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**posted on**

- David L. Jones

June 29, 2009, 3:14 am

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?

Dave.

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Re: OzLotto Randomness

"David L. Jerkoff"

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Imagin the seven balls being withdrawn one at a time out of 45 numbered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

The chance of picking one of them is 14/44 or 0.318

Similar arguement goes for each of the remaining 5 balls.

So P = 14/44 x 13/43 x 12/42 x 11/41 x 10/40 x 9/39

therefore P = 0.0004254

or 1 chance in 2350

With one draw a week, it means around 45 years until you expect to see such

a close grouping.

..... Phil

Re: OzLotto Randomness

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.

Sylvia.

Re: OzLotto Randomness

Which is OK if you say so, and provide an argument that shows that it

represents either an upper or a lower limit on the probability. As it

stands, it's just a calculation of a probability for a different problem

with no indiciation of how the result relates to the question asked.

That seems the obvious approach anyway. The figure I get is exactly 15

in 7052, or about 1 in 470.

For one draw a week, that's once every 9 years.

Sylvia.

Re: OzLotto Randomness

I wrote one. However...

There are:

39 ways in which the first and last balls extend over 7 numbers.

38 ways in which the first and last balls extend over 8 numbers. The

middle 5 balls can be laid out in 6!/5!/1! different ways.

37 ways in which the first and last balls extend over 9 numbers. The

middle 5 balls can be laid out in 7!/5!/2! different ways.

36 ways in which the first and last balls extend over 10 numbers. The

middle 5 balls can be laid out 8!/5!/3! different ways.

And so on until

31 ways in which the first and last balls extend over 15 numbers. The

middle 5 balls can be laid out 13!/5!/8! different ways.

So the total number of ways of laying out 7 balls such that they extend

no more than 15 numbers is

(39 + 38

*** 6!/1! + 37 ***7!/2! + 36

*** 8!/3! .... + 31 ***13!/8!) / 5!

I can't see any way of simplifying it, but it comes to 96525.

The possible ways of laying out 7 balls in 45 positions is 45379620, so

the odds are 1 in 45379620 / 96525, which is indeed 15 in 7052 or about

1 in 470.

Sylvia.

Re: OT: OzLotto Randomness

On Mon, 29 Jun 2009 13:14:40 +1000, "David L. Jones"

You first need to count the total number of ways that 7 balls can be

arranged in a group of 15 where there is a ball at each endpoint.

Ball 1 - 5 balls in 13 positions - Ball 15

Balll 2 - 5 balls in 13 positions - Ball 16

....................................................

Ball 31 - 5 balls in 13 positions - Ball 45

Then you need to do the same for groups of 14, 13, 12, ... 7.

The total number of possible "clumps" is ...

(31 x 13C5) + (32 x 12C5) + (33 x 11C5) + ... + (39 x 5C5)

The total number of ways you can select 7 balls from 45 is 45C7.

So the chance of a clump of 15 or less is ...

(31 x 13! / 8! + 32 x 12! / 7! + 33 x 11! / 6! + 34 x 10! / 5! + 35 x

9! / 4! + 36 x 8! / 3! + 37 x 7! / 2! + 38 x 6! / 1! + 39 x 5! / 0!) x

42 / (45 x 44 x 43 x 42 x 41 x 40 x 39)

http://www.google.com/search?hl=en&client=opera&rls=en&num25%&newwindow=1&q=%2831+x+13%21+%2F+8%21+%2B+32+x+12%21+%2F+7%21+%2B+33+x+11%21+%2F+6%21+%2B+34+x+10%21+%2F+5%21+%2B+35+x+9%21+%2F+4%21+%2B+36+x+8%21+%2F+3%21+%2B+37+x+7%21+%2F+2%21+%2B+38+x+6%21+%2F+1%21+%2B+39+x+5%21+%2F+0%21%29+x+42+%2F+%2845+x+44+x+43+x+42+x+41+x+40+x+39%29&btnG=Search

