Equity and EV
Fundementals of Equity and EV: The building blocks of modern poker theory.
Overview
The most fundamental concepts in poker theory are Equity and EV. The goal of this page is to introduce players who are already familiar with the rules of poker to these two fundamental concepts. Examples will use No Limit Texas Hold’em but the concepts are broadly applicable to all variants of poker.
Equity
Equity is your expected share of the pot if both players suddenly agreed to check all the way until showdown. There are three main contexts in which equity is usually considered:
Hand vs. Hand
Measures the equity a hand has against another hand.
- AA has ~82% equity against KK preflop
- AA has 50% equity against AA preflop
- AK has ~19% equity against JT on the board JT2
- KT has 100% equity against A2 on the board JT266
Hand vs. Range
Measures the equity a hand has against a range.
- AK has ~90% equity against a standard BB calling range on the board K72
Range vs. Range
Measures the equity a range has against another range.
- A standard BTN opening range has ~52% equity against a standard BB calling range on the board K72
A range is the probability distribution of hands someone could have.
EV
Expected value – usually referred to as EV – is defined as the average amount of chips you would win in a given spot. For example, the EV of a 30% chance to win 50 chips is 15 chips. When calculating EV, we consider money already in the pot as dead money, which has the convenient property of making all folds exactly 0 EV.
In a poker hand, if we sum up the EV of each player it will equal exactly the pot unless there is rake, in which case it will add up to less than the pot.
Examples
Try some examples to test your understanding of equity and EV:
Equity #1
The board is T7542 and you have AA
Your opponent could have any of these hands at equal probabilities:
72 or AT or 33
What is your equity?
Equity #1
The board is T7542 and you have AA
Your opponent could have any of these hands at equal probabilities:
72 or AT or 33
What is your equity?
66.6%
You lose to 72
You win against AT and 33
Since all hands are equally likely, you have the strongest hand 2/3 of the time. Therefore your equity is 66.6%.
Equity #2
The board is JT76 and you have AA
Your opponent has KK
What is your equity? Hint: There are 52 cards in a deck.
Equity #2
The board is JT76 and you have AA
Your opponent has KK
What is your equity? Hint: There are 52 cards in a deck.
95.5% (42/44)
There are 8 cards in play so there are 44 cards remaining in the deck.
Of those 44 cards, the only River cards that make you lose are K and K
Therefore your equity is 42/44.
EV #1
The board is T7542 and the pot is 100 chips. Your opponent has just bet all-in for another 100 chips.
There is a 60% chance they have a stronger hand than you. There is a 40% chance they have a weaker hand than you.
What is the EV of calling? What is the EV of folding?
EV #1
The board is T7542 and the pot is 100 chips. Your opponent has just bet all-in for another 100 chips.
There is a 60% chance they have a stronger hand than you. There is a 40% chance they have a weaker hand than you.
What is the EV of calling? What is the EV of folding?
The EV of calling is 20 chips.
60% of the time calling loses 100 chips.
40% of the time calling gains 200 chips.
(0.6)(-100) + (0.4)(200) = 20
The EV of folding is always 0 chips.
Since the EV of calling is higher than that of folding, we should always call in this scenario.