This post is going to be quite a long one because I will try to at least touch on the most important aspects of learning the beautiful game of No Limit Texas Hold’em so feel free to jump between the chapters that you are most interested in.

I will list them below and provide short descriptions so that if you are a beginner player, you can get a fair idea of what a particular chapter involves.

Feel free to skim through the text looking for the information that is most valuable for you first and then come back here whenever you need some more information on how to learn poker.

Ideally, for beginner players, I would recommend reading the all the chapters first, then setting up an account with an online poker room and practicing the game there playing the lowest possible stakes called micro stakes (usually $0.01/0.02) and coming back here to reread the topics as you regularly practice to get the best results.

You can learn how to play poker quite quickly, and to start winning versus recreational players, all you need is to learn poker fundamentals, but in order to beat regular players, you will need a lot more. You will need hours of practice and hours of studying the game. Your first hour of studying poker starts now.

Table of contents

  1. How the game of NL Texas Hold’em is played
    – what happens in a usual poker hand, what actions are available to players, how the hand plays out, and how the winner is decided
  2. Hand Rankings
    – how the winning hand is determined, what happens when two players have the same hand, what are the poker hand rankings
  3. Positions at the table
    – what positions do we distinguish, how positions affect the play, what are the best positions, and which positions are the worst
  4. Starting Hands
    – what hands you should play, what are the best hands in poker that you should always play, and what are the worst hands
  5. Bet Sizing
    – how to size your bets, when to bet, how the sizing affects the play
  6. Player Types
    – what types of players do we distinguish, what are their characteristics, how to play versus specific player types, what is the best player type
  7. Pot Odds
    – what are pot odds, how to calculate pot odds, what are outs, how to calculate the probability of hitting your draws
  8. Expected Value
    – what is expected value, how to calculate it, and how it can help you make better decisions

In the future, there will probably be more topics added and some of the topics will be described in a nutshell and will include links to a more thorough article with examples.

Let’s get started!

How to play Texas Holdem?

No-Limit Texas Hold’em is a game played usually on 6-max or 9-max tables so tables consisting of up to 6 or up to 9 players. There are also heads-up tables so one on one, 4-max tables, and 10-max, but the most common are 6-max and 9-max (also called full ring).

This poker variant is played for cash (cash games) or for chips (tournaments) and in cash games, players buy-in for a certain amount of big blinds i.e. 100 big blinds at a $0.01/0.02 micro stakes is $2.00 and a player can usually buy in for anywhere between 20 and 400 big blinds depending on the rules at a given table/casino.

In cash games, a player can also always add more chips (big blinds) but it has to be done between hands. A player can also always leave the table cashing out his stack for money.

Tournaments

In tournaments, a player buys in for a certain amount (tournament buy-in) i.e. $1 and receives a certain number of chips i.e. 100 000. The blinds start at a low level i.e. 10/20 and increase with every level i.e. every 30 minutes so that the starting stack of 100k can be 500 big blinds at the first level of 10/20, but after a few hours, it can be just 1 big blind at a level of 50k/100k.

Tournaments are played until we have a winner and there is usually around 10% of places that pay money and the pay structure heavily favors the top 3 players with the winner taking anywhere from 15 to even 50% of the whole prize pool.

Tournaments can have small fields of just 1 or a couple of tables (sit-and-go) or can have huge fields of thousands of players (multi-table). SNG vs MTT.

An example cash game poker hand

Here is a great video showing and explaining a sample hand:

Preflop betting round

The game starts with the dealer shuffling the cards and dealing each player a face-up card to determine who will start at the best position which is the button position (the highest card wins).

Then the player seated directly to the left of the button posts a small blind and the next player on the left posts a big blind. In a cash game of $1/$2, the small blind is $1 and the big blind is $2.

After the blinds are posted, the dealer starts dealing the cards starting with the small blind. After everyone has received their hand (2 hole cards), the action starts with the player seated directly to the left of the big blind.

