A Beginners Guide to Calculating Poker Expected Values (EV) with Speed
A Beginners Guide to Calculating
Poker Expected Values (EV) with Speed
Pokeretude.com
Table of Contents
Introduction
Exercise 1 – Recognition
Exercise 2 – Card Odds
Exercise 3 – Pot Odds
Exercise 4 – Expected Value
Final Note…
Answers
Introduction
Do you want to improve your poker? Improvement comes through ongoing practice of a specific technique. Tennis players practice their serve, musicians practice their scales, and now it’s your turn to practice your poker skills in the same way.
The aim of this free eBook from pokeretude.com is to help you improve your ability to recognise your expected value at speed, which is the key to your long-term profitability. You will do this through exercises, which have been broken down in to each stage of an expected value assessment process.
Recognizing your expected value at speed will help you to make good decisions as to whether you should bet based on fact – not feeling, intuition, or emotion. We don’t want to ignore feeling, intuition and emotion, but recognizing expected value will make sure they don’t get the better of us at the table.
The same exercises are available at pokeretude.com and have been designed to be repeated and practiced to improve your speed and accuracy of equating expected value at the table, leading you to greater profitability in the long term.
These exercises give you a chance to hone one of the key skills of poker away from the emotion of the tables – so you can focus on building your technique and skill in a safe, no-lose setting.
In this book we will be focusing expected value on post-flop, single out cards – that is the expected value that is possible with only one additional card, from the position of the flop having gone down. This is a good place to start to be able to grasp the concepts of expected value, and if you want to continue on, more exercises and tutorials are available at pokeretude.com.
This book is all about learning to make long-term profitable moves. Playing the long term odds mean you will win more, and ultimately come out on top!
Who is this book for?
This book is intended to be for people who understand the basics of Texas Hold Em’ Poker, and want to start understanding some of the intermediate to advanced topics.
If you are not completely confident on the basics, articles and tutorials are available for free at pokeretude.com.
What is Expected Value?
Expected value is a way of calculating on average, the amount you are likely to win in the long term from your current hand position.
Think of it like this, if you had to play the same hand over and over, and you knew you were 80% likely to win, you would keep playing. However if you knew you only had a 5% chance of winning, well, you wouldn’t keep putting your chips on the table!
This is a simplistic example, as a number of other factors come into play, but it should give you an idea of the concept.
The mathematical side of poker is something that people can get to grips through practice. If you’re scared of the numbers – don’t be! Continue practicing on a regular basis and there is little doubt you will memorize and master the numbers.
It will become a simple way for you to work out if playing a hand is worth your while, or if you should fold.
What is an out?
An out is a card which will improve your hand. For example, if you have a pair and want to turn your hand into Three of a Kind, there are two remaining cards in the pack that could do this. These cards are known as your outs.
Counting your outs is a way to quickly understand what the possibilities are, and what your hand could turn into in the next few cards.
What are Card Odds?
Card odds are the probability that you are going to hit one of your outs.
What are Pot Odds?
Pot odds proportion of chips you could lose when calling a hand compared to the amount you could win.
People can sometimes however refer to pot odds with the same meaning as expected value. In this book, we will only use it with reference to the odds you get from the chips in the pot, but it’s good to be aware of its alternate meaning.
Notes for book
In this book both percentages and ratios have been included. You can use either depending on what you find easiest, but there is not really a need for you to learn both. My personal preference is to use ratios, as I find it easier to calculate pot odds this way.
All percentages and ratios have been rounded to the nearest one decimal place. This has been done to provide enough detail to compare probabilities, but not to add any more complexity than is required. I would suggest learning the probabilities by heart to one decimal place, but when calculating your pot odds (as you will do in exercise 3), you may find it easier to calculate to less than that, or only do an estimated calculation.
Exercise 1 – Recognition
A simple first step is being able to recognize your hand. Recognition does not only include recognizing the hand you currently have, but seeing the hands that you could have after the next few cards.
We will only be looking at post-flop, single out hands, as this is a good starter set to learn the concepts. These are hands that can be achieved with only one additional card on the turn, just after the flop has gone down.
If you look at your hand post flop, there are always a limited number of hands you can get to with one additional card. For example, if you have a pair post flop, you are never going to get to four of a kind or full house. Understanding and learning what these limited number of hands you can make on the Turn can help you quickly work out the correct number of outs, and therefore your card odds for your current hand.
In this exercise, we’re going to be trying to reach a particular hand level, and if we reach it, we will have won the hand. In real life, you would try and guess what your opponents cards or hand was, and then try and beat it. But to keep it simple for the moment, we are just going to try and reach the hand we have specified, and work out the outs for that.
To keep you on your toes we’ve thrown in a load of zero out hands! Unfortunately not all your hands are going to be good ones, you’ll need to keep an eye out for those as well.
The table on the next page can be used as a reference guide, and is good information to know off by heart. Pokeretude.com has lots of exercises to help you learn the information, giving you a huge advantage of speed, knowledge and a cool head at the table.