http://preview.tinyurl.com/n6xgw9

= 0.00212705615

= 0.2%

= 1 in 500

- Franc Zabkar

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Re: OT: OzLotto Randomness

http://www.google.com/search?hl=en&client=opera&rls=en&num25%&newwindow=1&q=%2831+x+13%21+%2F+8%21+%2B+32+x+12%21+%2F+7%21+%2B+33+x+11%21+%2F+6%21+%2B+34+x+10%21+%2F+5%21+%2B+35+x+9%21+%2F+4%21+%2B+36+x+8%21+%2F+3%21+%2B+37+x+7%21+%2F+2%21+%2B+38+x+6%21+%2F+1%21+%2B+39+x+5%21+%2F+0%21%29+x+42+%2F+%2845+x+44+x+43+x+42+x+41+x+40+x+39%29&btnG=Search

That's around about the figure I would have expected by gut feel.

So if you take say a dozen games a week (fairly common) you'd expect to see

something like that in under a year. Then there's Lotto and Powerball too.

Thanks

Dave.

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Re: OT: OzLotto Randomness

http://www.google.com/search?hl=en&client=opera&rls=en&num25%&newwindow=1&q=%2831+x+13%21+%2F+8%21+%2B+32+x+12%21+%2F+7%21+%2B+33+x+11%21+%2F+6%21+%2B+34+x+10%21+%2F+5%21+%2B+35+x+9%21+%2F+4%21+%2B+36+x+8%21+%2F+3%21+%2B+37+x+7%21+%2F+2%21+%2B+38+x+6%21+%2F+1%21+%2B+39+x+5%21+%2F+0%21%29+x+42+%2F+%2845+x+44+x+43+x+42+x+41+x+40+x+39%29&btnG=Search

If you feel that that doesn't happen, then it suggests that using radom

machine picked numbers is a mistake, and you should instead be using

obviously non-random sequences.

The point being that it doesn't change your chance of winning, but does

change the chance that you'll have to share the jackpot with someone else.

Sylvia.

Re: OT: OzLotto Randomness

Computer generated random numbers are NOT truly random.

I've noticed when playing a lot of online games with randomly generated

loot drop, that at certain times of the day, the drop is consistently

better. I suspect all games rank game drop from lowest to highest value

and the underlying bias moves up and down the scale according to a random

number affected by time of day. N.B. tested over 1,000 drops, so do not

waste your money on Lotto (different number generation mechanism).

Re: OT: OzLotto Randomness

True, you cannot generate truly random numbers in software the pattern

will always repeat eventually. If you know the period of the algorithm

though, you can change the seed before anything repeats.

If you want true random, then you need to do it with hardware, the yanks

used radioactive decay to produce one time tapes for the hot line, and

the poms at least used to use gas discharge tubes for their premium bonds.

Re: OT: OzLotto Randomness

On Mon, 29 Jun 2009 13:14:40 +1000, "David L. Jones"

The chances of your numbers being consecutive are the same as them not

being consecutive.

The only reason you dont recall seing it is because you probably

haven't. I have spend a long time in the gaming and wagering industry

and I can assure you that I have seen numbers being drawn

consecutivley, from a hardware RNG and a ball cage.

Re: OT: OzLotto Randomness

To answer your question:

The "truth" is out there, but Australian lotteries commissions are tight

lipped with the answers.

"Normally" the numbers for a "quick pick" are selected by a Pseudo

random number generator, the seed for which is periodically updated

using a clock or timer input. The most commonly used random number

generator for this purpose is a type called a "Multiply With Carry"

generator.

Imperfections come about when the generator does not have enough "state"

and so not all combinations are possible. It should be possible to check

this with the lottery commissions as if it has been implemented properly

then it makes no difference if everyone knows how it was done. If it was

done badly it may be possible to prove that some historically winning

combinations were

***never***possible to pick with the PRNG, and hence,

every one who had a quick pick in those draws has a valid claim to

compensation.

My experience with Queensland golden casket is that no information is

forthcoming without an FOI application and even then they will obstruct

the process and stall beyond what is supposed to be legal.

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