In simple words, it is a state of mind which is mistaken. It also goes by the name of the Monte Carlo fallacy and the maturity of chances. A gambler believes that if a particular result is repeated frequently, it is likely to happen more. In reality, any outcome in a gambling game depends entirely on luck and chance and is not influenced by things that have happened in the past.
When a matter is described as independent of historical outcomes, it is known as statistically independent. The fallacy or error is prevalent among gamblers who are often trapped under a belief that the next outcome will come favourable. For instance, if the dice have been rolling a number less than six for some time, the gambler will believe that it is likely to give above seven.