Expected Value (EV) in Poker: How to Calculate It and Use It

You’re about to learn about EV, one of the most valuable concepts in poker.

Expected value (EV) is an important tool for poker players, guiding them to make profitable decisions. You can use EV to assess whether certain actions will win or lose over time. In this guide, we’ll explain what EV is, how to calculate it, and how to harness it to make better decisions in your poker game.

What is EV in Poker?

Expected value (EV) in real life and online poker is a mathematical concept that helps players determine whether a particular action will be profitable in the long run. Instead of focusing on short-term wins or losses, EV evaluates the potential average outcome of a decision if it were made repeatedly over time. In essence, it answers the question: “If I make this play 100 times, will I make money on average?”

Let’s use NFL quarterback Patrick Mahomes as an example. If he throws a pass to Travis Kelce, there’s a certain probability that Kelce will catch it. Over a full season, Kelce might catch 70% of the passes thrown his way. If Mahomes throws the ball 100 times, Kelce will catch about 70 passes, generating positive yardage. Each throw has an expected value based on the likelihood of success (a catch) and the potential outcome (yards gained).

Let’s return to poker. Every action, like checking, calling, betting, or raising, has an expected value. By choosing one, your EV becomes higher or lower. For example:

• You’re holding a drawing hand with a 20% chance of improving. 
• The potential reward is $500. 
• Expected value helps you decide whether calling a $100 bet is profitable. 

When deciding whether to call, you can use expected value (EV) to help. First, consider the probability of hitting your hand and multiply that by the potential payout. Then, subtract the probability of losing multiplied by the cost of the call.

In the example above, the EV is +20, meaning this is a positive EV poker situation. This means that, in the long run, calling the $100 bet will be profitable. You expect to win $20 on average per similar decision over time.

How to Calculate Expected Value in Poker?

It’s time to go one step further. Soon, you’ll know how to calculate EV in poker situations and choose profitable actions, but there’s a formula to know.

Expected Value (EV) = (Probability of Winning * Amount Won) + (Probability of Losing * Amount Lost)

The poker EV formula accounts for the likelihood of winning or losing and the money at stake. In a real poker game, EV looks like this:

You have a flush draw and another player bets $50. Since you want to play profitably, it’s time to calculate the EV of this decision.

1. List possible outcomes:
   • You hit your flush and win the pot.
   • You miss the flush and lose $50.
2. Assign probabilities:
   • You have 9 outs (cards that give you a flush) from 47 unknown cards, giving you a 19.2% chance of hitting the flush on the next card.
   • The chance of missing the flush is 80.8%.
3. Multiply probabilities by potential outcomes:
   • Assume the total pot after the call is $150. If you hit the flush, you win $150.
   • If you miss, you lose your $50 call.
     EV = (0.192 * $150) + (0.808 * -$50)
4. Calculate the EV: 
   EV = ($28.80) + (-$40.40)
   EV = -$11.60

Should you make the call?
The negative EV (-$11.60) indicates that calling the bet is unprofitable in the long run. Thus, folding is the better decision in this scenario.

The math in our example is difficult to remember, and even harder to calculate during the pressure of a real hand. Fear not! Even though the math feels intimidating, you’ll notice that situations repeat themselves. By practicing the EV for standard spots, like flush or straight draws, you’ll act with more precision. Eventually, the complexities of EV will be just another of your skills.

+EV vs. -EV: What Does Expected Value Mean for Your Game? 

In poker, +EV (positive expected value) means that, over time, a particular decision will make you money. A successful poker player must aim for +EV decisions and avoid -EV ones.

For example, let’s revisit the flush draw situation from earlier. From calling a $50 bet with 19.2% chance of winning $150, we calculate an EV of -$11.60. This is a -EV decision because, over time, you will lose money. Sometimes, reality ignores expected value. You might hit your flush a lot in the short term and beat the odds, but time will balance that out. In the long run, a -EV call is a bankroll-buster.

Sometimes, making a +EV play means folding in a given scenario, avoiding a negative outcome and protecting your long-term profits. Other times, calling is a +EV play, when the potential payout is higher than the cost of the bet, ensuring long-term profitability.

Focusing on +EV decisions helps minimize losses from variance (short-term swings) and keeps you profitable over the long haul. Regular players might play thousands of hands a day if they are on the right tables. Just imagine the impact of losing a dollar every time you make a certain decision, again, and again. Now think of the upside. Tweaking a few of your plays from -EV to +EV could generate a serious amount of profit over thousands of hands. 

This is why disciplined decisions based on EV poker strategy are crucial for success. Small victories become major wins over time.

How to Use EV in Real Games?

EV reveals the long-term outcome of actions like a call, fold, or raise, by weighing the probabilities of outcomes against rewards and risks. In real games, consistently applying EV principles helps you sidestep costly mistakes and stay ahead of opponents over time.

Now you understand that expected value (EV) is important for making profitable decisions, let’s show how it’s used practically in real games. 

EV in Decision Making

Let’s say you’re in a cash game, facing an all-in bet with a flush draw. You have a 35% chance of hitting your flush, and the pot offers a $200 reward if you win, while calling costs you $50.