This player seating at a position called Under The Gun (UTG) has 3 options:

  1. call the previous bet (which is the big blind)
  2. raise to any amount (no less than the previous raise so at least 1BB)
  3. fold their hand (give up the cards and no longer participate in this hand

These are the 3 options that are always available to you in poker. Call (or check if there weren’t any bets before you), Raise (or bet if there weren’t any bets before you), Fold.

The UTG player raises to 3BB, the action then moves clockward to the next player who has the same 3 options and decides to fold.

All the other players fold as well up until the action is on the player on the Big Blind who can now close the betting round by calling or folding or reopen the betting by raising.

The BB player decides to raise to 9 BB and the action is now on the UTG player who calls the bet.

The preflop betting round is complete and the dealer burns 1 face-down card and deals out 3 face-up cards which are called The Flop – AK5

The Flop betting round

The action on all the streets except preflop starts with the Small Blind. In this case the SB has folded preflop so the action starts with the BB player who checks (checking means finishing your action without either betting or folding).

The action moves to the UTG player who decides to bet 10BB. The BB player can now call the bet, raise, or fold, and decides to call.

The action is now complete and the dealer again burns 1 face-down card and deals out 1 face-up card which is called The Turn. It is the 6

The Turn betting round

The action again starts with the BB player who checks again, and the UTG player checks as well this time so the turn betting round finishes without any bets.

The dealer now burns a face-down card and deals out the last face-up card which is called The River. It is the 7

The River betting round

To make it more interesting we will do 2 scenarios of the action on the river:

1) The action again starts with the BB player who now bets 10BB, the UTG player raises to 30BB, and the BB player calls the bet.

The action is now complete and we have a showdown. The UTG player shows his cards first because the BB player called his bet.

He shows his 2 hole cards and makes the best possible poker hand out of those 2 hole cards and 5 community cards that are on the board.

He has 56 and the board is AK567 so he has two pair, sixes and fives.

Now the BB can show his hand but he can also muck it without showing (in this case the UTG player will win the pot automatically).

The BB player does show his hand and he has A7 so the best possible hand he can make from his hole cards and the board is two pair, aces and sevens.

The BB player thus has a better hand and wins the pot.

2) The action starts with the BB player who bets 10BB, but this time the UTG player bets all in for 96BB.

The BB player thinks long about it, but decides to fold. Now there is no showdown, the UTG player wins the pot and he doesn’t even need to show his hand, which is indeed the weaker hand.

That is the beauty of No Limit Texas Hold’em – you can win either by having the best hand or by making your opponents fold.

Hand Rankings in Poker

Here is a great video showing and explaining the poker hand rankings:

Let’s list them out starting with the best possible hand which is the straight flush and ending on the worst hand which is the high card.

  1. Straight Flush – 5 cards of sequential rank, all in the same suit
    e.g. J10987 (jack high straight flush) or 5432A (five high straigth flush)
  2. Four of a Kind (also known as quads) – 4 cards of the same rank with a kicker
    (the highest card of a different rank) e.g. AAAAK or 8888A
  3. Full House (also known as a boat) – 3 cards of the same rank with 2 cards of another rank (set+pair)
    e.g. AAAKK (aces full of kings) or 888AA (eights full of aces)
  4. Flush – 5 cards of the same suit, not in sequential rank
    e.g. AQJ72 (ace high flush) or 98432 (nine high flush)
  5. Straight – 5 cards of sequential rank, not in the same suit
    e.g. AKQJ10 (ace high straight) or 5432A (five high straigth)
  6. Three of a kind (also known as a set) – 3 cards of the same rank with 2 kickers
    e.g. AAAKQ (set of aces) or 888AK (set of eights)
  7. Two Pair – 2 cards of the same rank with 2 cards of a different rank with a kicker
    e.g. AAKKQ (two pair, aces and kings) or QQ88K (two pair, queens and eigths)
  8. One Pair – 2 cards of the same rank with 3 kickers
    e.g. AAKQJ (pair of aces) or 776JK (pair of sevens)
  9. High Card – simply nothing, 5 kickers
    e.g. AKJ109 (ace high) or 76542 (seven high)

How to determine the winner if two players have the same hand?

