OT: OzLotto Randomness

[Phil Allison]

"Sylvia Else"

Phil Allison wrote:
"David L. Jerkoff"
OT thought for the day...
Bought my ticket for tomorrows $90M draw and was told they are the
winning numbers, so I'm sitting pretty, but I digress...
Ever since I can remember I've always noticed something with the
"random" machine picked numbers.
The numbers always seemed quite spread out, no matter how many times
I've played the random pick over the years. Occasional clumps within,
but always appers to be one number at either end etc
I would have expected sooner or later to hit upon some numbers that were
all grouped at one end or the other, or in the middle etc, but I can't
ever recall that happening.
Anyone else noticed that?
Just wondering if it's truly random, or whether it uses some other
algorithm designed to "appear more random" to the average punter who
might be a bit miffed if the machine spitted out all numbers under 10
for example?
Any statisticians in the house that can calculate the odds of all 7
numbers being within a window of say 15 in a random pick?


** Forget all that probability stuff from your HSC Maths ??

OK :

Imagin the seven balls being withdrawn one at a time out of 45 numbered
balls.

Ball 1 can be any number.

Ball 2 must be within a group of 15 numbers of which ball 1 is a member.

So, there are 14 candidates for ball 2 in the group.

No, there are up to 28 candidates - 14 either side of the first ball -
except that there are fewer if the first ball is less than 15, or more
than 31.

After the second ball has been chosen, the number of remaining candidates
is determined by how far apart the first ball and second ball are; if the
second ball is at the other end of a 15 grouping, then there are only 13
candidates remaining. On the other hand, if the second ball is adjacent to
the first, then there are 26 candidates remaining - 13 either side of the
pair, but again subject to end effects.

So this probability calculation is nothing like as simple as you're
suggesting.

** My calc was a bit simplified.

But there is a group of 15 consecutive numbers at the end of the picking and
the 5 balls chosen are all members of that group.

Do it your way and tell us the answer.

Bet you have to write a program for it.


..... Phil