# computerised random number generation & infinity

would be a ‘rare’ event.
while i agree with your comment with the set of all the numbers being selected repeatedly.
i am refering to actual single numbers being selected more times than any other numbers.

certain numbers are selected more frequently.
this is a result of real science... it is not a theory it is evidenced.

why is it that the suggestion of the result having no bearing on the equation/process ?

scientific method would suggest there is bias to give a correlative result of similarity.

in 'theory' there should be no difference
yet, by choosing certain numbers, because those numbers come up more often, it gives you more chance of getting those numbers

i was at one stage looking at chaos theory to explain the situation.
then i was looking at mechanical process Vs computer process.

i wanted to see what mathamaticians & computer software engineers thought.

thanks thus far for your time and consideration

while i agree with your comment with the set of all the numbers being selected repeatedly.
i am refering to actual single numbers being selected more times than any other numbers.

certain numbers are selected more frequently.
this is a result of real science... it is not a theory it is evidenced.
What specific numbers are selected more often?

I'm aware of Benford's work.
In this thread, I see a mixing of randomly selected numbers and ordered sets of numbers generated by human schemes.
Returning briefly to lotteries, human prediction introduces a bias when selecting birthdates which form a restricted set of choices. Example:a 2-digit number as part of a winning result cannot be larger than 12, 31, 18, or 20.

What specific numbers are selected more often?

One occurs more often as the most sig dig in many natural sets.

This is Benford's law.

I'm aware of Benford's work.

... ?

your grasp of my question seems a little loose.
Example:a 2-digit number as part of a winning result cannot be larger than 12, 31, 18, or 20.

these are NOT numbers that are chosen by the selection process to draw a winning set.
these are numbers(you have suggested as birthday number possible sets) chosen by those seeking to purchase a ticket as a form of personal number preference.

maybe you sounded out the wall in your own thought and so your rendering down my question to try and avoid saying
"i dont know".

... ?

your grasp of my question seems a little loose.

these are NOT numbers that are chosen by the selection process to draw a winning set.
these are numbers(you have suggested as birthday number possible sets) chosen by those seeking to purchase a ticket as a form of personal number preference.

maybe you sounded out the wall in your own thought and so your rendering down my question to try and avoid saying
"i dont know".
You missed the point. Any lottery that draws 2-digit numbers will draw say from 01 to 80. The person betting on a birthdate, limits his chance of winning when the higher numbers are drawn.

...and they are more likely to share their prize with other winners.

You missed the point. Any lottery that draws 2-digit numbers will draw say from 01 to 80. The person betting on a birthdate, limits his chance of winning when the higher numbers are drawn.
No, this is not how probability works.

Any set of numbers is as likely to win as any other (in a fair lottery).

For a lottery requiring 7 numbers from 1 to 80, the odds are 1 in 16,010,650,656,000 (80 x 79 x 78 x 77 x 76 x 75 x 74).

Counterintuitive as it may seem, you can happily choose 1,2,3,4,5,6,7 for your numbers, and it will turn up as often as any other set.

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No, this is not how probability works.

Any set of numbers is as likely to win as any other (in a fair lottery).

For a lottery requiring 7 numbers from 1 to 80, the odds are 1 in 16,010,650,656,000 (80 x 79 x 78 x 77 x 76 x 75 x 74).

Counterintuitive as it may seem, you can happily choose 1,2,3,4,5,6,7 for your numbers, and it will turn up as often as any other set.
All numbers of a set are winners only IF you bet all numbers.
Consider a lottery where the player selects 5 2-digit numbers prior to a drawing with a popcorn machine randomly spitting out 5 2-digit numbers, ranging from 00 to 99. The player wins if his selection matches those drawn, regardless of order.

The player selects his ‘lucky’ birthday numbers, mm-dd-yy-yy,
with mm 1 to 12, dd 1 to 31, yy 19 to 20 and 20 to 99.
The probability of winning numbers for players using this system will be less than for those who select from the full range of 00 to 99.

The probability of winning numbers for players using this system will be less than for those who select from the full range of 00 to 99.
No it won't.

The chance that 00 will come up as one of the 5 balls is 5 in 100*.
The chance that 01 will come up as one of the 5 balls is 5 in 100*.
The chance that 02 will come up as one of the 5 balls is 5 in 100*.
...
The chance that 97 will come up as one of the 5 balls is 5 in 100*.
The chance that 98 will come up as one of the 5 balls is 5 in 100*.
The chance that 99 will come up as one of the 5 balls is 5 in 100*.

*It's actually slightly less, it's 5 x (1/100 +1/99+1/98+1/97+1/96), but the point is it's the same for every single number ball.

In other other words: the probability of the sequence 00,01,02,03,04 being the winner is exactly and precisely the same as the probability for any five numbers - such as 11,33,55,77,99 - or any other 5 numbers you care to pick.