In case two or more players have the same hand, the kickers are used to determine the winner.

For example if player A holds AK and player B holds AJ and the board is AQ1055

then both players have two pair, aces and fives, but player A has a higher kicker with the K

His hand is AAK55 vs player B’s hand AAQ55 and so player A wins the hand.

In case both players hold a flush or a straight, the winner is determined by the highest-ranking cards.

For example, an ace-high flush beats a king-high flush, and six-high straight beats five-high straight.

Or an ace-king-high flush beats an ace-queen-high flush, but king-high straight splits the pot with another king-high straight.

Positions at the table

Positions are very important in poker because having position on your opponent means that you are acting after them and thus have the informational advantage.

The best position at the poker table is the Button and in the long run the vast majority of your winnings (if you are a winning player that is :D) will come from the Button and Cut-Off, but first things first.

Having position over your opponent means you are acting after them and being out of position in a hand means you are acting before your opponent.

We can distinguish Early Positions, Middle Positions, Late Positions, and the Blinds. Let’s take a closer look at each group.

Early Positions

Early Positions are Under the Gun (UTG) and Under the Gun +1 and these are positions that act first pre-flop, and just after the blinds post-flop.

You can imagine what it means having many players act behind you. It means that each and every one of them can wake up with a premium hand and can raise reopening the betting preflop and will have position on you after the flop.

Playing from UTG or UTG+1 you can only have position over the blinds if they are in the hand so you should be playing the least amount of hands from these positions.

We will get more in-depth about what hands to play from which positions in the starting hands chapter, but for now what you can remember is that you should be playing the least amount of hands from early positions, something like the top 9-10% of hands.

Middle Positions

The next category is middle positions and here we have Middle Position 1 (MP1) and Middle Positions 2 (MP2, also sometimes called LoJack) – not too creative names I must admit.

As you can imagine your position is better when playing from middle positions as opposed to early positions, but it is still not very good so you should be playing slightly looser, something like the top 13-15% of hands.

You should also be very careful when early position opens (puts in a raise) because you should assume they have a pretty good hand and there are still many people to act after you who may reraise (3-bet).

Late Positions

Now the best category of poker positions – late positions. These are your favorite positions and you will win the most often when playing from them because you will mostly be in position.

We can distinguish HiJack, CutOff, and Button with each being better than the previous because only being on the Button guarantees that you will have position in the hand.

If you raise from HiJack, there is still CutOff and Button that are left to act after you and may reraise.

Therefore from HiJack you should play something like the top 20% of your hands, from CutOff something like 27%, and from the Button something like 45%.

Position is king and the button is the most profitable one because pre-flop there are only the blinds left to act and post-flop the button is always in position.

The Blinds

The blinds are the worst positions as they have to put money in without seeing their cards and post-flop they are almost always out of position.

The Small Blind is the worst position at the table because you are always first to act post-flop and pre-flop you still have the Big Blind to act after you.

The Big Blind is a bit better position because even though it is the least profitable seat (you are posting 1BB without seeing your cards every time you are on the Big Blind), you often get to realize your equity as you are closing the action pre-flop and often have great pot-odds to see the flop with a hand that has great potential to hit big.

Starting Hands in Hold’em

The hands you play determine your results by far so it is absolutely crucial that you understand and memorize what hands to play in Hold’em.

What are hands worth playing and what hands are considered trash and should be automatically folded no matter the position.

The Base

Let’s start with the base of hands that you can play from all the positions at the table unless there were some big raises or 3-bets before.

The base represents about 10% of all hands and it is the core of your game, these are hands you are almost always happy to play, but of course, these are not the only hands that you play.

You will add on other hands to your opening ranges depending on your position and I will give you some examples of the hands you will be adding on later on.

Pocket Pairs

Big pocket pairs like AA, KK, QQ, JJ, or 1010 are very strong hands that often make overpairs to the board on the flop.

Medium pocket pairs like 99, 88 or 77 are quite strongs, which can make overpairs, but you are not going to want to build big pots with them unless you hit a set.

