Expected Value and Poker?
Poker is a very famous game, both physically and online – the most famous of the poker variants being Texas Hold’em poker. It has a massive player base of over a hundred million players and has been around for nearly two centuries. Over the years, there have been many misconceptions about Texas Hold’em poker and other poker games from those new to the card game. Perhaps the biggest misconception is that poker is equivalent to gambling. Poker is a game of skill, and the best poker players know how to deal with weak hands, turning them into a winning hand, and can make a steady profit from most poker games. Another related misconception is that poker is all about one big win. Poker pros are not chasing a single million-dollar tournament win; it is quite the opposite. Poker is a grindy game; every good poker player knows how to see the game in the long term, ignoring individual hands and bad beats, and instead focusing on the overall results after hundreds of games. This poker guide is about one of the core concepts of long-term poker strategy: Expected Value.
1. What is Expected Value?
Expected Value, also known as EV, is a simple way of describing whether a poker play is profitable in the long run. It allows you to see past the short-term luck of poker and understand whether you should or should not make your decisions based on long-term profit. It is necessary because looking at individual hand results in poker is not seeing the whole picture. The short-term variance involved in poker can disguise how good your strategy truly is.
2. Expected Value analogies
Expected Value is a real-life mathematics concept often applied to poker. An easy analogy to explain it would be a bet on dice. A friend gives you a $5 bet with a balanced die. If it lands on three, he will pay you $5. If it lands on anything else, you have to pay him $5. You probably think, “this is a horrible deal,” and you are correct. Your chance of the die landing on three is significantly lower than the die landing on anything else.
Suppose he increases the amount you can win to $30. You have a ⅙ chance of winning $30, and he has an ⅚ opportunity of winning $5. Throughout many games, your deal should make you more money, as while the chances of you getting a three are five times lower than the chances of your friend getting anything else, $30 is more than five times $5. You take the bet, and the die lands on four. Your friend then takes his $5. You may wonder why you lost despite the Expected Value being in your favor. Expected Value tells you if making a decision is profitable over a long time. You must repeat a decision many times to realize your Expected Value. You can now see why Expected Value is so significant in poker. You may get caught up in a single lucky draw or lousy beat in a poker game, with your emotions clouding your judgment and stopping you from knowing whether your strategy was solid.
3. Expected Value Formula
The formula for Expected Value is simple. You have to multiply the amount of potential gain by the chances of it occurring. You must also do this with the possible loss. Then, you subtract the loss value from the gain value. A positive result is known as +EV, while a negative result is -EV. Let’s use the earlier dice example. Your gain is $30, while your chance of getting it is ⅙. Multiplying them together gives 30/6 or 5. Your loss is $5, while your chance of getting it is ⅚. Multiplying that together gives 25/6. Your EV ends up as ⅚. On average, you make almost an extra dollar each time you take this bet.
4. Expected Value in Poker
With all this in mind, it should be easy to see how Expected Value fits into poker. You will want to maximize your Expected Value at every opportunity to make the most money in the long run. Always focus your mindset on the long run and continue making good decisions regardless of your short-term luck. Here is a Texas Hold’em poker scenario that makes good use of Expected Value:
You are at the table with a stack of $77 against a single opponent now that everyone else has folded. Said opponent bets $25 and makes the current pot $74. The board is a five of hearts, a ten of hearts, a three of clubs, and a seven of diamonds. You have a jack and nine, both hearts. You have your opponent pegged as loose, so you want to know the EV of an all-in shove. This is complicated since there are three scenarios you must consider. The first is your opponent folding. Assuming they are loose, you can estimate a ⅔ or 66% chance they will fold to an all-in since they may be playing a weak hand. You must consider whether you will win at the showdown if they call. If they call, you believe they have a top pair, which only your flush or straight draws can beat. You estimate a 25% chance of you hitting your draws.
Now, it is time to do the poker math. They could fold, winning you the current $74 pot at a 66% chance. If they call, the other 34% of the time, you have a 25% chance of winning $126 from the current pot plus your opponent’s call and 75% chance of losing $77 that you went all-in with.
$74 x 0.66 = 48.84
($151 x 0.25) x 0.34 = 12.84
(-$77 x 0.75) x 0.34 = -19.64 since this is the EV of you losing.
Adding these together gives +42.04 EV, making this a profitable bet on average. You may have noticed that these calculations are much more difficult than pot odds, and you are wondering how to use these mid-game. The simple answer is that you don’t. EV is tough to calculate on the fly and is often best used to review your strategy post-game to ensure your decision-making and thought process is profitable.
The best site to play and practice poker
Expected Value, while a bit complicated, is essential to learning how to play poker. Poker is best played online, on sites like GGPoker, the world’s largest poker room. This is because of the numerous benefits of online poker, from playing many games simultaneously to poker trackers analyzing your playstyle to help improve your game. GGPoker even offers free poker tracking software to all its users, so sign up today!
Whether you’re a fan of high-stakes cash games or the excitement of multi-table poker tournaments, GGPoker is the premier destination for poker enthusiasts. For those aiming to compete for a prestigious WSOP bracelet, push through the ranks for a WSOP Circuit ring, or simply hone their strategies in classic games or poker formats, GGPoker has something for everyone. The platform offers a seamless online poker experience, with innovative features like Smart HUD, PokerCraft, and integrated staking, designed to elevate your game. Whether you’re grinding your way up in daily cash games or competing for life-changing prizes in major online series, GGPoker provides the best environment to play, improve your poker skills, and succeed in the world of online poker. And if you are not sure where to start, you can always play free poker games and learn at the GGPoker School.