A Cute Little Demo

[Bodarc]

This little program is a good visual of the law of large numbers. Start it and notice the bar chart a the bottom as it jumps around. Just for fun, let it run all night and look at it tomorrow.

http://www.mathsisfun.com/data/quincunx.html

[Bodarc]

For anyone who took the time to run the program for a day, you might notice that in the beginning, the columns jumped haphazardly but after so many trials, they leveled out into a normal curve. This is the same thing that happens when you start out playing blackjack. At first it is random and anything can happen but as the number of hands increases so the shape of your play begins to resemble the normal curve. If you'd like to read more along these lines here is an excellent article that explains it in detail. (I can't believe it. The site has closed down and it was such a good article. I am lucky I saved it in my library. It doesn't even show up on wayback.) http://www.blackjackstartup.com/N028.htm

The little bouncing ball program is nothing but Pascal's Triangle without the numbers and if the random number generator in the program is accurate and you run it enough times, your column totals should approximate the ratio as follows:
1 14 91 364 1001 2002 3003 3432 3003 2002 1001 364 91 14 1

How do you know this? Go here and read about Pascal's Triangle. http://www.mathsisfun.com/pascals-triangle.html
Go down 15 rows and get the answer.

If you put on a race with 8 runners and you'll give a case of beer to the first three to finish. How many possible combinations of eight people taken three at a time are there? That's easy, go to Pascal's little Triangle and move down 9 rows and across 4 columns (The first row and the first column are zero) and you'll find the answer is 56. Check it with your formula:

This and much more is answered by the little bouncing balls.

It is interesting reading and who knows where the links will carry you next.