Small pocket pairs like 66, 55, 44, 33, or 22 are really easy to play because you are mainly interested in hitting a set on the flop, or folding.

Big Aces

Big suited aces like AK, AQ, AJ, or A10 have great potential for hitting the top pair with a good kicker, as well as nut flushes and straigths.

Big off-suited aces AK, AQ, AJ have good potential for hitting the top pair with a good kicker as well as the nut straigths.

King Queen suited

The only other hand that makes up the base is King-Queen suited e.g. KQ and that is a hand with excellent potential.

And that is it. The base. All pocket pairs, big suited aces ATs+, big off-suited aces AJo+, and KQs. Pretty simple, right?

Other hands worth playing

If you read the part about positions in poker, you must be wondering what are the other 35% of hands you are supposed to play from the Button if the Base only makes up 10% of hands.

These are broadway cards, other suited and off-suited aces, and suited connectors and one- or two-gappers.

Broadway cards

Any combination of AKQJT e.g. J10, Q10, KJ etc.

Most valuable are the suited and connected combinations e.g. J10, QJ, but the less connected suited combos like K10 or Q10 are still quite good hands.

The bigger the gap the weaker the hand i.e. KJ is better than K10.

Suited and off-suited Aces

Suited cards are always stronger than their offsuit combinations because of the added probability of hitting flushes so suited aces are hands you are almost always happy to play.

All suited aces starting with A2 and finishing on A9 are solid hands that can be played from middle and late positions.

Offsuited aces starting with A2 and finishing on A10 are good hands that can be played mainly from late positions.

Suited connectors and one-gappers

Suited connectors are hands that contain two consecutive cards in the same suit e.g. 67, 45, or 910.

Suited connectors are excellent hands to see the flop with from middle and late positions as they have great potential for hitting straights and flushes.

One-gappers are quite similar, however, there is a 1-card gap between the ranks e.g. 57, 46, or 9J.

Similarily, two-gappers are hands with a 2-card gap between the ranks e.g. 47, 47, or 9Q.

Obviously, suited connectors are the most valuable hands in this category and of course the higher the cards, the better i.e. 89 is slightly stronger than 78.

Suited one-gappers are a bit weaker, and suited two-gappers are much weaker.

Offsuited connectors and one-gappers

This category is the same as the one above, except for the fact that the cards are not of the same suit.

These hands are much more common and they are weaker as they only have the potential for straights and not flushes.

They are usually played them from late positions.

Which hands to play and how to play them?

What I recommend is starting out playing pretty much just the base. It is a fool-proof way of making sure you are going to make money and what is better than making profit?

If you start your poker journey well, you will be more likely to stick and learn the game to compete with better players and on higher stakes.

Playing just the base is enough to win at micro stakes online or in home games with inexperienced players, but you won’t be able to get away with it playing with better players.

In the chapter about positions, I showed some examples of what your range should look like from which position so if you take a look there now, it will make much more sense to you as you will see it is the base + other hands worth playing and the better your position is, the more hands you can play.

What I also recommend is increasing the amount of hands you are playing from each position very gradually and starting with increasing the amount of hands from late positions.

It is better to play too little hands than to play too many hands and playing too many hands for a beginner player will usually end up badly so take your time.

You should be starting out playing the micro stakes so by all means, play the first few thousand hands by just playing the base, and then start adding more hands slowly as you’re gaining experience through practice.

Bet Sizing

How to size your bets in No-Limit Texas Hold’em?

We can distinguish bet sizing pre-flop and post-flop and let’s start with the first one.

Pre-flop sizing

In cash games, if you are first to open the pot (there were no raises before you), the rule of thumb is to raise to something like 3BB + 1BB per every limper (player who just calls the big blind).

In tournaments, the stack sizes are much smaller so usually players open to anywhere from 2 BB to 2,5BB + something like 1BB per every limper.

In cash games, especially live cash games, it is not uncommon to see a raise to 10 or more BB even with just a couple of limpers.

When it comes to 3-betting (re-raising) pre-flop, usually players will 3-bet to anywhere between 2.5-4x the previous bet.

