HOME DIGITAL BOOKS ANALYSERS BRIGHT IDEAS ARTICLES SNIPPETS LINKS STOCKS ABOUT
 
SEARCH SITE
SUBSCRIBE
 


  ARTICLES
Law of Averages
by Allan N Wilson


A general idea that many people hold goes something like this:

The longer a series of chance events goes on, the more likely it is that things will "even up". For example, the longer you drive a car, the more likely you are to have your share of flat tyres. The more children you have, the more likely you will have an equal division of boys and girls (assuming an even number of children). The longer you flip a coin, the more likely the number of heads and tails will equalise.

Actually, the latter two examples are identical, if certain simple assumptions are made. In the case of the coin, we shall suppose that the coin is "fair", so that on any one flip, head and tail are equally likely. In the case of the children, we shall rule out twins or other multiple births, and shall assume that the parents do not have any tendency to produce children of one sex as preferred to the other. Of course there is the practical consideration that one can flip a coin a lot more times than a woman can bear a child. So, it is more natural to use the coin for purposes of illustrating large samples. But for small samples, there is something unique about each child, which makes the family a marvellous illustration for stressing certain points.

3.1 The Law of Large Numbers

I have never actually seen a statement of a law of averages as such in any book on probability or statistics. However, I have seen references to a law of large numbers, which in rather loose language could be expressed this way: the greater the number of trials, the smaller will be percentage fluctuations away from the expected (or average) number of successes, but the larger will be the absolute fluctuations. Note carefully that this deals with fluctuations about the expected number of successes, and not with the expected number itself.

Let's see how this applies to our example of children in the family (or to the flipping of a coin). We shall consider the various boy-girl combinations that can occur in successively larger families, starting with two children, and ranging on up through 4, 6, 8, 10, 100, 10,000 and 1,000,000. In the last three cases, we shall, of course, switch over mentally from children to coins. We shall find these examples very instructive.

At each birth, there are two possibilities for the sex of the child, B (boy) or G (girl). In a two child family, therefore, there are 2 x 2 = 4 possible orders in which the two children are born. These are indicated in the following table.

DISTRIBUTION OF BOY-GIRL BIRTHS IN TWO-CHILD FAMILY
 
BOTH BOYS
EQUAL DIVISION
BOTH GIRLS
 
B-B
B-G/G-B
G-G
CHANCE
1/4
2/4
1/4
AS A %
25%
50%
25%

Now we move on to the four child family. There are 2 x 2 x 2 x 2 = 16 possible orders. (A more compact way to represent this is 2-4 which means 2 to the power 4, or the produce of four 2s). These 16 possibilities tabulate as in the following table.

DISTRIBUTION OF B-G IN FOUR CHILD FAMILY
4B
3B and 1G
2B and 2G
1B and 3G
4G
B-B-B-B
B-B-B-G
B-B-G-G
B-G-G-G
G-G-G-G
 
B-B-G-B
B-G-B-G
G-B-G-G
 
B-G-B-G
B-G-G-B
G-G-B-G
 
G-B-B-B
G-B-B-G
G-G-G-B
 
   
G-B-G-B
   
   
G-G-B-B
   
1/16
4/16
6/16
4/16
1/16
6 ¼%
25%
37½%
25%
6 ¼%

Notice that in the four child family, there is less chance of an exactl

Date Posted: 30-May-1999

Excerpt from "The Casino Gamblers Guide" by Allan N Wilson

 
 
Click here to login to Subscribers area Make urbino.net my homepage Add urbino.net to my favourites Check your Hotmail Search Google

  MORE ARTICLES


Savvy Casino Managers Are On to Something:
It’s Not A Myth: Size and Length Are Critical
Do You Hear the Flushing? Money Down the Drain
Is Your Casino’s Valet Service Driving Guests Away?
Casino Train the Trainer Program Has Unexpected Benefit – It’s Life Changing
Are Gamblers Really That Bad?
Here’s A Great Idea for Better Casino Customer
Casino Mystery Shoppers and Gaming
Lunar Poker Hits the USA
Casino Competition Will Become More Complex
Understanding or Confusion with Online Poker and Gaming
Casino Marketing Will Be Disrupted By Facebook Graph Search for 5 Important Reasons
Comment Cards Are the Dinosaurs of Casino Customer Feedback
Competition, Competition, Competition Will Be
Simple Things Make A Huge Difference
Are You in Casino Customer Service Training Hell?
Create Fun Unique Casino Special Events
Critical Success Factors For Asian Casino Developments
Secrets to Catching Big Fish
The World Has Changed and Casinos Need the Competitive Advantage of Real-Time Customer Feedback
Marketing Challenges for the Global casino Industry in the Year of the Dragon and Beyond
Casino Marketing in Good Times versus Bad Times
S.M.A.R.T Service Standards Help Casinos Create Outstanding Gaming Experience
Coupons, Groupons, and Daily Deals
A Global Communication Challenge
Money Talks – Techniques for Improving Guest Service
How to Grow Gaming Revenue in an Economic Downturn
White Tigers, White Lions and Casinos
Catch the Casino Ripple With Stellar Guest Service
Team Selling – Team Hosting in the Casino Industry
Casino Marketing Misses the Mark
ICATS = “An Incredibly Successful Casino Promotion”
Crank Up Service to Help Casino Guests Take A Break
Casino Credit without Risk
Little Bets Can Pay Off In Big Way

show more
 
 
HOME | DIGITAL BOOKS | ANALYSERS | BRIGHT IDEAS | ARTICLES | SNIPPETS | LINKS | STOCKS | ABOUT
SUBSCRIPTIONS

© Urbino.net 2017. All rights reserved.
Site by ojo online