Expected Value

A slight, slight improvement in your decision making can have a huge, huge impact on your long-term success.

Here’s an example to help illustrate:

Imagine I have a coin that’s rigged to come up tails 51% of the time. Would you wager money that it’d turn up tails if I gave you even betting odds? You definitely should!

If you bet $1 per flip, your expected value (EV) is my $1 bet + your $1 bet * 51% chance of winning = $1.02. So with each coin flip, you’re wagering $1 and expecting to win $1.02. That’s a $0.02 gain per flip.

The truly amazing part is it takes just a tiny bit to move from being neutral (a 50% winner) to be a massive, massive long-term winner. If you can make just slightly better decisions, the results compound.

But life isn’t as simple as our coin flip example:

• You don’t always make the same bet. Sometimes, you make a huge bet and sometimes you make a small bet. It can be OK to lose 80% of small bets if you win 20% of huge bets.
• Your chances of winning aren’t so neatly defined. There are a ton of possible outcomes with different probabilities of occurring. Some outcomes you know might happen. Other outcomes are entirely unpredictable and can come out of left field.

So how do we handle that? The formula is pretty simple:

1. Calculate the probability of all the various known outcomes
2. Calculate what you stand to gain / lose in all those possible outcomes
3. Multiply the probability of each outcome by what you stand to gain / lose.
4. Add it all together to get the EV.
5. If it’s positive, do it. If it’s negative, don’t do it.
   There are some exceptions obviously (e.g. moral reasons).