frequency of any Pick 3

[Bertil]

Each number in a Pick 3 game has a probability of 1 per 1000 of being drawn. Suppose 10 000 drawings have been run, then each number would come up 10 times on average, but there will be a standard deviation from this mean. Would it be 2.87 or 3.0 or some other value and if so, by what formula would it be calculated? E.g. what would be the odds of finding 1 vs 20 times for one number?
Stig Holmquist

 

[GillesD]

Pick 3 standard deviation

For a large number of draws for a Pick 3 lottery, the distribution of numbers (from 000 to 999) will fairly uniform.

I did not calculate the theorical value but after generating quite a few Pick 3 numbers (over 1.5 million), the average should be very near 499.5 and the standard deviation around 288.67, a little more than your estimate.

 

[Bertil]

I'm having difficulties understanding what you did. If you generate more than 1.5 million numbers and get less than 500
three digit integers you must have counted the number of digits
generated and lost a few integers.

If you generate 500 integers there will be about 300 not yet drawn, which is evident from the std.dev. It shows that two
std.dev. is greater than 500 because so many integers are missing.

I was looking for a theoretical formula .

Stig Holmquist

 

[Beaker]

The average frequency should be 500 for each position but the average of the numbers over millions of draws will be 499.5.
I'm not sure looking at the average and SD of this lotto is going to help you. but I could be wrong.

The distribution of the numbers is not Normal. If you decompose into 3-digits the sum of those digits is a better approximation.

 

[Bertil]

frequency of Play 3 numbers

My confusion about std.dev. for Play 3 numbers has beencleard up by a local High school teacher of math. He convinced me that the problem is a simple binomial type. Thus the std.dev. for the mean 10 must be square root of 10=3.16. For 500 it must be
square root of 500=22.36.

Bertil