The law of averages is really the belief that something must happen because it's happened before.

The reality is that if you toss a coin 100 times, it's an even chance that you will get less than 57.75% heads or tails.

If you extended that test to 1000 tosses, it's an even chance that you will get less than 52.133% heads or tails.

If you kept going till 1,000,000 tosses, the odds are that you will not get more than 50.0674% heads or tails.

In other words, the more times you trial an event, the nearer the result approaches the true theroretical probability.

The problem applying this to, say a casino roulette wheel if you are punting red or black, is knowing what every result on that wheel has been in the past which is of course impossible so you do cannot know at what stage any theroetical progression it has reached.

So you've stood there and watched black bob up 15 times in a row and your "law of averages theory" says red MUST be next. Wrong! How do you know red didn't salute 140 times out of the previous 200 spins and black is just "catching up" a bit?