What is Expected Value (EV) in Poker

Introduction 

Poker is a game of strategy, psychology, and mathematics. One of the most critical mathematical concepts in the game is ‘Expected Value’. Understanding EV helps you make the best decisions over the long run, guiding you to profitability even in the face of short-term variance.

This article will examine EV in-depth and discuss how it can enhance your poker game.

What is EV in Poker?

Expected Value indicates the average amount you could gain or lose from a specific action if repeated multiple times in similar situations. It assesses the profitability of decisions like calling, folding, bluffing, or raising.

Positive EV (+EV): Indicates a profitable decision in the long run.

Negative EV (-EV): Indicates a decision that will cause money to be lost over time.

Neutral EV: Suggests a break-even play with no gain or loss in the long run.

The EV Formula

The general formula for Expected Value is:

𝐸𝑉 = (Probability of Winning x Amount Won) − (Probability of Losing x Amount Lost)

Let’s break it down:

Winning Probability: The chance of your hand being victorious at the showdown.

Winnings: The total prize you'll receive if your hand remains strong.

 Chances of Defeat: The probability that your opponent's hand will surpass yours.

 Amount Lost: You risk losing money if your hand doesn't win.

Example:

You are facing a 50 bet into a 100 pot on the turn. You have a flush draw with a 20% chance of hitting by the river. Should you call?

Probability of Winning: 20% (0.2)

Probability of Losing: 80% (0.8)

Amount Won: 150 (the pot size if you call and win)

Amount Lost: 50 (the amount you’ll lose if you miss)

EV = (0.2×150)−(0.8×50) = 30−40 = −10

In this case, calling has a -EV of 10, so folding would be the better decision.

Types of EV in Poker

Understanding EV in Poker involves applying it in various contexts. Here are the most common types of EV calculations:

1. Pot Odds and EV

Pot odds compare the cost of a call to the potential reward from the pot. This helps calculate whether a call is +EV.

Example:

Pot: 100

Opponent Bets: 50

Your Call: 50

Pot Odds: 150: 50 or 3:1

If your chances of improving your hand are better than the pot odds (greater than 25% in this case), calling is +EV.

2. Implied Odds and EV

Implied odds extend beyond the current pot size by factoring in potential future bets you can win. This is especially useful for drawing hands like straights or flushes.

Example:

Current Pot: 100

Opponent Bets: 50

You estimate winning another 100 if you hit your draw.

Consider the total reward (250) rather than just the current pot size in this scenario. If the implied odds make up for the deficit in pot odds, a call can be +EV.

3. Bluffing and EV

Bluffing is an integral part of poker, and its success is measured by fold equity (the percentage of times your opponent folds).

Bluff EV Formula:

EV = (Probability of Fold × Pot Size) − (Probability of Call × Bet Amount)

Example:

Pot Size: 100

Your Bluff Bet: 50

The opponent Folds 60% of the time (0.6).

EV = (0.6×100) − (0.4×50) = 60− 20 = +40

This bluff has a +EV of 40, making it a profitable play in the long run.

4. Value Betting and EV

Value betting involves a strong hand to extract maximum value from worse hands. Calculating the EV of a value bet requires assessing how often your opponent will call.

Example:

Pot Size: 150

Your Value Bet: 50

Opponent Calls 70% of the time with worse hands.

EV = (0.7×200) − (0.3×50) = 140 – 15 = +125

A +EV value bet earns you 125 on average over the long term.

How to Use EV in Poker Strategy

Preflop Decisions: Based on hand strength, position, and the opponent’s style of play, assess whether raising, calling, or folding has the highest EV.

Postflop Analysis: Use pot and implied odds to evaluate drawing hands and determine whether to bluff or value bet.

Adjust to Opponents: Bluffs have higher EV against tight players, while value bets shine against loose players.

Minimize Mistakes: Avoid emotional decisions. Stick to +EV plays, even if they sometimes feel counterintuitive.

The Long-Term Perspective of EV

Poker involves both short-term fluctuations and long-term reliability. While a decision with a positive expected value (EV) doesn't promise an instant victory, it will yield a profit over the course of thousands of hands. 

Example:

A 70% probability of winning a pot indicates a 30% likelihood of losing.

If you repeat the same scenario 1,000 times, the results will closely match the expected value calculations.

Common Mistakes When Applying EV

Ignoring Implied Odds: Not accounting for future bets can lead to -EV calls.

Overestimating Fold Equity: Assuming opponents will fold too often can make bluffs -EV.

Emotional Decisions: Chasing losses or tilting often leads to ignoring EV.

Misjudging Opponent Ranges: Inaccurate assumptions about opponents’ hands can skew EV calculations.

Tools to Master EV

Several tools can help you understand and apply EV effectively:

• PokerTracker/Hold’em Manager: These programs monitor your hand histories and deliver detailed analyses to help you spot trends in your expected value (EV). By examining previous sessions, you can identify where you are making profitable or unprofitable decisions, enabling focused enhancements in your gameplay.
• GTO Solvers: These tools aid in making mathematically optimal decisions to maximize expected value, whether you are competing against unknown opponents or a particular player profile.
• Equity Calculators: By inputting your hand and the community cards, these calculators show you the probability of winning against an opponent's range, providing a clear view of the EV of your actions in each hand. This allows you to make more informed, EV-maximizing decisions throughout the game.

Frequently Asked Questions

What is EV in Poker?

EV, or Expected Value, is the average amount of money you can expect to win or lose in the long run from a particular decision. It is calculated based on the probabilities of all possible outcomes and their respective payouts. Positive EV decisions are profitable over time, while negative EV decisions result in losses.

How do I calculate EV in Poker?

Use the formula:

EV = (Probability of Win × Amount Won) + (Probability of Loss × Amount Lost).

Multiply the chances of each outcome by the monetary result, then sum them. This helps determine if a decision is profitable in the long term.

What is the difference between EV and pot odds?

Pot odds tell you the ratio of the current pot size to the cost of a call, helping you decide if calling is mathematically justified. EV considers not only pot odds but also implied odds, fold equity, and future betting scenarios to measure the profitability of a decision over time.

Conclusion

Understanding the concept of Expected Value (EV) is crucial for any serious player. Poker isn't about winning each hand but making wise decisions over the long run. Incorporating EV into your strategies for preflop moves, post-flop play, and bluffing can help you consistently outwit opponents and boost your profitability.