| Law Of Averages |
Article Index for Law Of |
Website Links For Law |
Information AboutLaw Of Averages |
| CATEGORIES ABOUT LAW OF AVERAGES | |
| adages | |
|
Simply put, every outcome in a fair game exhibits identical probabilities equal to the underlying probability of the game. In order to understand this it is important to realise that no outcome in a fair game is at any point, in any way whatsoever affected by any other past or future outcome within the game. The formal mathematical result that supports the law of averages is called the Law Of Large Numbers . It states that a large sample of a particular probabilistic event will tend to reflect the underlying Probabilities . For example, after tossing a "fair coin" 1000 times, we would expect the result to be approximately 500 heads results, because this would reflect the underlying 0.5 chance of a heads result for any given flip. Note, however, that while the average will move closer to the underlying probability, in absolute terms deviation from the Expected Value will increase. For example, after 1000 coin flips, we might see 520 heads. After 10,000 flips, we might then see 5096 heads. The average has now moved closer to the underlying .5, from .52 to .5096. However, the absolute deviation from the expected number of heads has gone up from 20 to 96. There are common ways to misunderstand and misapply the law of large numbers:
There are situations in which a very small imbalance in probabilities can lead to a large imbalance in outcomes, contrary to the usual notion of the law of averages. The Gambler's Ruin is one such scenario. GRAPHICAL REPRESENTATION The following graphical representation illustrates one possibility for a game of heads or tails. Notice how the gamblers fallacy is erratic and essentially unpredictable whereas the average will always tend towards the underlying probability of 0.5 in this case. Over 100 random samples Over 1000 random samples |
|
|