A stopping time with respect to a sequence of random variables "X"1, "X"2, "X"3, ... is a random variable τ with the property that for each "t", the occurrence or non-occurrence of the event τ = "t" depends only on the values of "X"1, "X"2, "X"3, ..., "X"t. The intuition behind the definition is that at any particular time "t", you can look at the sequence so far and tell if it is time to stop. An example in real life might be the time at which a gambler leaves the gambling table, which might be a function of their previous winnings (for example, he might leave only when he goes broke), but he can't choose to go or stay based on the outcome of games that haven't been played yet.