For some purposes, the [weak law of large numbers][1] is superior to the strong law.  This is one of those purposes.  The weak law is **quantitative**, unlike the strong law.  

Let $X$ be a random sample of size $n$ from a given distribution with mean $\mu$ and variance $\sigma^2$. Then for any $\epsilon>0$
$$
P(|X-\mu| \ge \epsilon) \le \frac{\sigma^2}{ n \epsilon^2}
$$

  [1]: http://mathworld.wolfram.com/WeakLawofLargeNumbers.html