What is Expected Value in Poker ?

Expected value is the value you expect to get out of a hand. The term started out as a basic probability math term, and was brought into the poker world. It is used to figure out the average outcome of any given situation over the long term. Since poker should be played as a long-term game, it works out well. Your goal as a poker player should be to win over the long run.

With that said, you are probably wondering how you would figure out the expected value. This is where it can get a bit tricky. There is actually some real math involved here so prepare yourself.

The idea here is to try to figure out what the best move would be in any given scenario. You want to try to figure out if you should check, bet, raise or fold based on mathematical probabilities. This is just one more concept where math is used in poker. So we will look at an example here.

Example:

A common example for expected value is with small to medium pocket pairs. While playing Texas Holdem, you will often find yourself in this position. There are really three different things you could do assuming that your opponents are all limping in.

A) You could simply call and limp in.
B) You could raise.
C) You could fold.

Since nobody is raising and you do not have much to lose here, we will automatically rule out C. There is obviously no value in folding in this position. There is much more to gain than to lose here.

Note: We are going to assume that you must hit a set in this situation in order to win the hand.

Raising would not be the best move here because you want to get the best possible pot odds with a hand like this. You will only hit a set on the flop 1 out of every 7 times on average. If you add in implied odds, you can say that you want at least 4:1 pot odds going into the flop, if not better. If you raise, you are likely to get most people to fold leaving you heads up or maybe three handed, which will give you 3:1 pots odds at best. The more players and the better pot odds before the flop with smaller pairs, the better your expected value would be.

So the best move here would be to just simply call.

There are some fairly specific calculations that could be made for every single situation. This is just the simple overview of expected value in poker, which should help you understand the concept

Different uses for Pot Odds in Poker

The better more consistent poker player’s, use pot odds for more than deciding when to call a bet. They also use the Pot Odds to tell them when they should lead out with a bet or raise a bet, and by how much. For example, in Texas hold’em if you have flopped a set, and there are two cards to a flush or straight on the board, you want to make your bet high enough that any player drawing to that flush or straight will not have pot odds to call. If there is $1,000 in the pot, you can make the pot odds only 2 to 1 for any potential caller on a draw simply betting the size of the pot ($1000) yourself.

It is important that if the player on a draw calls you when you raise in that situation like this, that you understand that he paid too much for that call, even if he does draw out on you. Even if you made the correct play by raising and still get called just continue to play your hand by concentrating on the task at hand. Most amateurs get upset when this happens, but most pros care little about the results of any one given hand. They will look at players who make that call as mini-ATM machines.

The Concept of Outs in Poker

The odds of getting the cards needed to make a hand are known as “outs”. An out is simply a card that would get you “out” of the jam you’re currently in, facing a stronger hand when all you have is a draw.

When you have four cards to a nut flush, it’s easy to count the outs. Since there are 13 cards to every suit and you know there are four cards in one suit between the board cards and the cards in your hand, there are exactly 9 cards left to make your flush. You have nine outs.

So the question is how do you figure the pot odds, once you figure how many outs you have?

It’s easier than you think!!!

First subtract the number of outs from the total number of unseen cards. Which is 47 after the flop, or 46 after the turn. You start with 52 cards in the deck and subtract the cards you’ve actually seen on the board and in your hand.
So, to calculate the odds of making a flush draw on the turn, you subtract your outs from the unseen cards.
46 – 9 = 37

And the odds against your drawing to the flush you need are simply the ratio of this total, to the number of your outs. In this example, the pot odds are 37 to 9 or just over 4.1 to 1 against you. So, if you get pot odds of 4.2 to 1 or more for your flush draw, you make the call.

I hope the example can help you understand that many other factors can come into play with the understanding of pot odds, and outs.

Read more of our poker strategy articles below:

Understanding Pot Odds in Poker

Understanding Implied Odds in Poker

Understanding Expected Value (EV)

Introduction to Implied Odds

There are two different kinds of odds you want to think about while making a decision to call or not call a bet. The first is pot odds and the next is implied odds. If you remember reading about pot odds, you will know that this depends on the amount of money in the pot. Implied odds is a little different, because it has nothing to do with anything you can calculate for sure.

