What is Expected Value in Poker?

If ​you've been playing poker a while, you'll be well acquainted with the ups and downs of the game. Every poker player has experienced the satisfaction that comes with playing your cards perfectly and getting that big win, and also the heartbreaking times when your “can't-lose” poker hand is beaten, defying all logic and reason.

Poker is a game of variance, and understanding poker odds and probabilities is crucial in managing these ups and downs. What separates the average players from the good ones is the ability to manage the unpredictable nature of the game and make decisions that lead to a profitable outcome. Contrary to popular belief, the goal isn't to win every single round, but rather make decisions that result in more wins than losses, and a positive expected value.

What is expected value?

Expected value can be loosely defined as the anticipated return on an investment. Mostly used in statistics and probability analysis, expected value in poker is calculated by multiplying the possible outcomes by the likelihood of them happening, and then adding them all together. Expected value can be expressed as pure data or a monetary value, depending on your intended use. There are two different ways to convey expected value, both positive, and negative:

• Positive expected value​ —​ Positive expected value (+EV​) is a decision that will lead to – on average – more wins than losses.
   
• Negative expected value​ — ​Negative expected value​ (-EV​) is a decision that will lead to – on average – more losses than wins.

Making a play with a positive expected value doesn't always lead to a good outcome, and choices with a negative expected value don't always result in a bad outcome. Instead, it is assumed that on average, these actions will result in more negative or positive outcomes. A variety of professions use expected value—scientists, investors, economists, and last but not least, poker players.

Expected value in poker

Expected Value (EV) in poker is the amount a player expects to win or lose through a specific action. The most straightforward example is the flip of a coin: out of 100 flips, on average you'd expect it to land on heads 50 times and 50 tails. If you were speculating on the outcome, with SC20 on heads, then you can expect to win and lose at least 50 times each. Poker EV (Expected Value) strategy plays a similar role in the decisions you make at the table.

Most choices in poker—raise, bet, and fold, have an expectation to either gain you more chips or lose them. Some plays will win more chips than others on average, and the trick lies in the ability to identify these actions and consistently make the choices that will get you the highest positive expected value. In essence, the positive expected value choices earn you more chips; negative choices lose them.

For example, if you are last to act, and the three people preceding you have gone all-in for SC50, creating a total pot of SC150, then it could be considered positive expected value to bet and potentially win a total of SC150 while only risking SC50.

However, the choice also needs to take into account your cards. If you're holding 2,7 – statistically one of the worst hands – and the flop, turn and river are still to come, the odds of winning are small, so speculating the SC50 is unlikely to result in winning the whole pot, resulting in a negative expected value.

If the game continues past the flop and the other players continue to bet, the first question you should ask yourself is, "Will there be any profit if I call?" There are plenty of situations where the answer to that is a resounding “no.” For example, if there is no speculating until the last round – the river – then another player bets SC500, you have to ask yourself whether it is worth risking SC500, to win only SC500.

The same can be said for chasing cards to complete sets, straights and flushes. Chasing one card on the river to complete a flush, with significant raises every round does not have good odds for achieving a positive expected outcome. Odds will go up and down depending on how many cards you need, but you have to decide whether the card you need is likely to be dealt.

What are the odds of completing my hand?

That's one of the first questions you should ask yourself every time the flop comes down and you haven't hit anything. Poker odds and probabilities are essential in determining your expected value. Chasing long shots can result in heavy and frequent losses, when you know the odds aren’t in your favor. Knowing when to fold, rather than chasing cards for a flush or straight, plays a big part in working out the expected value in poker.

Playing a hand that is suited only improves your hand by 2%, so playing low ranked cards that are suited might not be an action that results in a positive expected value. If you are one card short of a full flush after the flop, you've only got around a 35% chance of completing the flush - that’s a third - and so it could be worth chasing, provided you understand the consequences of failure (and are able to accept them!).

If you survive until the river with only a high card, your chances of making a pair increase by around half, when two pairs go head to head, the bigger pair generally wins 80% of the time. The chances of getting a flush on the flop are only 0.8%. If you have two pair on the flop, the chances of making a full house by the river are 16.74% and if you flop three of a kind, the odds of making a full house are 1 in 3 or 33%.

When it comes right down to it, each player needs to decide for themselves. Some people like chasing the long shots, and risking their stacks for the chance of maximizing profit, while others will play tighter and have smaller wins, with less risk. It all comes down to what suits your playing style.

