  The weak law of large numbers states that where each trial has an expected value of \(\mu\), for any arbitrarily small real numbers \(\epsilon \gt 0\) and \(\delta \gt 0\), there is some finite number of trials \(n\), such that for all \(m\) greater than or equal to \(n\), with probability at least \(1-\delta\), the gambler's average gains for the first \(m\) trials will fall within \(\epsilon\) of \(\mu\). In other words, in a long run of similar gamble, the average gain per trial is highly likely to become arbitrarily close to the gamble's expected value within a finite amount of time. So in the finite long run, the average value associated with a gamble is overwhelmingly likely to be close to its expected value.