So if the open is to 3BB, the standard 3-bet may be to 9BB in cash games, and in tournaments, if the open is to 2.2BB, the 3-bet may be to 5.5BB.

These are just the standard sizings, each player may use a slightly different one, but in general, the majority of players will fall use sizings in this range.

Post-flop sizing

After the flop, on all later streets, we use sizings that indicate the percentage of the pot we are betting i.e. 50% of the pot or 120% of the pot.

Of course, with practice, you will gravitate towards sizings that work best for you, but for beginner players, I would recommend using the following bet sizings:

  • 33%
  • 67%
  • 133%

Start out only using the first two ones, the 33%, and the 67% pot bet, and gradually as you gain experience add the third one, which is an overbet to 133%.

When to bet?

In poker, you may want to bet mainly for two reasons:

  1. For value
  2. As a bluff

If you are value-betting, it means you think you are likely to have the best hand and you want your opponent to pay you off so that you can win a big pot.

If you are bluffing, it means you think you are likely to have the worse hand and you want your opponent to fold his hand so that you can win the pot.

For beginner players, I suggest to start off focusing mainly on when to bet for value, but also trying to recognize good spots for bluffs and trying to pull off a bluff bet once in a while.

With practice, you will learn what are the good spots for bluffing and it will become second nature to you, but at the beginning, it is much better to bluff rarely and gradually increase the frequency as you gain more experience and can recognize the best spots for bluffing.

Which sizing to use?

In general, when you are betting for value, you want to bet as much as you think your opponent is likely to call and when you are bluffing, you want to bet as little as you think is enough to make your opponent fold.

It is very important to keep your sizings consistent in similar spots no matter if you are value betting or bluffing because otherwise, your opponents can pick up on your betting patterns and easily read your game.

For example, if the board is A538K, you want to use the same sizing for when you are betting for value with AK and when you are bluffing with a missed flush and straight draw with67.

This way your opponent can never be too sure if you are betting for value or bluffing and that should be your goal in poker.

Player Types

In poker, there are two simple characteristics we can use to divide players into easily recognizable types.

We can look into how many hands they play and how they play their hands.

If a player plays a lot of hands we will say he is a loose player, and if he plays few hands, we will say he is a tight player.

If a player often bets or raises, instead of checking or calling, we will say he is an aggressive player, and if a player often checks or calls, rarely betting or raising, we will say he is a passive player.

Loose Aggressive

The first player type we will analyze is the loose-aggressive player, also known as LAG or maniac.

This player plays a lot of hands and he plays them aggressively often betting or raising.

This is the hardest player to play against as they are capable of betting big on all streets with close to nothing and they love to make other players fold.

The aggressive style of LAGs makes it difficult to fight for pots with mediocre hands and makes bluffing more expensive as they do not like folding.

How to adjust to loose aggressive players?

First of all, do not bluff them, unless you are willing to go all the way. It will rarely take just one bet to get them to fold and they will strike back at the first sight of weakness.

Secondly, play tight versus them, make sure you’ve got the goods before getting involved in a big pot, but once you get involved, stick to your strategy and do not fold easily just because they are betting big.

Remember that it is just part of their style, they like to bet big and they bluff way too often so if you have a strong hand, take advantage of their style and allow them to come out blazing at you.

Lastly, play passively versus them, if you are out of position. Set traps on the Turn and River if you think they are likely to take the bait. Just check to let them smell weakness and force them to put out a big bet, and then raise it.

Loose Passive

The second player type is your favorite kind of player and is often called a calling station or ATM.

Loose passive players play a lot of hands and they play them very passively, mostly checking or calling, and rarely if ever betting or raising.

This is the easiest player to play against as they do not like folding and the fact that they play a loose range of hands means they often hit something.

How to adjust to loose passive players?

Never, ever bluff them. It just doesn’t make sense, because they might call 3 streets with just a third pair.

If you have a good hand, bet and bet big. Remember, they don’t like folding and they will often keep calling with a weaker hand so take advantage of that.