To calculate if an action in poker will have a positive expected value requires a decent understanding of the card rankings, and the odds. Beginners to the game might still be grappling with this, and that's fine; at the moment it's more important to focus on the basic rules of poker, keep in mind the concept of expected value, but don't concern yourself with it too much yet.

How can expected value improve your poker game? 

Every single action you take in poker, regardless of whether you are aware of it or not, revolves around trying to maximize your expected value. The goal of every poker player is to walk away with more chips in their stack than when they sat down. Obviously, making the right decision every single time is impossible; even when you make all the correct choices, you can still walk away with nothing. It's all about maximizing your chances, then hoping the cards fall in your favor. At their most basic, all poker strategies boil down to making decisions that will see you walk away with a profit.

Working out the expected value in every little act at a poker table with other players isn't possible, it will slow play down to a snail's pace and more than likely result in everyone else leaving the table in frustration. The key is to pick your battles. You will never know the exact amounts winnable in every situation, but understanding expected value in relation to poker can allow you to make the best choice available. You may win or you may lose, but you can be confident it was the best option. That’s one of the keys to a successful long-term poker strategy.

One of the best ways players can use expected value to improve their poker is in post-game analysis. Figuring out which plays resulted in a positive outcome, and trying to replicate them next time, while avoiding the choices that resulted in a negative. It can be a useful tool in improving your overall game in the long run. Only making plays that result in positive expected value should result in more wins over time, in the same way, negative ones will lead to losses. Pocket Aces beat pocket Kings 80% of the time, that still leaves a 20% chance that pocket Kings will win, but in the long run, pocket Aces should —on average—provide more wins.

Learning the ins and outs of expected value also has the benefit of providing peace of mind. It's very easy to be rattled by losses, especially when all the statistics indicate you've made the right decision. This often results in more bad choices and a steady decline of your bankroll. Understanding the expected value can allow you to worry less about the short-term losses in every poker hand you play, and more about the long-term wins over the course of many games.

The more positive expected-value choices you make should ensure that in the long run, you win more than you lose. However, sometimes all your strategies and best-laid plans won’t work as expected and it can feel like the cards are (literally) against you. Poker can be unforgiving. Sometimes the more you lose, the more reckless you become. If you find yourself making choices based on emotion, rather than the statistics, it might be time to walk away and come back another day. The game isn't going anywhere, and coming back refreshed the next day will ensure you make better calls.

Expected value isn't just about two outcomes – winning or losing. Rather, it’s about maximizing the value of each hand you play. Deciding what the maximum amount you can bet and still have other players call, raise and whether to slow play or make a big bet are some of the factors you​ ​should take into account. Learning the best way to react in these situations only comes with time at the tables and a thorough understanding​ ​of expected value.

Takeaway: Play Smarter, Not Harder

Expected value is just another way to think about your decisions while playing poker, and whether those decisions will result in a positive outcome (more wins in the long run), or a negative outcome (more losses). Winning every hand is impossible; however, understanding expected value and how it relates to poker will ensure that you get the maximum value out of your cards. Working out the expected value won't guarantee walking away with a hefty profit in poker, but it will provide all the tools necessary to help reduce the chances of losing.

Expected Value: Frequently Asked Questions

1. What is expected value in poker?
Expected value (EV) is a statistical concept that represents the anticipated return on a specific action in poker. It helps players assess whether a decision is likely to yield a profit or a loss over time. Positive expected value (+EV) indicates a choice that should, on average, lead to more wins than losses, while negative expected value (-EV) suggests the opposite.

2. How do I calculate expected value in a poker hand?
To calculate expected value, multiply the potential outcomes by their probabilities and sum them up. For example, if a player can win a pot of SC150 by risking SC50, the calculation involves considering the likelihood of winning that pot against the cost of the bet.

3. Can I always rely on expected value to make decisions in poker?
While expected value is a crucial tool for decision-making, it doesn't guarantee success in every hand. Variance and luck play significant roles in poker. Players should use EV to guide their choices while also considering the specific context and their playing style.

4. How can understanding expected value improve my poker game?
By focusing on expected value, players can make more informed decisions that maximize their chances of long-term profitability. Analyzing past hands for their EV can help identify which strategies yield positive results and which do not, leading to improved gameplay over time.

5. What should I do if I find myself making emotional decisions at the poker table?
If you find yourself making decisions based on emotion rather than strategy, it may be beneficial to take a break. Stepping away can help clear your mind and allow you to return with a better focus on making statistically sound choices that align with maximizing your expected value.