Expected Value (EV): A calculation of the average money expected to be won or lost over time from a specific poker decision.

Expected Value (EV) is one of the most fundamental concepts in poker. It refers to the **average amount of money** a player can expect to win or lose from a particular decision over time. In poker, players often use EV to evaluate the profitability of their actions, whether it’s calling a bet, raising, or folding, by analyzing the long-term outcome of those decisions.

## How Expected Value Works

Every decision in poker can have a **positive (+EV)** or **negative (-EV)** expected value:

**+EV**: The action will make money in the long run.**-EV**: The action will lose money in the long run.

While the immediate result of a single hand can be a win or a loss, EV focuses on the **average result** if the same situation were to happen many times. For example, even if you lose a hand where you have pocket aces, making that play was still +EV because pocket aces are statistically favored to win most of the time.

## Formula for Calculating EV

EV is calculated by multiplying the potential outcomes by their probabilities and adding the results together. Here’s the basic formula for expected value:

Where:

- P(win) is the probability of winning the hand.
- “pot size” is the size of the pot or reward.
- P(loss) is the probability of losing the hand.
- “bet size” is the amount risked in the hand.

You can copy and paste each MathML block separately as needed.

### EV in Practice: Example

Imagine you’re in a cash game, and you need to decide whether to call a $100 bet for a chance to win a $500 pot. After thinking about your opponent’s possible range and the cards on the table, you estimate that you have a **30% chance** of winning.

To figure out if calling is a good idea, you use the **Expected Value (EV)** formula:

This formula works by calculating the average outcome if you made this call many times. The **0.30** is your chance of winning, so you multiply it by the $500 pot (your potential win). The **0.70** is your chance of losing, so you multiply that by the $100 you’re risking.

In this case:

- Winning earns you
**$150**(0.30 x 500). - Losing costs you
**$70**(0.70 x 100).

So, the EV is **$150 – $70 = +$80**. This means that in the long run, you would make $80 on average by calling, so it’s a profitable decision.

### Positive and Negative EV Decisions

**Positive EV (+EV)**: If the EV of a play is positive, it’s a profitable decision. For instance, betting with a strong hand against a weaker range of opponents is a +EV move because, on average, it will win more money than it loses.**Negative EV (-EV)**: If the EV is negative, you are expected to lose money over time. For example, chasing an unlikely flush draw when the pot odds don’t justify the call is a -EV decision.

## Long-Term Significance

One key aspect of EV is its **long-term focus**. You may make a correct decision that ends up losing in the short term, but over a large enough sample of hands, the EV of your decisions will reflect the true profitability of your play. This concept helps players avoid being results-oriented, where they focus only on the immediate outcome of the hand, rather than the quality of their decisions.

Understanding and applying EV helps poker players improve their decision-making and increase their profitability by focusing on plays that yield a positive outcome in the long run.