How many games does it take to conclude that you're a winning player? Is your ROI reliable? Knowing your confidence interval is the first step to determining if you're a profitable player.
Your confidence interval is determined by two things: your win percentage and your sample size. As you can see from this chart, having a large sample size is the only way to make conclusions about your actual ROI.
1 - Confidence Interval Chart
To interpret this table, first, find the number of games you've played and your winrate. Say you've played 500 games, and you've won 55% of them. Looking at the table, We can determine that there's a 95% chance that your winrate is at 55% +/- 4.4% (between 50.6% and 59.4%). As such, we can not empirically conclude that you are winning player, as you need a winrate of at least 52.5% to be a winning player. If you were to maintain a 55% winrate for 2,000 games, there is a 95% chance that your actual winrate would be 55% +/- 2.2% (between 52.8% and 57.2%). As such, you would be pretty certain that your true ROI falls somewhere between 0% and 9%.
2 - What is my Winrate?
To calculate your winrate, use the following form. Convert ROI into Winrate.The equation for this calculator is (where r = your ROI):
Easy peasy, lemon squeezy!