Understanding Implied Odds

Implied odds is how much money you think you will get out of your opponent later on in the hand. Implied odds are normally used when a player is trying to decide if they should or should not chase some sort of draw.

For example, if you where on a flush draw you would want to think about two different things. First, think about the pot odds. So you could figure your pot odds and possibly make a decision right then and there. Once you do that you can move on to the implied odds.

All you have to think about with implied odds is how much money you could possibly win from your opponent. So if you are going for a flush and you know for whatever reason that you are likely to take all of your opponent’s money (which is a good amount of money) when you hit your flush, then this is good implied odds. If you are playing an opponent that only has a very small amount of money in front of them and you really do not stand to gain anything, you will have bad implied odds.

When to use Implied Odds

For the most part implied odds will not need to be used. The pot odds are much more important and will be used a lot more. Implied odds are just something that you want to have in mind during play. It is a very simple concept that does not take much thought. Just be aware of what is in front of your opponents, and be aware of how they play. If you know you stand to gain a lot more than you could lose during a hand, it will have more value in making a tough call.

Read more of our poker strategy articles below:

Understanding Pot Odds in Poker

Understanding Odds and Outs in Poker

Understanding Expected Value (EV)

Like our soybean analogy, poker hands are high-risk investments also, with no guaranteed return. For example, a flop comes down with two spades and you have AK of Spades, you don’t have anything but an Ace high right now, but if any spade comes up you will have the nut flush. So if someone before you bets you must decide if it is worth the investment. All you have in your hand is potential and if you have been playing long enough most of the time a flush doesn’t materialize. For you to call a bet, I extremely go against raising in this position, because you bring luck into the equation more than strategy, you have to decide if the Pot odds are in your favor to call. For your call to be profitable, the pots you win when you do make your flush have to pay enough for you to cover all those times your flush doesn’t come and then some for you to profit. If you don’t make enough when you hit your flush to cover your prior losses you’ll lose money like all bad investors.

Pot odds are simply the ratio of the amount of money in the pot (potential return) to the cost of a call (potential investment). Let’s use another example, you have A 4 spades and this time the flop comes down Q-9-2, with only one card being a spade. Neither player bets on the flop, you bet hoping to take the pot down right there, but both the players call. On the turn comes a King of spades, making the board Q-9-2-Kwith two spades, giving you four cards to a possible nut flush. Let’s say the first player bets and the second raises all-in.
At this point, all you have is a nut flush draw. You are certain at this point that you are beat my both players. With only one card to come, and if that card is not a spade, you know you won’t win this hand with an ace high. If an ace comes on the river you might have top pair but one of your opponents might have A-K or A-Q and that could cost you a lot of money. So in retracing this hand the only logical way to look at it would be that have to have a spade to win. So the question you have to ask yourself. Do I call an all-in bet for a nut flush and is that a good investment?

This is a math problem pure and simple and the first step to answering the question is pot odds. Again the pot odds are the ratio of the amount of money in the pot to the cost of the call. If the size of the pot is $1000 and it is $100 to call the pot odds are 10 to 1. Just remember if you plan on playing recreationally or gambling professionally, the understanding of pot odds is very important if you want the numbers to fall your way. You will be doing simple mathematics like this in every hand you play and the more hands you play the better you get at understanding the nuances of pot odds.

Read more of our poker strategy articles below:

Understanding Implied Odds in Poker

Understanding Odds and Outs in Poker

Understanding Expected Value (EV)

Definition of a Bad Beat in Poker

A bad beat is pretty simple, but is often mistaken. The basic meaning of a bad beat is when you lose a hand that you should not have lost.

Understand that poker is a game of statistics and odds. If you know the odds and the probabilities, then you are more likely to understand what a bad beat is. It is a bad beat when your probabilities of winning a hand are high, and you still end up losing a hand.

