For some purposes, the weak law of large numbers 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 $\epsilon>0$ $$ P(|X-\mu| \ge \epsilon) \le \frac{\sigma^2}{ n \epsilon^2} $$