Correctly understood, this law states the truism 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 .5 chance of a heads result for any given flip.
There are two common ways to misunderstand and misapply this law:
- "If I flip this coin 1000 times, I will get 500 heads results." False. While we expect approximately 500 heads, it is not the case that we will always get exactly 500 heads results. Similarly, getting 520 heads results is not conclusive proof that the coin's true probability of getting heads on a given flip is .52
- "I just got 5 tails in a row. My chances of getting heads must be very good now." False. Many probabilistic events are independent of one another, which means the result of one event does not in nay way influence the outcome of another. Coin flips are independent events. The coin does not magically "remember" what it has flipped previously and self-adjust to get an overall average result. The coin is not "due" for a heads. The probability remains .5 for each individual flip.