The Difference Between Equity & Expected Value
When talking about poker, the terms ‘equity’ and ‘expected value’ are often used interchangeably - but they're not the same thing, and confusing one with the other will bungle your ability to make good decisions.
We’re going to delve into a pretty simple topic here, but – despite its overt simplicity – understanding the minute intricacies of the subject matter can make it a rather sophisticated idea to unpack.
When talking about poker, the terms ‘equity’ and ‘expected value’ are often used interchangeably. It’s easy to understand why; both concepts deal with your probability of winning. Moreover, consideration of one will almost always lead to consideration of another. However, while the concepts may be inextricably linked, they are not actually the same thing.
The Difference Between Equity and Expected Value: By Definition
Equity (pot equity/poker equity) refers to what percentage of the pot belongs to you; it gives you an idea of how often you can expect to win with your hand on average from a particular point in the hand going forward.
Expected value (EV), on the other hand, is expressed in terms of money, not percentages and can be either positive or negative. It tells you the amount of money you can expect to win or lose on average by taking a certain action in a particular hand. Unlike equity, this term should not be thought of as pertaining to a specific circumstance, but should be viewed as an indication of your action's merits in regards to that particular hand in the long run.
The Relationship
As mentioned before, while these concepts are not synonymous, they are interconnected - namely because you have to know your equity to determine your expected value. Your equity allows you to get a better look at helpful numbers.
Let's look at an example to illustrate the connection between these two concepts:
Player 1 has an A♥, K♠
Player 2 has J♣, 9♣
The flop comes down with A♣, A♦, 4♣
Player 1 has 75.35% equity in the pot and Player 2 has 24.65% equity.
Now we use that equity to factor into our EV calculation.
EV = how much you stand to win – how much you stand to lose.
Let's say there is $200 in the pot as it stands, and Player 2 goes all-in with $100, bringing the pot to $300. Player 1 must decide whether or not to call the bet. A good way for Player 1 to make this decision is to determine how much he can expect to win or lose on average whenever he calls with this hand in this draw. In other words, he should work out his EV.
Player 1 will win the whole $300 75.35% of the time, which equates to $226.05
Player 1 will lose his $100 bet 24.65% of the time, which equates to $24.65
Since EV = win - lose, then Player 1 can plug these numbers into the equation to determine how much he stands to gain or lose on average.
EV = $226.05 - $24.54
EV = $201.40
So, Player 1's expected value is + $201.40. By the same measure, Player 2, on the other hand, has an expected value of - $1.40.
A Final Word: A Common Mistake
While it makes sense to think that you have to have good equity to have good EV, this isn't always the case. If our bet size is diminutive compared to the amount we stand to win, we are actually very likely to have a positive EV if we act. The reason is that, in the long run, we will risk less, and win more.
In the end, you should use both equity and expected value together to help yield the best, most predictable results for long term success at the tables. You should, however, understand the difference between equity and expected value so you can also see how they compliment each other and create a powerful, united front in the battle against bad beats.