Numbers can lead to even more confusion involving the nature of chance. Let's say we flipped a coin 100 times and it lands 60 heads to 40 tails, which is quite likely to happen with such a small sample. A common misconception is that the number of tails should even out during the next 100 flips by landing 60 to 40. Each flip is totally independent and a fair coin has neither a memory of past events nor a moral sense of fairness. Let's say you find someone who will flip a coin one thousand times or one thousand people flipping a coin all at the same time. After those first 100 flips you see that there are 60 heads to 40 tails for a difference of 20 and the proportional difference is 20%. After 1000 flips you find there are now 510 heads to 490 tails. The difference of 20 has remained the same but the proportion of heads is down to 51% for a difference now of 2%. Now, as you can see, It is much closer to its theoretical value of 50%. This concept is known as the Law of Large Numbers and was an important discovery for, most notably, the insurance industry and gambling houses. For pollsters, it has given them the confidence to make projections from population samples.

These links will explain more:

Probability and the Law of Large Numbers
...... Karl Dahlke
...... BookRags.com

Law of Large Numbers and Simulations
… AlgebraLAB, Mainland High School

Applets
...... The Heart of Mathematics
...... Introduction to the Practice of Statistics

First discovered by Jacob Bernoulli and sometimes referred to as Bernoulli's Law its misunderstanding has led to the ruin of many a gambler as this article about the Italian lottery shows.

Number 53 brings relief to Italy

Coincidence