and hang up on you :thumbdown:

 

That does sound very odd, epescially as the only different digit is the last one and its only one higher than the previous line. However I guess (and I havent done stats/probabilities for a long time) the actual probability of both numbers coming up is the same (they are both just a randomly generated number and just as likely to come up as each other or any other number combination), but having them one after the other is a very very long shot. OK so thats not quite true if you know how computers and random number generators really work, but when they designed the random number generator they wont have coded it as just doing +1 :lol:

 

Yes a huge misconception that things are random. Calculators use formula to 'generate' random numbers but they aren't. By even having the lottery numbers drop into the machine in numerical order is already inducing bias, there will be weight variations in the balls etc etc, nothing is truly random ;)

 

But yeah on this occasion, the odds are pretty much non existant that it could have happened at random, that you draw a set of numbers, then draw the same again expect the last one which is one digit higher. I might even sit down and try remember probability class and work it out...

 

edit: worked it out, odds are of getting the same first four numbers from 50, then the next number one digit higher, followed by the same two numbers from the draw from eleven balls is = 116,531,800 to 1

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I guess that what you worked out as 116,531,800 to 1 is actually the very same odds as winning with all numbers correct.

I think it is wrong that you should include in the calculations that the last number was incremented by 1 as this is still a unique number and has exactly the same chance as any other. I think (check my math) this would bring it down to 2330636 to 1.

Of course if your first 4 and both stars had came out up you would have won the same prize twice (£2,824.30 x 2 according to Wiki estimate) so overall you were at no disadvantage.

Given the sheer volume of tickets sold these oddities probably crop up more often the one might think.

Just checked the odds of getting 4 main and 2 stars correct and it comes out at 517919 to 1. And if I can get my head around this, this is exactly what you have done (if you imagine that you first line was what the machine drew and your second was what you drew). Cant quite get my head round why this figure is not 116,531,800 / 50 as I originally thought.....

My head hurts. :surrender:

Probability is a complicated beast.

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Pretty sure it has to be 116m odd, as I am not selecting a random 5th ball from the remaining 46 balls, it has to be the one incremental to the one selected in the other draw...to do the numbers you need to look at the draw probabilities

 

so 5/50 x 4/49 x 3/48 x 2/47 x 1/46 (this is the debatable one, as my different ball was one digit higher therfore can only be one of the 5 actually drawn you could assume that if it was random then it changes the whole formula to start from 4/50) for the main draw, but, I also got exactly the same bonus numbers so that an additional 2/11 x 1/10 multiplied against the other calc which brings up 116m :thumbs:

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I don’t have the mathematical dexterity to argue the point about the last main ball but I still cant agree.

Imagine the last main ball was one lower and not one higher. You would then have just swapped the lines over (making one ball still 1 higher) and still calculated the odds at 116m to 1.

But we know the odds are now lower as there 2 possible numbers that could have been selected to effectively achieve the same odd looking outcome.

I am no expert but I can’t understand why the last number being a consecutive number as being significant when it has the same chance as any other number left in the draw.

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Because the first line is random, then the goal is to achieve the same except for the last ball which has to be specifically one number higher than the one drawn on the other line, the odds of it being that specific number is 1 from the remaining 46. Its a condition of the probability. We have to assume that the first line has been drawn and we are looking for OtherDrawBall+1 in the second draw. Easiest thing is to write it out and convert it into numbers

 

Ball 1: Looking for five specific numbers from the draw so 5/50

Ball 2: Looking for four specific numbers from the draw minus one ball drawn so 4/49

etc

Ball 5: Looking for one specific number (which is the other draw ball +1, this is a condition of the probability) so 1/46.

 

If Ball 5 was any random ball from remaining balls it would be 1 or 46/46 not 1/46 which shortens the odds as you pointed out.

 

...didnt mean this thread to get so long - just a random post I put up after being fobbed off :lol:

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"Ball 5: Looking for one specific number (which is the other draw ball +1, this is a condition of the probability) so 1/46. "

 

Now I agree.

And its indeed the exact same odds as getting.

1 2 3 4 5 1 2

1 2 3 4 5 1 2

or

1 3 5 7 9 1 3

2 4 6 8 10 2 4

or indeed any 2nd line of numbers that have a 'relationship' to the first line.