You need to extract as much value from these players as you can so even with mediocre hands, you may often get some thin value.

That means you can play a slightly looser range versus these players preflop, but postflop, you shouldn’t build pots without hitting a decent hand as you will have to win on showdown versus calling stations.

Tight Aggressive

The tight-aggressive player type is the one you should be aiming for and it is the most profitable playing style.

Tight aggressive players (also known as TAGs) play a carefully selected range of hands and they play those hands aggressively, often betting or raising.

Good hand selection pre-flop makes the decision-making process much easier on later streets and the aggressive way of playing allows TAGs to be the biggest winners in the game.

How to adjust to tight aggressive players?

You will often find that the regulars at micro stakes or small stakes will play the TAG style, but you should not fear them.

After all, if they were any good, would they be playing small stakes?

You can easily find leaks in their game. It might be not bluffing enough (you counter that by giving them more respect when they bet big).

Or bluffing too much (you counter that by giving them less respect when they bet).

It might be not 3-betting enough or folding to 3-bets too often (you counter that by opening a wider range of hands or 3-betting wider).

It might be having easily readable betting patterns (i.e. they bet close to full pot when they have it and they bet half pot when they are bluffing).

What is important here is the fact that TAG is indeed the optimal playing style, but there is a lot of terrible TAG players and in poker there is a ton of mistakes to be made and your goal when playing is to take advantage of your opponents mistakes and to try and make as few mistakes yourself as possible.

Tight Passive

The tight-passive player (aka nit) is another playing style not to be feared.

These are players who play a tiny amount of hands and they play them passively, often checking and calling, rarely betting or raising.

How to adjust to tight passive players?

They are very easy to play against and they are often losing or at best break-even players.

Their tight hand selection pre-flop means they usually have a good hand when they enter the pot, but their passive playing style means you can often try to outdraw them cheaply.

When they bet, beware, as this means they hit big and you can easily fold pretty good hands.

You can get away with stealing their blinds 100% of the time as they will rarely fight back.

Which playing type is the best?

The tight aggressive player type is by far the most profitable one in the long run and this is the style you should aim for.

With time and practice, you will develop your own style which will be a variation of the TAG.

You will develop your own ranges which will be on the tighter side or on the looser side, and your aggression may be on a normal side or taken up a few notches, but it will never approach the LAG stats, as there is a certain number of hands you can profitably play and if you play more than that even if your game is excellent, you simply will be losing money on all those extra hands, thus lowering your overall win rate.

Pot Odds

Pot odds in poker are a very important aspect of the game as they allow you to make better decisions.

Before discussing pot odds, I believe it is important to explain what are outs and how to calculate the probability of hitting your outs.

I recommend watching the following video which explains all these concepts:

What are outs?

An out is a card that can improve your hand for example if you hold an open-ended straight draw, there are 8 cards that can fall on later streets which will improve your hand to a straight and that means you have 8 outs.

e.g. you hold 910 and the board is JQ5

There are four sevens i.e. 7777 and four kings i.e. KKKK that can come on the Turn or on the River improving your hand to a straight.

Another example would be holding the same hand 910 on a 278 board and assuming that a 9 or a T can also be enough for you to win the pot.

If that is the case, you have 14 outs – four sixes 6666, four jacks [invalid notations], three nines 999, and three tens 101010

How to calculate the probability of hitting your outs?

Once you count the number of outs that you have, you can use that number to calculate the probability of hitting those cards on later streets.

To quickly calculate the probability of hitting your outs, you can just remember the rule of two and four.

On the flop multiply the number of your outs by 4 i.e. if you have 10 outs, you have a 40% probability of hitting them on the turn or river.

On the turn multiply the number of your outs by 2 i.e. if you have 10 outs, you have a 20% probability of hitting them on the river.

That’s it. Very easy to remember and extremely helpful when playing. Especially when you know how to calculate the pot odds.

How to calculate the pot odds?

Pot odds in poker represent the ratio between the size of the pot and the size of the bet that you need to put into the pot.

For example, imagine that you are heads-up on the river, there is $200 in the pot, and your opponent bets $100.

