Certainty of edge betting profits

Subject to constant betting on positive edge bets, profits are mathematically certain

The law of large numbers

The law of large numbers states that the mean of the results obtained from a large number of trials (bets) will get close to its expected value. This means that if we toss the coin many times, we should expect it to land heads and tails approximately the same amount of times, 50% heads, 50% tails

If we map out the different outcomes and their probability after 1,000 bets, we get the following bell-shaped curve:

With 1,000 bets there is a 7% risk that the distribution of heads and tails will be uneven

The law of large numbers (continued)

With 5,000 bets the risk of an uneven result reduces to 0%