I'm currently gathering data points on sports betting. Each bet is small, only around $5. Depending on the odds that I get each bet will result in +$5~ or -$5~. For example, a 5 bet sample set could be +5, +5.35, +5.8, -5.15, -5.4. That's just an example. I'm interested in the sum of these numbers. In this example, the sum is +5.6.

Obviously a sample size of 5 is not statistically significant so I would not be able to claim that these bets have positive expected value. My question is this. Say I want to be 95% sure that my results are not coincidence. How do I figure out how big a sample size I need for my results to be significant?