Example of a Bad Beat

If you are up against your opponents and you have pocket Aces before the flop, the proper move is to get as much money as you can into the pot and to make sure that you are only playing against one other player (two at the most). So assuming you do that in this position you will be heads up with just one other player who will re-raise you all in. Of course you would call with the best hand in Texas Hold’em.

You flop over your hand and your opponent shows you pocket kings and gives a big gripe. Of course you would be very happy to know you are more than an 80% favorite in this hand. On the flop you catch an ace, which makes you even surer that you will win. But wait a minute, then comes a King on the turn. Now you are still pretty sure you will win but that chant (NO KING NO KING!) comes out as you sweat a bit. Then, sure enough that king comes on the river. You had a 99.9% chance to win after the flop, and still lost.

That is a Bad Beat!

Bad Beat Misconceptions

Many people think that they have gotten bad beats but in reality they are very wrong. It is possible to have gotten a “bad beat” because you played the hand the wrong way. A lot of people think that you cannot lose with pocket aces and that if you do, you are getting a bad beat. Those are the same players that try to slow play a hand like that. This is the surest way to get beat by pocket aces. If you are in a hand with 7 other players and you have pocket aces going into the flop, you are probably going to lose. It is not a bad beat if you do because you did not play the hand the right way.

If you lose when you have a very high chance of winning, and you have played the hand the right way; you can then say you have received a bad beat.

Some say poker is a game of luck, while others defend it as a sport. We say you can play poker as a game of luck and lose a lot of money, or apply your intellect to it and start reaping pots like never before. By applying the laws of probability to your poker game you will make more educated decisions and gain an indisputable edge over players who see poker as mere “gambling.”

For those completely unfamiliar with odds, let’s take this from the very top. Imagine a standard coin with the usual two sides: heads and tails. In terms of odds the chance of you tossing tails is “two to one” – spelled 2:1 – since there are TWO options available (heads and tails) and ONE way you can get your desired outcome (heads.) Piece of cake? Indeed! Now think of a standard 6-sided dice, and calculate the odds of throwing a 5. If you said 6 to 1 you were absolutely right! Now for a tad of math: if you want a percentage all you have to do is divide the small number by the large one and multiply by 100. In the case of the coin you have odds of 2:1, so divide 1 by 2 (calculator allowed) and you’ll get 0.5. Multiply by 100 and you get 50, which means that odds are 50% that you’ll toss heads. Use the same procedure for the die and you will get odds of 16.6% (or 17% if you’re in a hurry.) Are you ready to advance to the next level?

Our thing is poker, so let’s start talking about cards. If you have a well shuffled deck, what are the odds of picking the Ace of Spades? Well, since there is just one Ace of Spades out of a total of 52 cards, the odds are 52:1, or less than 2%. What about the odds of picking any Ace? Well, since there are 4 Aces in the deck the odds would be 52:4, but since odds always have to be “something to 1″ what you do is divide the first number by the second to get 13:1. To get percentage odds you divide 4 by 52, which will give you 7.6% (8% is fine too.) And for one last example, what about the odds of picking any Spade? There are 13 Spades in total, so the odds are 52:13 – or rather, 4:1 – for a 25% chance.

Let’s summarize what we know so far: the odds of something happening are

THE TOTAL NUMBER OF OPTIONS YOU HAVE : THE NUMBER OF WAYS IT CAN HAPPEN

Now let’s see how we can apply this powerful mathematical tool to poker!

Simple Hand odds:

Hand odds are the odds of making a hand in the flop, turn or river, to make the most of your hole cards. This can get complicated, so let’s start with a very simple example: you have two spades in your hand, there are two more in the flop, and a flush would just make your day. What are the odds of that happening in the turn? Let’s start by counting the remaining spades: since 4 are already out in plain view it follows that 9 must remain in the deck, so you have 9 “outs,” which are the 9 ways in which you can complete your flush. Now let’s count the number of cards that are still unseen: since you can see 5 cards (your hole cards and the flop) then 47 cards remain unseen, since you have a whole deck of 52 minus the 5 you can see. Now we can apply the Universal Formula of Odds we just learned, and get odds of 47:9, which any calculator will tell you equals 5.2:1, or a percentage of 19.1%. What if you did not catch your flush in the turn? Let’s calculate it for the river: you have 9 outs, and now only 46 cards remain unseen (because you can see the turn card now) so the odds are now 5.1:1 or 19.6%.