You have to call $100 to win a pot of $300 ($200 in the pot at the start of the betting round + $100 your opponent bet).

That means your pot odds are 300 to 100 or simply 3 to 1.

Knowing that your pot odds are 3 to 1 you also know that you need to win at least one out of four times (1/4) to break even.

In order to change the odds to percentages, you can divide your bet by the size of the pot with your bet so in our example $100/$400 = 1/4 = 25%.

Why are pot odds important in poker?

Knowing that you need to win at least 25% of the time allows you to make better decisions.

For example, if you have 10 outs on the turn, and you use the rule of two and four to calculate that your equity is 20%, you should not call a bet that is offering you 3 to 1 odds.

On the other hand, if your opponent bets $50 to the pot of $200, offering you odds of 5 to 1, you can comfortably call the bet knowing that your call is profitable because you will hit your hand more often than 1 out of 6 times (16.67%).

You should always consider the pot odds offered to you and be aware of what they mean. They illustrate how often you need to win (how much equity you need to have) in order for this call to be profitable.

Expected Value

Expected value in poker helps you make better decisions. Once you understand this concept, you will also use it to make better decisions in life in general.

Expected value is a concept used to describe the average outcome of a given scenario and it is best to describe it with some examples.

Coin flip example

You flip a coin that has a 50% probability of coming up heads and 50% probability of coming up tails. Someone offers you a $1 bet that if on the next throw the coin comes up heads, they will pay you $1 and if the coin comes up tails, you will lose your $1 bet.

What is the expected value (EV) of taking the bet?

In order to calculate it, you need to multiply the possible scenarios by their probabilities and their sum will be the EV.

So we have 50% * $1 (coin comes up heads) + 50% * (-$1) (coin comes up tails) = $0,50-$0,50 = $0.

The expected value of taking such a bet is zero. In the long run, if you flip the coin a million times each time taking this $1 bet, you will end up neither losing money or making profit.

Let’s say if the person offering the bet started paying $2 per each coin flip coming up heads.

The expected value would now be 50% * $2 + 50% * (-$1) = $1-$0,50 = $0,50.

If the expected value of a decision is positive, it means this decision is profitable in the long run so in our case if we take this bet and flip the coin 100 times, we will make about $50 (100*$0.50).

Expected Value in poker

We hold AA on the river versus a single opponent and the board is AJ9105.

The pot is $1000 and our opponent bets $1000.

Based on the action on previous streets and our knowledge of the opponent, we estimate his range here to be:

  • 50% straights (combinations of KQ or 87)
  • 30% sets and two pair combos
  • 20% missed flush draws or other bluffs

What is the expected value of calling this bet?

It is 50% * (-$1000) + 30% * ($2000) + 20% * ($2000) = -$500 + $600 + $400 = $500.

Whenever our opponent ends up having the straight, we will lose the $1000 bet, and in times where the opponent shows a set, a two-pair hand or a bluff, we will win a $2000 pot.

The expected value is positive $500 so we can comfortably call knowing that in the long run, we will make $500 on such a call.

Aces versus Kings all in preflop

What is important here is the fact that individual outcomes do not matter.

Let’s say you hold AA and after a couple of raises and reraises you end up putting them all in versus another player holding KK.

Your pocket aces will win around 82,36% of the time so if the pot is $1000, your expected value is $823,60.

That doesn’t mean that you will win every time. The other player will win 17,09% of the time and his EV in this pot is $170,09.

So if this other player wins, his outcome will be $829,91 above EV and if you win, your score will be $176,40 above EV.

On the other hand, if you win, your opponent’s outcome will be $170,09 below EV and if your opponent wins, your outcome will be $823,60 below EV.

Running above or below expected value is a good indicator of luck in poker.

Even though you are a huge favourite, you may lose a couple of such situations in a row and have a session where you lost $500 but your EV was at +$500.

That means your session was very unlucky and you ran $1000 below EV. In the long run (millions of hands) it all averages out so if you are unlucky now, just keep playing and you will be lucky again 🙂