A LITTLE PROBLEM

Sep 16, 2003 9:05 AM

Imagine, if you will, a special party thrown by Keno Lil for 20 or 30 keno managers from all over the state! Imagine further, that as hostess, Lil is responsible for all of the hats belonging to all of the keno managers.

During the party, Lil becomes, well, slightly tipsy, and can't seem to remember which hat belongs to which keno manager. After the party, Lil proceeds to hand out hats at random to all of the departing managers. The question is, what are the odds that at least one keno manager has received the right hat?

Or to put the same problem another way, if you took a set of keno balls numbered 1 through 80, put them in a bowl and started drawing them, counting as you draw, what are the odds that the number on at least one ball will match the order in which it is called? (For example, the ninth ball drawn being the ball numbered 9, or the twelfth ball drawn being the ball numbered 12.)

The odds in favor of either of the occurrences above are rather surprisingly, about 2-1. You can even try the same experiment yourself at home with a deck of cards. Shuffle thoroughly and deal the deck face up while counting "Ace of clubs, two of clubs, three of clubs...etc" up through the kings of all four suits. In about two of every three runs through the deck, you will get a match! (You probably know someone who will bet you even money that you can't do it!)

This little problem in probability was proposed and solved by a mathematician named Montmort in the year 1708. You can read about it in a great little paperback book called "Lady Luck" by a man named Warren Weaver, published in 1963. I've owned several copies of this book, the last one purchased at a used bookstore for 35 cents!

Many of you have written in asking about the basics of statistics and probability, and this book will give you a great start. Some of the chapter titles will give you some idea of the scope of the book, and what a value it is. Chapters include Mathematical Expectation (What you expect to win), The Law of Averages, (The REAL law of Averages), Binomial Experiments, (Pascal's Triangle), The Law of Large Numbers, Rare Events, Occurrences and Coincidences, and many more.

Any of you out there who either are interested in gambling for recreation, or who gamble seriously and do not have a background in mathematics should read this book! It is written with the layman in mind, and although it does contain some formulas, they are not necessary to the understanding of the book's contents. Almost any fair sized bookstore should either have a copy in stock or be able to order it for you.

Well, that's it for now. Good luck! I'll see you in line!