In general, hand odds for the turn or river will be calculated like this:

NUMBER OF UNSEEN CARDS REMAINING : NUMBER OF OUTS

This is good for calculating odds a card at a time, but experts agree that if you want to go all-in you should only do it after considering the combined odds for both turn and river. How is this done? Unfortunately it is not as easy as the previous ones, but we will break it down for you, and teach you some tricks as well. But first, let’s talk about outs.

Outs

Let’s take the simplest scenario: you have a pocket pair, and you are hoping for a set. How many outs do you have? Well, if you are holding 2 Aces then it follows that 2 more remain unseen in the deck. You have 2 outs to hit that third Ace.

That was easy, wasn’t it? Let’s try a slightly more difficult case – after the flop you have 2 pair, and are now aiming for a boat. For the sake of the example let’s say you have a pair of 6 and a pair of Kings. Since either a 6 or a King will complete your full house, you have 4 outs: the two remaining sixes and the two remaining Kings. Of course you would prefer a King, but beggars can’t be choosers and we are only counting outs anyway. If you have two pairs, you have 4 outs for making a full boat.

Let’s think of straights now, shall we? There are those nasty little inside straights that keep you on the edge of your chair for the whole hand; let’s say 7, 9, 10, J for this example. All you need to be happy is an 8, and there are 4 of those in every normal deck, which leaves you with 4 outs. On the other hand, if you have a friendlier open-ended straight such as 8, 9, 10, J you could complete your hand with either a 7 or a Q. Every deck is supposed to have 4 of each of those, which leaves you sitting pretty with 8 outs.

Flushes are very generous when it comes to odds. If after the flop you find yourself with 4 cards of the same suit, lady Luck could well be smiling at you: since there are 13 cards of each suit, and 4 are already out there, the remaining 9 must be still in the deck trying to find their way to you. If you hold 4 to the flush, you have a whopping 9 outs, which is not bad at all.

But odds-wise, possibly the best hand you can hold is an open straight flush draw, the one that is open for almost everything, say 7, 8, 9, 10 all Hearts. Your flush draw has 9 outs, as we just found out, and an open straight draw has 8. However, we must take into account that the 6 and Jack of Hearts have been counted twice: once as part of all remaining Hearts (for the flush) and once as outs for the straight. So the total number of outs for an open straight flush draw is 9 + 8 – 2 = 15 outs.

On the second part of this series you will learn how to calculate combined odds and pot odds, and how to apply these ratios to your decision-making process. Use your brains at the tables and become a shark in no time!

You see it all the time online. A bad beat or and horrific bad beat send somebody to the rail prematurely. Usually that player was well ahead in the hand, when the chips went in the middle. The next thing you know, the chat box is a rattling with more profanity than you can find on late-night television.

Most new players cannot control their anger when this happens to them. And because the frequency of it seems higher in online poker, frustration is often the mood of the day. Then, anyone at the table can be subject to verbal abuse by the frustrated player, who simply knows no better. The worse the beat, the more likely there is to be an exchange of a heated nature.

A lot of this activity really boils down to experience. The more experienced a player has, the less likely he is to flip out after a bad beat. This is partly because of his understanding of the game, but as well because of his proper bankroll management. In other words, anyone would be more likely to freak out if they lose a pot when they are playing with 50% of their bankroll as opposed to 2% of their bankroll. Think about that. If you know that you cannot realistically avoid bad beats, and that they are truly part of the game that you know and understand, then bankroll management should in fact, prevent any type of bad beats from hurting your emotions too much.

