Let’s twist the example of a single coin toss a little bit and put some money into the mix!

Let’s assume you have a friend called Tom. Tom is very eager to pay you $1 every time you manage to flip heads, and every time you flip tails, you will pay him $1.

How much can you expect to make?

I can hear you scream the answer, but when the random event becomes more intricate (as with trading and business), you will feel the need for a repeatable, concrete formula that allows you to calculate your “expected value” or “profit expectation”.

Let’s summarize our knowledge about the coin toss:

·        There are two possible outcomes (heads or tails)

·        In the previous example, we have figured that the probability of either outcome is 0.5 (50%)

·        If you flip heads, you make $1

·        If you flip tails, you lose $1

Taking this information into consideration, now we can make use of a “profit expectation” formula and calculate the exact amount of profit which we are supposed to expect from the deal you made with Tom.

Profit expectation = (Profit scenario) + (Loss scenario)

Profit expectation = (Profit x Probability of Profit) + (Loss x Probability of Loss)

Profit expectation = ($1 x 0.5) + (-$1 x 0.5) = $0

As can be seen from the results, the mathematical probability of your expected profit in this situation is $0. I think that you already knew it would be so, even before we calculated it. Now let’s skew the numbers a little bit more and see if we can find a way to make money from a coin toss.

At this time, you negotiate with Tom to see if you can make a better deal. The agreement goes like this: if you flip heads he still pays you the same $1, however, if you flip tails you shall only pay him 90 cents. That 10 cent difference has a potential to be a game changer.

Profit expectation = (Profit scenario) + (Loss scenario)

Profit expectation = (Profit x Probability of Profit) + (Loss x Probability of Loss)

Profit expectation = ($1 x 0.5) + (-$0.9 x 0.5) = $0.05

After the new agreement with Tom, every time you flip the coin, you have a profit expectancy of 5 cents.

So statistically speaking, if you toss the coin 100 times, you are estimated to make $5. In order to gain an edge in the game, you “cut your losses short”.

In trading world, one of the methods to have an edge in the market is by “cutting our losses short” with the use of trailing stops.