Bulgarian Lottery

[YouBunt2]

Identical lottery numbers drawn twice in a row

17 September 2009 | 12:34:29 PM | Source: SBS staff and agencies
lottery

No-one won the first draw, but a record 18 people picked the correct numbers second time around

An investigation is under way in Bulgaria, after the same national lottery numbers were drawn twice in the space of four days.

Bulgaria's lottery - known as 'The Tantalizer' is drawn live on television, in front of a studio audience, and independent inspectors.

Punters were stunned when the same balls - 4, 15, 23, 24, 35 and 42 - came up in consecutive games on 6 and 10 September.

Experts say the odds of the same lottery numbers being drawn two weeks in a row are one in four million.

'Freak coincidence' claim

But the company that runs the game insists the results were a freak coincidence, pointing out that the numbers were drawn in a different order the second time around.

The government has launched an inquiry into possible game fixing.

"Yesterday a commission was established to inspect those numbers, [we] will have the answers towards the end of this week," said Svilen Neykov, Bulgaria's Minister of Physical Education and Sport.

Nobody won the first lottery draw on 6 September, but on 10 September a record 18 people picked all six numbers

My Question is why are the odds 1 in 4 million? why should the odds be any different to any other draw? i.e. if 1,2,3,4,5,6 came up then the chance of the same numbers coming up next week is the same is it not?
since the draws are mutually exclusive the odds should not increase?
Any staticians about?

 

[Azza]

Derren Brown at it again...

 

[Sinque]

If it was fixed then surely the person who fixed it would have tried to stop the other 17 winners to get it all?

 

[Azza]

If it was fixed then surely the person who fixed it would have tried to stop the other 17 winners to get it all?

Or the person needed 17 other people to help rig it. And they all wanted in on it.

 

[V4NT0M]

It's a separate probability you're looking at. The probability of those numbers coming out at any one time are the same but the probability of them coming out consecutively are more unlikely.

Think of it like this, if you roll a dice the probability of any one number is 1 in 6, but if you to roll 6 consecutively each time you roll a six the probability that the next roll will be a six diminishes.

 

[phil675]

If someone was going to rig a lottery they wouldn't do it as obviously as that surely.

 

[V4NT0M]

If someone was going to rig a lottery they wouldn't do it as obviously as that surely.

That's what they want you to think.

 

[pingwing]

HAX!

 

[qwerty]

Think of it like this, if you roll a dice the probability of any one number is 1 in 6, but if you to roll 6 consecutively each time you roll a six the probability that the next roll will be a six diminishes.

fail

 

[Teknobry]

It's a separate probability you're looking at. The probability of those numbers coming out at any one time are the same but the probability of them coming out consecutively are more unlikely.

Think of it like this, if you roll a dice the probability of any one number is 1 in 6, but if you to roll 6 consecutively each time you roll a six the probability that the next roll will be a six diminishes.

Previous results have no bearing on future ones.

You roll a dice, odds are 1/6 of getting a six.

Roll it again, odds are still 1/6 of getting a six, previous result has no effect on future probability.

 

[fez]

The odds of getting a 6 on a 6 sided die are always 1/6 even if you have rolled 20 6's in a row. Thats the whole idea of the lottery, there is just as much chance of the same balls coming out two weeks in a row as any other combination.

 

[D D Danneh]

Previous results have no bearing on future ones.

You roll a dice, odds are 1/6 of getting a six.

Roll it again, odds are still 1/6 of getting a six, previous result has no effect on future probability.

True, but the odds of getting two 6's in a row, are 1/6 x 1/6, so 1/36.

Since the odds of winning are 1 in 13,983,816 - 1 / (6/49 x 5/48 x 4/47 x 3/46 x 2/45 x 1/44), the odds of getting the same two combinations in a row are 1/13983816 x 1/13983816, which is 1/195,547,109,921,856, or 1 in nearly 200 trillion.

HOWEVER, this is the same for EVERY combination of numbers. There's a 1 in 200 trillion chance of getting 1,2,3,4,5,6 and then getting 5,7,32,39,41,45, but that doesn't mean it can't happen, and indeed, one of those 1 in 200 trillion chances will occur. It does seem a bit of a coincidence it happening one week after the last, but there was no less chance of that happening than anything else.