This is all getting a bit random but :thumbs: for the interesting conversation.

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Not getting into the probability side of things, I work in IT and we use random number generators when we generate SSL certificates for web servers. If we ever found out something that is meant to be random, isnt, we would investigate. Given the facts raised by OP I am amazed that they havent investigated, image if there was a bug somewhere in thier software and the numbers where not being generated randomly all the tickets that have been sold over the years.

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Yeah I know, although I got a follow up email out of the blue just now from a customer services director saying that they are 'investigating' the case :snack:

 

To be honest my initial exasperation has long since passed and I am not too bothered. Mind you if it was a glitch, and hundreds of other people buying EM tickets at the same time got the same numbers as me I would be narked if they came in and shared the money with them all :lol:

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It may be worth contacting some trashy newspapers as it's something that should not happen and points to an error in their number generating software (it may be just chance but papers like to make a story out of things). I'd imagine someone would run with it and would even calculate the odds for you.

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Not getting into the probability side of things, I work in IT and we use random number generators when we generate SSL certificates for web servers. If we ever found out something that is meant to be random, isnt, we would investigate. Given the facts raised by OP I am amazed that they havent investigated, image if there was a bug somewhere in thier software and the numbers where not being generated randomly all the tickets that have been sold over the years.

 

You work in IT and you dont know that a computer is unable to generate a truely random number?

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Even if computers cannot generate truly random numbers they can generate a very close approximation unless you now everything about the way the system generates them.

E.g. Calculations since last reboot, time since last reboot, keystrokes since a specific time, cpu usage time against idle etc. there are a number of variables that can be incorporated into the random number generator calculation to make it almost truly random (to everyone except the software developer).

This is why the Lotto is drawn using a mechanical device that not only produces random numbers which rely on chaos theory but can be appreciated as random to the general public.

As coldel has already said there are factors that make the draw machine not truly random but I think this would have been picked up statistically by now and the bias corrected or another solution sought.

I think coldel’s situation is due to the fact that the numbers are as random as possible. To quote “AK350Z†who quoted “Douglas Adams†“Million to one chances crop up nine times out of ten.â€

I presume this translates to “nobody reports things which happen all the time (like two lines of numbers with no relation to each other which happens often), but when you get something which seems odd you just have to tell someoneâ€

Anyway very interesting.

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Even if computers cannot generate truly random numbers they can generate a very close approximation unless you now everything about the way the system generates them.

E.g. Calculations since last reboot, time since last reboot, keystrokes since a specific time, cpu usage time against idle etc. there are a number of variables that can be incorporated into the random number generator calculation to make it almost truly random (to everyone except the software developer).

This is why the Lotto is drawn using a mechanical device that not only produces random numbers which rely on chaos theory but can be appreciated as random to the general public.

As coldel has already said there are factors that make the draw machine not truly random but I think this would have been picked up statistically by now and the bias corrected or another solution sought.

I think coldel’s situation is due to the fact that the numbers are as random as possible. To quote “AK350Z†who quoted “Douglas Adams†“Million to one chances crop up nine times out of ten.â€

I presume this translates to “nobody reports things which happen all the time (like two lines of numbers with no relation to each other which happens often), but when you get something which seems odd you just have to tell someoneâ€

Anyway very interesting.

 

I think Douglas Adams though is somewhat misqouted on this occasion, to draw a line of numbers, then to draw them again with the digit I had different is very highly inprobably. To draw two lines of numbers which have no relation is very highly probable. Again it comes back to the hypothesis you are testing rather than post calculating the probability of drawing those numbers. The probability of drawing 6 random numbers in the lottery is 100% (so more than 9 out of 10!) the probability of drawing 6 preselected numbers is something like 13m to 1.

 

I guess if the odds of their computer system making an error are higher than the odds of 116m to 1 then 'the odds are' are it was a freak occurance rather than a computer error :lol:

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I guess if the odds of their computer system making an error are higher than the odds of 116m to 1 then 'the odds are' are it was a freak occurance rather than a computer error :lol:

If it was anything other than a pure coincidence then a developer will be having their P45 handed to them :lol:

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