after a run of heads, and the temptation is to believe that tails is somehow now ‘due’ so that the proportion gets balanced out – this is known as the ‘gambler’s fallacy’ and is a psychological bias that (from personal experience) is rather difficult to overcome. But the coin has no memory – the key insight is that the coin cannot compensate for past imbalances, but simply overwhelms them by more and more new, independent flips.
