OT: OzLotto Randomness

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Imagin the seven balls being withdrawn one at a time out of 45 numbered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


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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



"Sylvia Else"
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** 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



Re: OzLotto Randomness


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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.


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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



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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"

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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


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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
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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


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Is there more than one OzLotto draw a week?

Sylvia.

Re: OT: OzLotto Randomness


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Forget that, I misread your original posting.

Sylvia.

Re: OT: OzLotto Randomness


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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
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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




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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


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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"

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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


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Er, hardly.

The chance of any given sequence, whether consecutive or not, is the
same as the chance of any other given sequence. But that's a different
thing entirely.

Sylvia

Re: OT: OzLotto Randomness



 
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what are the other forms of sequence?


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Re: OT: OzLotto Randomness



"terryc"
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** Anything you like - does not have to follow any rule like these do.

 2,4,6,8,10,12  ....

 1,3,5,7,9,11,13 ...

 1,3,5,11,13,17 ....


....  Phil









Re: OT: OzLotto Randomness


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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.


Re: OT: OzLotto Randomness



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Actaully, the PRNG is typically determined by the regulator. In
Queensland, that was Knuth, now its Mersenne-Twister. Visit the OLGR
website, its all documented there somewhere.

Re: OT: OzLotto Randomness


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All I said was MWC was the most used PRNG - which it is. In this regard
I said nothing about specific regulators or any choice they may have
made. I ruled out no other possibilities, so please don't put words in
my mouth.

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