Statistical independence is a term you will hear when the subject of probability theory come up. It’s a term that many gamblers may not be aware of, but they may indeed know what it is. Statistical independence means that the outcome of one event, has absolutely no bearing on the outcome of the next, and perhaps the best example is that of flipping a coin. When a coin is flipped, there are 2 possible outcomes, heads or tails. There is exactly a 50% chance that the coin will land on either the first time it is flipped. Let’s say that heads was the outcome of the first flip and it’s now time to flip the coin again. There is still a 50% chance of the coin landing on heads again, and again, and even again ad infinitum. This is because there is always a 50% chance of the coin landing on heads, as one flip has no bearing on the other.

## Statistical Independence in Betting Systems

Statistical independence is often overlooked where betting systems are concerned, and all too often assumptions are made that if there is one outcome of a game once, then the chances of the opposite happening next are higher, and this is simply incorrect. Betting systems that alter the size of the bets, can cut the house edge and make the game a little less one sided, however systems that fail to take into account statistical independence are intrinsically flawed.

## The Gamblers Fallacy

Many betting systems are fine examples of what is known as the gambler’s fallacy. The gamblers fallacy means that, should one set of results appear, i.e a run of heads when a coin is flipped, that at a future stage it is certain that the exact opposite will occur. For example, if a coin was flipped 10 times and all 10 resulted in heads, then the next result is likely to be tails, however, the coin is an object with no memory of landing on heads 10 times and the 11th time the coin is flipped it is just as likely to be heads as it is tails. Perhaps the most noted ambassador for the gamblers fallacy was Jean le Rond d’Alembert the French mathematician. Despite being recognized as a brilliant statistician, sadly he will always be remembered for his work on betting systems that simply failed to take into account statistical independence.