Expected value (EV) is the sum of the probability weighted outcomes.

To explain further, let's use a simple example and assume you have five pieces of paper in a velvet bag, all of them numbered 1-5. If you pull any one number, you will have a 20% chance of choosing any of them. (1/5=.2)

To better visualize this concept, let's run some quick math. We have a 20 percent chance of pulling a 1, 2, 3, 4, or 5.

• 1*.2 = .2
• 2*.2 = .4
• 3*.2 = .6
• 4*.2 = .8
• 5*.2 =  1

If we combine all the outcomes we get a total of 3.

Assume we play a game and we charged \$3.25 to play. If you pulled a 5 out of the bag we paid you \$5. If you pulled a 1 we paid you \$1, meaning you lost \$2.25 etc. So, would you take that bet?

Since we did the math we knew the EV was 3, but we were charging \$3.25 for each pull, so in the long run we averaged +.25  profit a pull. ( .25 cents bought you 1/2 a ramen packet back then btw)

Now let's apply this to Options.

Let’s say we want to buy a 45k call that expires tomorrow. Let’s also say that BTC has a 20% chance of being worth 40k, 42k, 45k, 48k, 50k.

At expiration the 40k, 42k, and 45k will be worth \$0. But the 48k will be worth \$3k, and the 50k strike will be worth \$5k. If we do the math it will look like the following:

• 0*.2 = 0
• 0*.2 = 0
• 0*.2 = 0
• 3,000*.2= 600
• 5,000*.2 = 1000

Sum = 1,600

If the probability weighted the outcome of buying the 45k Call Option is \$1,600.

To wrap up, EV is a helpful statistical measure to predict how profitable a strategy may be and can help you determine if the price of an option justifies its risk profile.