DUPLICATES ARE NORMAL AFTER 4,000 RANDOMLY GENERATED PICK 6, POOl 49 LOTTO NUMBERs
Colin Fairbrother
table 14,000,000 random Pick 6, Pool 49 numbers in about 45 minutes.
A link to the code and a table of the repeats is located here: -
Random Lotto Numbers using the Mersenne Twister
http://lottoposter.com/forum_posts.asp?TID=661&PN=1
Colin Fairbrother
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Colin Fairbrother
====================================================
Hi Colin,
How do you generate your "random" lines, do you:
for the first ball, pick a number between [1-49]
for the second ball, pick a number between [1-49] and discard it, if it is
already picked?
and same principe for the others numbers ?
Thanks for your answer
//
Colin Fairbrother
Random Lotto Numbers using the Mersenne Twister
http://lottoposter.com/forum_posts.asp?TID=661&PN=1
"I ran a simple routine first using the Randomize and Rnd function to
initialize init_genrand() and then making sure for a line each integer
was unique produced 100,000 6/49 numbers in a few seconds using
genrand_real2() which includes 0.0 but excludes 1.0 to give the
following Integer Group, Count and Sort."
Colin Fairbrother
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From the link: -
Colin Fairbrother
===================
You can get the same results by getting a single random number in the range
[1, 13983816].
and see how collisions evolves.
You will need few seconds to produce your stat.
I ran 1000 times a collision checker for 4000 random lines and i get than
in ~54% there is no collision(540), in ~33% there is one collision(332)
in ~11% there is two collisions(107), in 2% (19) three collisions and in 2
cases 4 collisions.
(this depends highly of the random generator quality of course)
and so it gives an experimental probability of 54% to NOT have any
collision.
If you search a little bit on the net for the "birthday problem" you will
find a straight way to compute
"given n random integers drawn from a discrete uniform distribution with
range [1,d], what is the probability p(n;d) that at least two numbers are
the same"
For n=4000 and d=13983816 it gives a probability of 0.4356 to have a
collision, which implies that in 56% there is no collision.
So Colins affirmation that "duplicates are normal after 4000 randomly
generated pick6" can be considered true with a probability of .45 and false
with a probability of .55
Conclude what you want.
KR
//
nigel
This has been discussed here a few times. The break-even number for a
6/49 lottery is 4400 draws I believe, after which you are more likely to
encounter a collision than not.
Evil Nigel
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0pour100 wrote:
>
>
> "Colin Fairbrother" a écrit dans le message de groupe de discussion :
Evil Nigel
===
Yes, I know and you are closely right. It's just a way to ponderate loudly
affirmations of some unfair guys that pretends to know everything.
Colin Fairbrother
combinations are distinct after randomly generating 14,000,000 using
the Mersenne Twister algorithm. See -
Random Lotto Numbers using the Mersenne Twister
http://lottoposter.com/forum_posts.asp?TID=661&PN=1
Do a few runs of 4000 combinations and you will find about 60% have a
duplicate with about 20% to 30% having 2 duplicates.
Colin Fairbrother
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Colin Fairbrother
======================================================
No, it's mathematicaly impossible or your generator if badly used.
With many runs of 4000 combs you must converge to around 43 % with a
duplicate.
I have done the experimentals runs you request on 1000 runs and i got an
experimental 46%.
Do you ever read and attempt to understand what others posters write ?
nigel
I used to know how to calculate the value iteratively in a spreadsheet
so that the appropriate cell in row 4400 contains the value closest to
0.5, but premature senility seems to have eradicated that memory.
I ran a quick trial using Excel's inbuilt rand function. After 100 runs,
36 had contained one or more duplicates. Obviously for such a short
trial the difference isn't significant.
What really caught my attention was that in run 9 the lexographic number
of the first combo was 1 representing 1,2,3,4,5,6.
I know it must have happened many times during all my number crunching,
but that was the first time I'd actually seen it 'live'.
Evil Nigel
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0pour100 wrote:
>
>
> "Colin Fairbrother" a �crit dans le message de groupe de discussion :
Evil Nigel
=====================================
Hi Nigel
If you use the birthday paradox law (wikipedia is your friend), it's very
easy to implement it in spreadsheet.
BR
Colin Fairbrother
at some time ago in this newsgroup of 4400, as far as the likelihood
of a duplicate CombSix in randomly generated numbers is closer to the
mark ie more than 50% chance. After extensive testing I came up with a
figure of 4375. Of course,as in the Bulgarian Lotto game you can get a
duplicate in two draws and not get one in a lot, lot more than 4375.