Understanding the backbone of finances and mathematics in poker can assure in any newfound depth in dealing with losses at the table. No longer should you be emotionally drained to suck outs the way your opponents are, and in fact, you may then find yourself past a point of cosmic return and be able to turn those horrible plays of your opponents into cash in your poker account.

So the next time you are the victim of a bad beat, try and look at it in the way that you got your opponent to do exactly what you wanted them to do. They made a big mistake, you were way ahead, and they won the pot. That is very likely a positive EV play that you’ve executed perfectly, and even though you did not win it this time, you have actually won.

When you get to the point where you can laugh off the biggest bad beats that goal against you, you are very likely on your way to poker freedom.

Most of us know that when you shove a pinball a bit too hard, the machine ’tilts’. You then lose your turn, or the game! In poker, a mental condition called ’tilt’ operates much the same way.

When your emotions start shoving your logic machine a bit too hard, you are said to be ‘on tilt’. Typically, you commence to lose your buy-in, or worse, your bankroll. We have all witnessed, and (sad to admit) personally experienced some of the more extreme, unpleasant examples.

There are also lesser degrees of tilt. Small concerns that break our concentration just enough to throw our game off. And, there is creeping tilt. It begins unnoticeable, incubates for awhile, then slowly grows into a monster.

Tilt is like a disease without a cure, but with an important difference. Even though its potential is always with us, we can willfully control this demon. We can never entirely rid ourselves, since the emotions that cause tilt are part of our mental hard wiring.

Willful control begins with self monitoring.

This might be the easiest part. We start simply by ‘thinking about what we are thinking’. Remember how you felt and what you were thinking, the last time you played really great poker? It is important to remember those thoughts and feelings. They will become your ‘standard’ for comparison. Try to mimic them whenever you play. Then learn to notice whenever you are straying from your ‘standard’.

Here is an illustration. When you are playing your best, you might characterize yourself as being calm, cool and collected. A regular 007. Nothing deters you from your mission. You are also focused, disciplined and patient.

Now, enter a little fatigue, a distraction, an unpleasantness, or an irritation. And, your thoughts begin to stray from your ‘standard’. Your focus, discipline and patience start to unravel. Your mind is soon full of thoughts about getting back to even. Or, getting even with the donkey that just rivered an inside straight to beat your pocket rockets. You watch helplessly as the harder you shove your agenda, the deeper you slide into the abyss. You are spiraling out of emotional control. This is being ‘on tilt’, the perfect emotional storm.

Note that the downward spiral began when your thoughts started to stray from your ‘standard’. This is where ‘thinking about what we are thinking’ becomes important. It is up to us to notice when our mood or thoughts shift. At that moment, it is up to us to mentally correct the course of our thinking. We must learn the techniques to near instantly calm ourselves, cool our emotions, and collect our thoughts. Otherwise, without a course correction, we are in for some nasty consequences.

So, here are some tips for corrective action.

1) If you are fatigued, take some time off to rest up.

2) If you received a bad beat, stop playing for awhile. Until the sting goes away.

3) If a player has become your Nemesis, change tables.

4) If you cannot collect your thoughts and refocus, stop playing.

5) If you are behind and feel yourself pushing to catch-up, stop for the day.

6) If you just do not feel right, wait until another time to play.

7) If you are in a bad mood, do not play.

And, for calming down, try these.

1) Take deep breaths.

2) Walk around for awhile.

3) Use a stress ball. (My favorite.)

4) Visualize serenity.

5) Laugh it off.

These tips look pretty simple, right?

But, emotions like greed, envy, revenge, and anger are tough, really tough to turn off like a light switch. The negative emotions that cause tilt are powerful forces. Only through intense desire and discipline can we take back emotional control of ourselves.

Job one? Do not devolve into tilt in the first place. Your goal should be to immediately recognize when you are straying, and to then immediately take corrective action. With discipline, you can apply this formula, and never suffer the consequences of tilt again.

Ultimately, it is our concentration that is the principal foe of tilt. And, it is our lack of concentration that feeds the monster.

Avoiding tilt, or “tilting”, is an important part of any poker player’s game. Going on tilt happens to all poker players eventually. The key is how you recognize and handle it.

