Hi,I am sorry, but, for the fourth time, your “law” is provably false. We can calculate, via the probability theory, that the larger the number of the lower the probability that the H an T are equal.

And Mr Al is equally wrong in arguing that it converges at infinity. A series that starts at 1/2 and is monotonically decreasing cannot converge to 1! In fact, for an infinite number of trials, the probability of an equal number of H and T is infinitesimal.

Bob

Not sure what you are saying with your first statement.

It is interesting though that with your second statement starting with "And MrAl..." sounds like it is just the opposite of what i am saying. I am saying that if you generate random numbers 0 through 10 and add up the numbers and divide by the number of times you generated these samples that the average would get closer and closer to 5.

So for heads and tails calling heads 1 and tails 0, that would mean that if you tossed a lot of times the more you tossed the closer the sum divided by the number of times would be 1/2. So i dont know what you mean by 'converting to 1'. or whatever you are saying there. What that means is that for a very large number of tosses the number of heads would equal the number of tails very closely, and it seems logical that as you toss more and more each single contribution becomes less and less important, much like a low pass filter with a very long time constant, and so once we get near the 1/2 way point it would start to fluctuate less and less from that mean.

This is another case of "try it and see". On the computer i tis easy to generate pseudo random numbers, sum the results of N samples, and divided by N. The result will be the mean of the allowed random numbers (like for integers 0 through 10 the mean is 5).

To state that it would get 'farther' from the mean does not make any sense to me, but i cant be sure what you are saying because you seem to think that something will somehow converge to '1' when i dont think i said that or implied that.

I could easily post some experimental results to show how this works.

A really quick example would be the first 17 digits of pi:

3.1415926535897932

Add them up and divide by 17 and we get 4.7647 approximate. The mean would be 4.5 which is close already.