# The Threshold

**Disclaimer : Nothing I say or write should be construed as financial or any type of advice. My posts on sports betting are exclusively for illustrating probability and statistics concepts, using examples from the real world**

Thus far we have talked about The Line and The Rake, we should talk about - The Threshold too

Last week we talked about how the house takes a 10% rake. It’s fairly typical to bet $ 110, to win $ 100 - in most casinos or sports books

Let’s do this intuitively

One risks losing $ 110, to win $ 100. Let’s consider the probability of the team winning to be p, and the team losing to be (1-p)

So, when you set expected gains to 0 (we set it to 0 because we are trying to see how many times I need to win out of 100 times, to at least break even)

(-110 x (1-p)) + (100 x p) = 0

-110 +110p + 100p = 0

210p = 110

p = (110/210) = 52.38%

This is the most important threshold rate in sports betting. For one to make money in the long run, that person needs to win more than 52.4 times out of a 100

Think about this intuitively, right ? Under normal circumstances, if someone says, you win if you get heads, and you lose if you get tails (when flipping a fair coin) - on an average you’d make profits if you get heads more than 50% of the time, and not 52.4% of the time

That difference in 2.4% is because of the Rake. You bet 110 to get 100, and hence the $ 10 rake makes it harder for you to win money in the long run

You can keep increasing the rake and see how your threshold gets worse and worse. Now, instead of 10%, if the house takes a 40% rake, instead of 110, one needs to bet 140 to get a payout of 100

In this case, the above equation leads to a p of 58.3%

Now, one needs to win 59 times out of 100, to make any money in the long run

The house moves the line to optimize betting on both sides and sets the rake - and this drives the number of times you need to win to make profits in the long run

Unless you are Patrick Mahomes, in which case, you can throw drop-dead gorgeous spirals under ice cold conditions - to make money !

Picture Credit : Pro Football Focus