So, you calculate EV using this formula:

EV = (Probability of Winning * Amount Won) + (Probability of Losing * Amount Lost)

When you plug in the numbers, it looks like this:

• Probability of Winning = 35%, Amount Won = $200
• Probability of Losing = 65%, Amount Lost = $50

Remember, your probability of winning or losing must always total 100%. Once you have that worked out, it’s a simple case of adding the money to the formula, just like this:

EV = (0.35 * 200) + (0.65 * -50) = $70 – $32.50 = +$37.50

Since the result is positive, this is a +EV decision, meaning you should call in this situation because it will be profitable over time. As we know with flush draws, the suit you want doesn’t always show up. In a single hand, this +EV call might fail, but it generates long-term profit.

EV in Tournament Play

In tournaments, the concept of EV poker strategy is more complex due to factors like stack size, ICM (Independent Chip Model), and payout structures. Unlike cash games, where every chip has a fixed value, the value of your chips in tournaments changes depending on the stage of the event and your relative position to other players.

For instance, near the bubble (where only a few players need to be eliminated before payouts begin), calling an all-in with a marginal hand may be -EV even if you have favorable pot odds. This is because losing the hand and getting knocked out would cost you a chance at cashing, making the risk not worth the reward. Therefore, EV decisions in tournaments must take into account the unique dynamics of tournament play.

In this example, you are playing in a tournament:

• Scenario: You’re close to the bubble, holding a medium stack.
• Action: An opponent with a similar stack shoves all in.
• Your Hand: You’re holding A♠ 10♠, a marginal hand.
• Pot Odds: The pot odds might justify a call based purely on EV.
• Risk: If you lose, you’ll be short-stacked or may be eliminated before making money.
• ICM Consideration: ICM analysis shows that losing here would cost you more in tournament potential winnings than doubling up would gain.
• Decision: Despite having decent pot odds, folding is the correct +EV decision because it maximizes your chance of making it to the payout stage.
• Conclusion: Factoring in tournament dynamics, avoiding this -EV all-in situation protects your tournament life. By not making the -EV call, you can live one to fight another day, potentially winning or placing higher. 

This kind of situation is why tournament professionals make strange folds from time to time. They might have a strong hand that is likely to win, but pros think about the big picture. Keeping a healthy chip stack is a priority, which makes a seemingly “easy” call questionable.

The ICM model is another tool that helps you evaluate whether gaining chips is worth the potential risk. By factoring in these elements, you can better navigate high-pressure situations and make decisions that maximize your chances of climbing the payout ladder.

Expected Value and Pot Odds

Pot odds and EV work hand-in-hand to improve your decision-making process. Pot odds refer to the ratio between the current size of the pot and the cost of a call, while EV determines whether the call is profitable over time. Together, they help you decide whether it’s worth continuing in a hand.

For example, suppose the pot is $100, and your opponent bets $25. The total pot is now $125, and you need to call $25 to stay in the hand. This gives you pot odds of 5 to 1 (you’re risking $25 to potentially win $125). If you estimate that you have a 20% chance (or 4 to 1) of completing your hand, the pot odds are favorable compared to your odds of winning.

Now let’s calculate the EV:

• If you win: EV = (20% * $125) = $25
• If you lose: EV = (80% * -$25) = -$20

Total EV = $25 – $20 = +$5

Since the EV is positive, calling is a +EV decision. By combining EV and pot odds, you gain a clearer picture of whether a play is profitable, helping you make smarter decisions in real games.

Real-Game Scenarios

Understanding expected value (EV) helps you to make informed decisions in real-game scenarios, distinguishing profitable plays from costly ones. EV gives you a mathematical basis for evaluating whether a play will be profitable in the long run. While variance can lead to short-term wins or losses, focusing on positive expected value (+EV) plays leads to long-term success, while avoiding negative expected value (-EV) plays minimizes unnecessary losses.

Let’s look at some real-world poker examples to clarify the difference between +EV and -EV decisions.

Positive EV Play: Calling a Shove with a Strong Draw

You don’t need to close your eyes, but imagine you’re in a cash game holding A♦ Q♦ on a flop of K♦ 9♦ 4♠. Things are going well for you. With the Ace of Diamonds, you’ve got a strong flush draw with nine outs to lock up your victory. 

But suddenly, your opponent shoves all in, and the pot offers you 2 to 1 odds. You know that with a flush draw, you have about 35% equity to win by the river. Comparing the pot odds with your chances of hitting the flush, you find that calling is a +EV play because your chance of winning (35%) exceeds the breakeven pot odds (33%).

Over time, calling in these situations will yield profit, even though you won’t always win the hand. Even if you lose, be proud that you made the same decision a professional would probably make. The combination of pot odds and your hand’s equity makes it a strong decision.

Negative EV Play: Chasing a Long-Shot Draw with Bad Odds

Now, let’s consider a hand where you hold 8♠ 7♠ on a flop of K♠ 6♦ 4♥. You have a gutshot straight draw (four outs), and your opponent bets half the pot. The pot odds are 3 to 1, but your chances of hitting the straight are only around 8.5%. Calling here is a -EV decision because the odds of making your hand don’t justify the risk.

Understanding these real-game scenarios helps you avoid the trap of chasing low-probability hands and reinforces the importance of consistently making +EV decisions.

Conclusion

Expected value is not a beginner concept, so congratulations on learning the basics.

Mastering EV in poker is essential for long-term success. By consistently making +EV decisions and avoiding -EV traps, you increase your profitability over time, even if short-term variance sometimes produces unpredictable results. Incorporating EV into your decision-making process helps you make calculated, rational choices, whether you’re playing cash games or tournaments.

We recommend putting your expected value knowledge into practice in our wide range of games at CoinPoker. A great starting point is our low-stakes games, where you can play comfortably within your bankroll while honing your skills – Definitely a +EV move!

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