Understanding variance

While the average result was just under a four unit increase in bankroll, the difference between the best (+38 units) and worst (-30 units) outcomes is substantial. As a bettor it is important to understand variance and be aware that a 4% edge doesn’t guarantee a 4% profit. With this simulation of 100 bets, 90% of the time a bettor can expect a return of between -12 units and +20 units. A 10 unit drawdown (from your starting bankroll) can be expected around 20% of the time, however just 2% of the time a bettor will experience a 20 unit drawdown. Interestingly, 32% of the time a bettor can expect to be down after 100 bets, despite a 4% edge on every bet. If we increase the bettor’s edge to 10% (true probability of 55% for a wager at 2.0), a loss occurred 13% of the time after 100 bets. The chance of a drawdown of 20 units or more was just 0.4%. Of course, as the edge increases, the likelihood of a bad run decreases, but what happens when the number of wagers is increased to say 5,000. The chart below shows the first scenario above (52% true probability, betting at odds of 2.0) simulated 10,000 times.