SA lottery - nobbled?

[classic33]

I was thinking along those lines too!

Maybe there are hundreds of them which have each run a thousand times or so? In that case you could be talking about low millions of draws. The chance of a particular draw once in all of that time would be reduced from billions-to-one to maybe tens-or-hundreds-of-thousands-to one?

Then you would have to look at the question "What IS an odd-looking draw?" There are clearly quite a lot of possibilities, which reduces the odds further...

Consecutive rising numbers separated by 1... 1-6, 2-7... 15-20. 15 sets.
Consecutive falling numbers separated by 1... 20-15, 19-14... 6-1. 15 sets.
Consecutive rising numbers separated by 2... 1-11, 2-12... 10-20. 10 sets.
Consecutive falling numbers separated by 2... 20-10, 19-9... 11-1. 10 sets.

And so on. I reckon you could come up with a hundred or so sets of numbers which people would find odd. Now we are perhaps talking of hundreds-or-thousands-to-one - still unlikely, but no longer astoundingly unlikely!

Odds of that sequence of numbers coming up/being drawn being given as 42,000,000 to 1.

https://news.sky.com/story/south-af...-draw-produces-numbers-5-6-7-8-and-9-12149669

 

[Accy cyclist]

You’d hate it. Too far south, isn’t it?

True. I haven't been south of Bolton in nigh on 20 years!🧐

 

[ColinJ]

Odds of that sequence of numbers coming up/being drawn being given as 42,000,000 to 1.

Approximately...

If my 47 year old recollection of how permutations and combinations work is correct then it is (50! x 20) / (45! x 5!) which is 1:42,375,200.

If the order of the first 5 balls were significant then it would be 120 times less likely, 1:5,085,024,000.

I'm sure that if I am wrong then @si_c or one of the other forum mathematicians will soon be along to correct me!

 

[classic33]

Odds of that sequence of numbers coming up/being drawn being given as 42,000,000 to 1.

https://news.sky.com/story/south-af...-draw-produces-numbers-5-6-7-8-and-9-12149669

Approximately...

If my 47 year old recollection of how permutations and combinations work is correct then it is (50! x 20) / (45! x 5!) which is 1:42,375,200.

If the order of the first 5 balls were significant then it would be 120 times less likely, 1:5,085,024,000.

I'm sure that if I am wrong then @si_c or one of the other forum mathematicians will soon be along to correct me!

They were only slightly out on the odds then?

 

[ColinJ]

They were only slightly out on the odds then?

I'm a bit of a pedant when it comes to numbers... Think of Spock in ST and Data in STNG!

 

[classic33]

I'm a bit of a pedant when it comes to numbers... Think of Spock in ST and Data in STNG!

There's only a slight difference between 1:42,000,000 and 1:5,085,024,000 though.

 

[si_c]

Odds of that sequence of numbers coming up/being drawn being given as 42,000,000 to 1.

https://news.sky.com/story/south-af...-draw-produces-numbers-5-6-7-8-and-9-12149669

So about the same as the UK lottery then.

It's not that unsurprising really, unlikely but not unexpected if lottery games are played over a long enough time. What would be really curious would be if they came out in that order - the odds of that happening are much smaller, but definitely non-zero.
Edit: for the powerball, about 1 in 3billion.

 

[ColinJ]

There's only a slight difference between 1:42,000,000 and 1:5,085,024,000 though.

Indeed, just a matter of 5! (5 x 4 x 3 x 2 x 1; 120)...

 

[Accy cyclist]

So i take it there's more chance of Accrington Stanley winning the 'European Cup' three years in a row than winning the damned thing?🧐

 

[si_c]

So i take it there's more chance of Accrington Stanley winning the 'European Cup' three years in a row than winning the damned thing?🧐

No, you're more likely to win the lottery. That's the difference between fantasy and reality

 

[ColinJ]

No, you're more likely to win the lottery. That's the difference between fantasy and reality

Did you just edit your post?

I got an alert saying that you had quoted me, but by the time I checked you were quoting Accy instead!

 

[ColinJ]

I altered the 'European Cup' to European Cup. Thinking surely everyone knows it's now called the Champions League.

That's interesting... for some reason it seems to have thrown the forum software out, unless si_c edited his post too?

 

[ColinJ]

I altered the 'European Cup' to European Cup. Thinking surely everyone knows it's now called the Champions League.

I wouldn't have a clue! I watched England win the World Cup in 1966 but then went to a grammar school where football was banned and rugby was played instead. I lost interest in football after that (but didn't get interested in rugby!)...

 

[Accy cyclist]

That's interesting... for some reason it seems to have thrown the forum software out, unless si_c edited his post too?

Hey,don't worry about it Colin. It's only a bit of fun.

Have you been south of Bolton by any chance recently?🤔

 

[si_c]

Approximately...

If my 47 year old recollection of how permutations and combinations work is correct then it is (50! x 20) / (45! x 5!) which is 1:42,375,200.

If the order of the first 5 balls were significant then it would be 120 times less likely, 1:5,085,024,000.

I'm sure that if I am wrong then @si_c or one of the other forum mathematicians will soon be along to correct me!

In terms of lotteries the probability of a given set of numbers is a function of the number of balls and the selected number of balls.

So it's 1 in the total number of combinations, this is calculated as 59! / (6! * 53!) in the case of the UK lotto - or about 1 in 45million. For the SA powerball example you have an initial pick of 5 balls from 45, and one powerball from 20. To calculate this we would use the permutations instead - we want one very specific permutation of these balls, so we calculate the number of permutations ( 45! / 40! ) and multiply by the 20 possibilities of the powerball to get the estimate I mentioned above.