Average Properties Become Predictable
The properties of individual parts of a random system, like an individual coin flip, are quite often unpredictable. (See random systems for other examples.) However, if enough coin flips are tallied, approximately half of the flips will show heads while about half show tails.
This principle, that the average behavior of a random system is predictable, is quite general. If enough leaves are measured from the same species of tree, the average leaf length will be extremely similar from one tree to another, even though individual leaf lengths vary widely.
This is the also the basis for opinion polls. If one person is asked a question, not much is learned about the nation's opinion. Now suppose that a news station asks 1000 people the same question, and suppose that 700 respond "yes" while 300 respond "no". This sample is likely large enough that any other group of 1000 people would also split roughly 70/30 on the question, and it can be assumed that this reflects the opinions of the whole nation. (Whenever live subjects are involved, various sources of bias could enter; these have been neglected in this example.)
Exercises to Illustrate Equilibrium
The Big Picture
© Andrew M. Rappe