## How to use the value betting simulator

Here you can see what kind of results you can make value betting with RebelBetting.

You can see the expected average profits, and also the probability of reaching higher and lower.

Enter a low number of bets, say 500, and click Simulate a few times. You can see pretty wild swings because of the high variance caused by a few streaks.

Then enter 3000 bets, and see that the profit chart is now much smoother because of lower variance.
This is because of two statistical tendencies:
the law of large numbers and regression to the mean.

Please click "Explain these numbers" at the bottom of the page to get more details.

## How to read the chart

The chart consists of two lines and three filled areas.

The colored line shows the profit.

The darker straight line shows the expected profit (or expected value - EV) of your strategy, based on the average odds and yield you entered.

The three colored areas are the confidence intervals, or the probability that your results will be inside a particular range.

The top area is showing the 5% top results you could expect.

The middle area is showing the most common range of outcomes, 68% of all results fall within this area (within one standard deviation).

The bottom area is showing the 5% worst results you could expect. 95% of the time, your results will be better than this.

Hover over the chart to get a tooltip showing the exact profit you could expect.

## For statistics geeks

We calculate the p-value using a one-tailed t-test because our hypothesis is that we're profitable.

We consider p-value below 0.01 to be "highly statistically significant", but feel free to use a stricter threshold.

(A p-value of 0.05 still means 1 out of 20 punters betting randomly on these odds would reach this outcome purely by chance -
not exactly a reliable betting strategy).

We use a baseline yield of 0% as the null hypothesis. It would be more accurate to use the average bookmaker margin, around -6%,
which would make it easier to reach statistical significance. But using 0% is standard practice and makes it easier to compare with other results and services.

The expected maximum drawdown is calculated using the algorithm in the paper *"On the Maximum Drawdown of a Brownian Motion"* by Malik Magdon-Ismail et al.