Random Lotto Numbers using the Mersenne Twister
http://lottoposter.com/forum_posts.asp?TID=661&PN=1
Colin Fairbrother
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Colin Fairbrother
=============================================================
Hi,
We are in a well known area, the math formulas are well known and easy to
understand
http://en.wikipedia.org/wiki/Birthday_problem#Generalizations
using such baggage (and knowing that there is only 13983816 possibilities in
a 6/49 lottery)
it's easy to find that the mark is at 4403. Even the windows "calc" is able
to compute that.
You were kindly advised of your pasts mistakes, and now you claim with a
candid precision
that the mark is at 4375 and you still believe that many experimentals tests
are better than
a proven law.
It is very pathetic; that you the guy so prompt to fire on anyone that
pretends having discovered
some law in the past draw; emits, with so certitudes, so unproof and inexact
results.
Comparing their attitude and your, I am not so sure to say who is the most
mystical. :-D
Nice shot for your first trolling hunt this year..
Colin Fairbrother
integers generated using Mersenne Twister code from a pool of 45 into
2,800 segments.
See
The first segment starts at 1 the second at 5,000 etc.
Testing each segment for 4575 combinations I found 1409 had at least
one duplicate and 1391 had none. ie 1409/2800 * 100 = 50.3%. Testing
for 4550 gave 1391/2800 * 100 = 49.7% with at least one duplicate.
Each test took well less than a minute to run.
The original heading for this post was basically a throw away catchy
line and for most people a rounded number like 4000 is near enough.
However,it appears inadvertently I have wandered into the super voodoo
area for Lotto nutcases such as Ion Salui who don't believe Lotto
draws are independent events and that the history along with distorted
adaptions of the birthday problem calculations can be used
beneficially to win the Lottery. For a debunking article see
ANALYSIS OF LOTTO DRAW HISTORY - THE FINAL WORD
http://lottoposter.com/forum_posts.asp?TID=638&FID=46&PR=3
The birthday problem in a nutshell says on average 23 people randomly
congregated are needed to get at least two people with the same
birthday. Only an upstart puffed up buffoon that has been proved wrong
repeatedly and uses a shared, anonymous email address would think that
any student of mathematics and probability would be unaware of the
birthday paradox, problem etc.
Colin Fairbrother
Colin Fairbrother
Colin Fairbrother
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Colin Fairbrother
=============================================================
Ok, privately, in our exchanges the only one who was wrong every time is
you.
On the current thread, you start at 4000, then at 4375 and now with no shame
4575.
Hope that, every body can see your lack of foundation and the poverty of
your affirmations.
Talking like a pitbull will not change anything to that.
Well, still enough days this year to send others jokes, you are welcome.
//
Colin Fairbrother
this to endure semi-illiterates who think they know everything about
anything and prattle away with pontificating, pompous, pretentious
overtones and an excessive zeal for the accuracy of a probability
calculation which is basically just an indication, due to the wide and
wild divergence from the average. Some would notice how he enjoys
predicting Lotto numbers which is a dead give-away for being a nut-
case.
The results on the 14 million combinations generated using Mersenne
Twister beg the question as to just how accurate are some of the
probability formulas where 13,983,816 is plugged in but where in
actuality only 8,845,381 or 63% are distinct. See
Random Lotto Numbers using the Mersenne Twister
http://lottoposter.com/forum_posts.asp?TID=661&PN=1
For a calculator applying the formula you can replace the 365 with
13983816 here -
http://instacalc.com/?d=UGx1ZyBpbiB0aGUgZGVzaXJlZCBwcm9iYWJpbGl0eSBvZiBtYXRjaCBhbmQgdGhlIHRvdGFsIG51bWJlciBvZiBpdGVtcy4gWW91IG5lZWQgbiBwZW9wbGUgdG8gaGF2ZSBhIG1hdGNoIHdpdGggdGhhdCBwcm9iYWJpbGl0eS4gRnJvbSBbYmV0dGVyZXhwbGFpbmVkLmNvbV0oaHR0cDovL2JldHRlcmV4cGxhaW5lZC5jb20vYXJ0aWNsZXMvdW5kZXJzdGFuZGluZy10aGUtYmlydGhkYXktcGFyYWRveC8pLg&c=cHJvYmFiaWxpdHlfb2ZfbWF0Y2ggPSA1MCV8dG90YWxfaXRlbXMgPSAzNjV8biA9IHJvdW5kdXAoIHNxcnQoLTIgKiBsbigxIC0gcHJvYmFiaWxpdHlfb2ZfbWF0Y2gpKSAqIHNxcnQodG90YWxfaXRlbXMpICkgLy8gaXRlbXMgbmVlZGVkIGZvciBtYXRjaHx8fHw&s=sshssss&v=0.9
Colin Fairbrother