Why Expected Value (EV) Is The Only Thing You Need To Know To Make Millions

5 min readOct 4, 2021

If you pay attention to how some of the biggest players in crypto talk — think Alameda with its two famous Sams — you’ll have noticed that they often use the term Expected Value, or EV for short.

Today, I’ll explain to you what this means and, most importantly, how you can make use of it yourself to take both your trading and investment strategies to the next level. If you understand it properly, you’ll see that EV is the only thing you need to know in order to make more money than you can imagine. Everything else — TA, FA, sentiment analysis and so on — is only an extra tool to help you calculate EV, which is the one number that does all the work.

EV is essentially a way of calculating the value of situations that have multiple possible outcomes. The concept comes from probability theory, but in terms of finance and trading, it’s simply the way you calculate the future value of a trade or investment. If you know how to do this, then literally the only thing you need to do is to make decisions that have the highest expected value and you’ll be profitable.

But how do you calculate the future value of something? The key here, which every trader will tell you is also the key to trading in general, is to think in terms of probabilities. Let’s take the example of a completely random coin toss: for a certain price, you get to flip a coin and, if the coin comes up heads, you win $100, and if it comes up tails, you don’t win anything.

How do you decide the value of that coin toss? When you’re buying a car, for example, you know for certain what you’ll get and (hopefully) how much it’s worth, but with this coin toss, you only know that you have a chance to win something. This is where EV comes in: you take the value of every possible outcome, multiply each with its probability and sum up the resulting values.

This is extremely simple for the coin toss, as you only have two possible outcomes with 50% probability each:

EV of coin toss = $100 * 50% + $0 * 50% = $50

So the EV is 50$, meaning that you should be willing to pay anything less than $50 for a single coin toss. If someone offers you that coin toss for $40, that’s a deal you should take, since you’ll make an average of $10 on it (which is 25% of your initial investment). Note that I used the word average: of course, you have a 50% probability of paying $40 for the coin toss only to have it come up tails, losing your initial investment. But the point is that, if you can buy a huge number of those coin tosses for $40 each, you’ll end up making a ridiculous amount of money.

You probably see how this is just the same as trading. When you create a trade setup, the point isn’t that you have to make money with that particular trade, but rather that you have a strategy with positive EV. That way, if you keep implementing the strategy, it will make you money in the long run, regardless of how any single trade turns out. When you take probabilities and repeat them a sufficient number of times, they effectively become certainties.

Now we can take a more practical and slightly more complicated example, one that directly relates to trading. Think about a situation where Bitcoin is currently at $45k and you believe that it’s very likely to go to $50k in the coming weeks. Let’s also suppose that there’s one support level right at $45k and another one below it at $42.5k, and you want to buy 1 BTC. Where should you place your bids?

Of course, this is a question that you have to use TA to answer, but let’s see how we can answer it based on EV alone, by calculating the EV of each of the two possible situations: placing a bid right at the current level and placing a bid at the lower support level.

If you place your bids at $45k, they will definitely get filled. So, if they do and BTC goes to $50k, the EV is $5,000, as that’s what you’ll make from the price increase. But let’s say that you place your bids at $42.5k, and that there’s only an 80% chance that they will get filled before BTC goes to $50k. The EV would be: EV = $7,500 * 80% + $0 * 20% = $6,000.

Even though there’s a 20% chance that your bids at $42.5k won’t get filled, the EV of placing your bids there is still a whopping 25% higher than if you place your bids at $45k. So, the rational decision is to accept the 20% risk that you won’t make anything and shoot for the higher profit by placing your bids lower. Yeah, it might just happen that they don’t get filled, but you’ll make more money in the long run by following the higher EV approach. That’s how probabilities work.

Needless to say, this example is an extremely simple scenario, and real-life calculations tend to be a bit more complicated, but the exact same principles still apply. Regardless if you’ve got two possible outcomes or hundreds of them, the EV calculation is still the same. And of course, you’re often only able to estimate the probability of each outcome, but the beautiful thing with estimates is that they tend to be very reliable on average, even if you’re way off with any particular estimate.

Here’s another practical example, this time with investing. Let’s say you find a low-cap token that you think has a 10% chance of pulling a 10x in one year, a 50% chance of staying close to the same price and a 40% chance of rug pulling and going to zero.

What would the expected value be if you buy $10k worth of it?

EV = $90,000 * 10% + $0 * 50% — $10,000 * 40% = $5000

So, on average, you’ll make a 50% annualized profit by making investments like that (since the $5,000 you’d make on average is 50% of your $10k initial investment), meaning that it’s a good strategy to follow.

That’s it for today, I hope you now get the gist of what EV is and why it’s important. Basically, as long as you keep making bets with positive EV, you’ll get rich. Sure, you might lose money on the first one, but that’s why you should never go all in on one investment. Even if that one investment has positive EV, it can still end up losing you all your money. Instead, allocate capital responsibly and make sure that you can make as many positive EV bets as possible. Do that and you’ll make it. Simple as that.

Note: there are some technical differences between EV and expected returns, and I’m using those terms loosely in the article above. But these differences don’t matter from a practical perspective: we’re here to get money, not a math degree!