Tilting refers to letting your emotions interfere with your ability to play poker. Generally it occurs in the middle of a bad streak but it can also happen when things are going well. Poker is a game that requires reasoning and a clear mind. Any kind of disruption in your ability to keep your emotions in check will threaten your game. Controlling your emotions in poker is necessary if you are going to be a successful player. A player on tilt may go all-in when the decision is clearly a poor one. Some players on tilt make one bad decision after another until the downward spiral snowballs completely out of control. This problem can prove to be very costly.

Poker is not a fair game! Play long enough and you’ll have your share of lucky and unlucky streaks. Eventually it all evens out and that’s why avoiding tilt is so important. Learn to control your emotions and in the long run you’ll be rewarded. It is absolutely critical that you stay focused and rational while playing. Player’s who get too emotional, upset, and can’t stay focused will likely lose all of the money they brought to the table. Don’t let this happen to you.

Usually, tilting happens to a player after a huge bad beat, or if they can’t seem to win a single hand. At that point the player going on tilt starts to play reckless. Some player’s, although not too many, actually tilt after a big win! The player tilting from losing will more likely tilt for a longer duration than the player tilting from winning.

So how can you go about avoiding tilt or tilting? Actually you can’t avoid it because it is a natural part of the game. The most important factor is that you must recognize when it’s occurring so you can limit any damage that may follow. If you can’t, then you’ll find yourself tilting over and over and possibly losing a lot of money. Once you’re able to recognize when it’s occurring, you’ll then be able to control your emotions. You must be able to control your emotions if you are to make smart decisions. If you make smart decisions, you control your game.

Making smart decisions may include sitting out a game or two, or possibly waiting until the next day to resume playing. Do whatever it takes to get your composure and mind-set back. I recommend sitting out for awhile and going for a long walk, run, or another type of exercise. You’ll be more relaxed afterwards both physically and mentally. You should then be in a better frame of mind to resume playing.

Do you ever notice players on television listening to music while they play in big tournaments? Listening to music can be a big help when it comes to avoiding tilt. The enjoyment the music brings you will help counteract the negative emotions from a bad beat. If you do happen to suffer a bad beat, make sure you change the song you were listening to at the time.

Avoiding tilt may not be possible. How you recognize and handle it will determine your fate.

You have a lot about bad beats in texas holdem poker play. What exactly is a bad beat? Well, in short, it’s having the dominant hand only to lose on the turn or river when a card hits that gives your opponents the winning hand.

Bad beats drive texas holdem poker players crazy. Which is why what I’m about to say may surprise you. Bad beats are a good thing. Now how can that possibly be?

Most texas holdem players think poker is about winning. It isn’t. I know, that sounds as strange as wanting bad beats so let me explain. Playing texas holdem is about making the right decisions at the table and putting yourself in the position to win.

While there is a lot more skill in playing poker than non-poker players think, there is still an element that we’ll call luck for lack of a better name.

Luck, also known as the bad beat, occurs when a player with a dominant hand does everything right only to see his opponent hit the only card that can win him the hand on the river.

For example, you’re down to the showdown with another player at the table. You’ve played your pocket aces perfectly to develop a big pot. We’re down to the river card, there’s only one ten in the deck and that’s the only card that can beat you.

And guess what? The ten hits on the river. You did everything right, made all the right decisions, and still lost the hand.

That’s a bad beat. But guess what? If you continually make the right decisions, you’re going to be a winning texas holdem poker player over the long haul. And that also means that you’ll experience bad beats more often than other players.

The best poker players see the most bad beats because they make the right decisions. You can’t have a bad beat go against you unless you made all the right decisions in the hand to make the bad beat possible.

So if you’re seeing a lot of bad beats, consider it a good sign. It means you’re making the right decisions at the poker table and in the long run, those decisions will pay off in an increased bankroll.

So don’t let those bad beats get you down. See them for what they are. A stepping stone on the way to becoming a better texas holdem poker player.