Also, the article did it's numbers wrong. Even if the bulgarian lottery used 1 to 42 (it can't use less because the highest number was 42), the odds would still be about 1 in 27.5 trillion.

 

[Aod]

The odds of getting a 6 on a 6 sided die are always 1/6 even if you have rolled 20 6's in a row. Thats the whole idea of the lottery, there is just as much chance of the same balls coming out two weeks in a row as any other combination.

yes, the result of the next roll is completely unaffected by the result of the previous one.

however, the chance of rolling a SPECIFIC pair of results is considerably lower.

when working out the probability of rolling two separate results you add the probabilities (1/6 + 1/6 = 1/6) but when calculating the probability of two specific results you multiply them (1/6 * 1/6 = 1/36)

therefor, the probability of getting a SPECIFIC set of numbers on five dice (or 20 dice, or 30,000,000 dice) is not one in six.

<edit> Damnit D_D_Danneh!

 

[Rainmaker]

This is, admittedly, one of life's little curios. But it's hardly breath taking, surely? After all the odds of it happening are a quoted one in four million, versus one in fourteen million odds of you picking all six numbers (provided you play of course ).

So for every person who wins, it was actually almost four times more likely that the numbers would be the same as last week than them winning?

I think...

EDIT: Just seen D_D_Danneh's post. Ignore this one lol

 

[D D Danneh]

This is, admittedly, one of life's little curios. But it's hardly breath taking, surely? After all the odds of it happening are a quoted one in four million, versus one in fourteen million odds of you picking all six numbers (provided you play of course ).

So for every person who wins, it was actually almost four times more likely that the numbers would be the same as last week than them winning?

I think...

Nah, the "experts" got their numbers wrong. The odds of getting the same numbers twice in a row are 1 in 195.5 trillion, so they're 14 million times more likely to win than the same numbers coming up again.

 

[Rainmaker]

Nah, the "experts" got their numbers wrong. The odds of getting the same numbers twice in a row are 1 in 195.5 trillion.

Indeed. Suffice to say I wish I'd had a recurring bet with William Hill:

Same six numbers drawn for two consecutive lottery draws. £1 stake.

I'd love to have seen their faces this week at those odds!...

 

[YouBunt2]

It's a separate probability you're looking at. The probability of those numbers coming out at any one time are the same but the probability of them coming out consecutively are more unlikely.

Think of it like this, if you roll a dice the probability of any one number is 1 in 6, but if you to roll 6 consecutively each time you roll a six the probability that the next roll will be a six diminishes.

good lad, thats exactly what i was thinking in my head but could not put it into words.
And i did maths stats at A-level, amazing how much you forget!!!

 

[YouBunt2]

True, but the odds of getting two 6's in a row, are 1/6 x 1/6, so 1/36.

Since the odds of winning are 1 in 13,983,816 - 1 / (6/49 x 5/48 x 4/47 x 3/46 x 2/45 x 1/44), the odds of getting the same two combinations in a row are 1/13983816 x 1/13983816, which is 1/195,547,109,921,856, or 1 in nearly 200 trillion.

HOWEVER, this is the same for EVERY combination of numbers. There's a 1 in 200 trillion chance of getting 1,2,3,4,5,6 and then getting 5,7,32,39,41,45, but that doesn't mean it can't happen, and indeed, one of those 1 in 200 trillion chances will occur. It does seem a bit of a coincidence it happening one week after the last, but there was no less chance of that happening than anything else.

Also, the article did it's numbers wrong. Even if the bulgarian lottery used 1 to 42 (it can't use less because the highest number was 42), the odds would still be about 1 in 27.5 trillion.

Voted best explaination!

 

[Rorschach]

Nah, the "experts" got their numbers wrong. The odds of getting the same numbers twice in a row are 1 in 195.5 trillion, so they're 14 million times more likely to win than the same numbers coming up again.

Your maths is wrong. What you have effectively calculated is the odds of getting a specific set of numbers (eg 1,2,3,4,5,6) 2 weeks running. What you need to work out is the probability of getting any combination of numbers 2 weeks in a row.

Going back to your dice example, the chances of getting any 2 numbers in a row is 1/6. This is because when you first roll the dice, you get a number between 1 and 6, which we call x. On the 2nd roll, the chances that the result is equal to x is 1/6. The same applies to the lottery, therefore odds of getting the same set of results 2 weeks in a row is approx 1/14M.