He could happily bet the numbers 01,02,03,04,05 as many lotteries as he wants, knowing that his numbers are as likely to win as any other 5 numbers.

Full stop.

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Looking at it a different way:
Say you decide to choose from all the numbers between 0 and 99.
Say you pick 08, 11, 23, 37, 41, 69.
What are the odds that number will win if you play it week after week?
Each week, the odds are the same: 1-in-16 trillion.

I decide to choose from only numbers 0 to 20.
I pick 02,04,07,11,17.
What are the odds that number will win if I play it week after week?
Each week, the odds are the same: 1-in-16 trillion.

But what if you decide to let a die pick your numbers for you? (use a 100-sided die) Once chosen, you will use those numbers every time.
You roll the die five times, and use the five numbers it rolled. Random, right?
OK, it rolled 23, 08, 31, 17, 26.
Even though you choose from all the numbers from 0 to 99, the actual choices you made were all under 50 - no wait, they were all under 40. No wait, they were all under 32!
Have you just killed your odds of winning the lottery?
No, the odds are the same: 1-in-16 trillion.

BTW, it doesn't matter if you keep your numbers the same from week to week (as above), or change them. you could choose
00,01,02,03,04 for week 1, then
05,06,07,08,09 for week 2, then
10,11,12,13,14 for week 3, etc.
In any single draw, any five numbers has the same chance as any other five numbers.
Even if you repeat the single draw multiple times.

I have not read all the posts to this Thread. My apologies if some person has alrady posted remarks similar to the following.

From RainbowSingularity Post 45
The computer in theory randomly selects from a known range

yet when looking at the results, some numbers are chosen more often.

some numbers seem rarely chosen.
First: I am not sure how a computer randomly selects numbers from a range.

Second: Consider selecting randomly 200 times from the range 00 to 99 (Assuming you guide the selection process by some process known to be random).

If each number was selected exactly twice, one would surely question that the selection was random.

Hence you would expect a random selection to select some numbers more than twice and some numbers less than twice.

Similarly, if you randomly selected 1000 times from the range 00 to 99, you would not expect each number to be selected exactly 10 times.

Looking at it a different way:
Say you decide to choose from all the numbers between 0 and 99.
Say you pick 08, 11, 23, 37, 41, 69.
What are the odds that number will win if you play it week after week?
Each week, the odds are the same: 1-in-16 trillion.

I decide to choose from only numbers 0 to 20.
I pick 02,04,07,11,17.
What are the odds that number will win if I play it week after week?
Each week, the odds are the same: 1-in-16 trillion.

But what if you decide to let a die pick your numbers for you? (use a 100-sided die) Once chosen, you will use those numbers every time.
You roll the die five times, and use the five numbers it rolled. Random, right?
OK, it rolled 23, 08, 31, 17, 26.
Even though you choose from all the numbers from 0 to 99, the actual choices you made were all under 50 - no wait, they were all under 40. No wait, they were all under 32!
Have you just killed your odds of winning the lottery?
No, the odds are the same: 1-in-16 trillion.

BTW, it doesn't matter if you keep your numbers the same from week to week (as above), or change them. you could choose
00,01,02,03,04 for week 1, then
05,06,07,08,09 for week 2, then
10,11,12,13,14 for week 3, etc.
In any single draw, any five numbers has the same chance as any other five numbers.
Even if you repeat the single draw multiple times.
You are explaining the probability of a 10-digit number appearing randomly from a population of 100 2-digit numbers.
My point is the probability of the player winning for any 2-digit number he selects.
Considering each 2-digit number:
01-12 wins, 13-99 loses, 01-31 wins, 32-99 loses,...
Doesn't the player lose more often than win, because of restricting his choices?

My point is the probability of the player winning for any 2-digit number he selects.
Now I'm not sure what scenario you are describing.

For a lottery, as being discussed, no set of numbers is more or less likely than any other.

Counterintuitive as it may seem, you can happily choose 1,2,3,4,5,6,7 for your numbers, and it will turn up as often as any other set.
My ex wife had a "system" for picking winning lotto numbers... She tried explaining it to me. I confess I didn't pay much attention. But I then asked her why doesn't she just pick 1,2,3,4,5? She said, "Do you know what the odds are of that coming up? I laughed and said, "yes - do you?".

She refused to accept that it was exactly the same as any other pre-selected set of 5 numbers.

My ex wife had a "system" for picking winning lotto numbers... She tried explaining it to me. I confess I didn't pay much attention. But I then asked her why doesn't she just pick 1,2,3,4,5? She said, "Do you know what the odds are of that coming up? I laughed and said, "yes - do you?".

She refused to accept that it was exactly the same as any other pre-selected set of 5 numbers.

your discussion is different to my discussion.

some concepts are like this

What's the second number on the top-row? I cannot see it. :-(

Correction, it's two. ☺