Lets run through some examples to clarify.
Starting with No Hand, to get to…
…Pair means you’ll have 6 outs
…Straight (Gutshot) means you’ll have 4 outs
…Straight (Open Ended) means you’ll have 8 outs
…Flush means you’ll have 9 outs
Starting with a Pair, to get to…
…Two Pair means you’ll have 9 outs
…Three of a Kind means you’ll have 2 outs
…Straight (Gutshot) means you’ll have 4 outs
…Straight (Open Ended) means you’ll have 8 outs
…Flush means you’ll have 9 outs
Starting with a Two Pair, to get to…
…Full House means you’ll have 4 outs
Starting with a Three of a Kind, to get to…
…Full House means you’ll have 6 outs
Starting with a Straight, to get to…
…Flush means you’ll have 9 outs
Starting with a Flush…
…means you can’t improve your hand on the next card! No outs
Starting with a Full House, to get to…
…Four of a Kind means you’ll have 1 out
Starting with a Four of a Kind…
…means you can’t improve your hand on the next card! No outs
Example 1
My Cards – JC 2H
Flop – 2S 3S 2C
You currently have a Three of a Kind and are looking to increase to Full House or higher.
Full House – JS JD JH
Four of a Kind – 2D
You have 3 cards that would take your hand to Full House, and 1 card that would take you to Four of a Kind. In total, you have 4 outs to hit Full House or higher.
Example 2
My Cards – 9C 9S
Flop – 5S 4C QD
You currently have a pair, of which both cards are in your hand. On the next card you would be able to achieve Two Pair, or Three of a Kind, but not a Straight or a Flush.
Two Pair – 4S 5C QH 4D QC 5H 5D QS 4H
Three of a Kind – 9D 9H
You have 9 cards that would take your hand to Two Pair, and 2 cards that would take you to Three of a Kind. If you were aiming to hit Three of a Kind or higher, you would have 2 outs.
Example 3
My Cards – JD 7H
Flop – 5S 6H 6S
You currently have a pair, but so does everyone else at the table! In this case we are not able to count our hand as a pair as we have no card in our hand that improve our hand higher than everyone else’s. In reality, you currently have No Hand.
Two Pair – 7D 7C JC JH 7S JS
You have 6 cards that would take your hand to Two Pair.
Example 4
My Cards – 9D KC
Flop – AD KD 2D
You currently have a pair. On the next card you would potentially be able to achieve a Three of a Kind or Flush.
Three of a Kind – KH KS
Flush – 5D 3D QD 10D 4D JD 7D 8D 6D
If you are aiming to hit a Flush or higher, you have 9 cards that would take you to that level.
The next pages have exercises for you to practice recognizing single card outs, and speed up your recognition ready for you to use your improved skill at the tables. See answers at the end of the book, and if you want more exercises to continue your practice, sign up to pokeretude.com.
Ex 1.01
My Cards – 4S 4H
Flop – AD KS 9C
Aiming for at least – Two Pair
Out Cards –
Outs Total –
Ex 1.02
My Cards – 6D AD
Flop – 4H 2H 2D
Aiming for at least – Three of a Kind
Out Cards –
Outs Total –
Ex 1.03
My Cards – AH 8S
Flop – 5H 6S 9D
Aiming for at least – Straight
Out Cards –
Outs Total –
Ex 1.04
My Cards – 3D 10H
Flop – 9S QD QH
Aiming for at least – Full House
Out Cards –
Outs Total –
Ex 1.05
My Cards – KS 2H
Flop – 3D 10H JC
Aiming for at least – Straight
Out Cards –
Outs Total –
Ex 1.06
My Cards – 8D 5S
Flop – 3S JC 4C
Aiming for at least – Pair
Out Cards –
Outs Total –
Ex 1.07
My Cards – AH 9H
Flop – 6H 5H 7S
Aiming for at least – Two Pair
Out Cards –
Outs Total –
Ex 1.08
My Cards – KD 7H
Flop – 9C 8C 5C
Aiming for at least – Pair
Out Cards –
Outs Total –
Ex 1.09
My Cards – 7C 5H
Flop – JD 4D QC
Aiming for at least – Pair
Out Cards –
Outs Total –
Ex 1.10
My Cards – 7C 4C
Flop – 8C AS 5H
Aiming for at least – Straight
Out Cards –
Outs Total –
Ex 1.11
My Cards – 10D 5D
Flop – 5S QH 10C
Aiming for at least – Three of a Kind
Out Cards –
Outs Total –
Ex 1.12
My Cards – 7D 10S
Flop – 7H 7S 6H
Aiming for at least – Straight
Out Cards –
Outs Total –
Ex 1.13
My Cards – AH KH
Flop – KS 8D 9C
Aiming for at least – Two Pair
Out Cards –
Outs Total –
Ex 1.14
My Cards – 2S 6H
Flop – 7D 7C 3C
Aiming for at least – Straight
Out Cards –
Outs Total –
Ex 1.15
My Cards – JD 8D
Flop – 3D 10C 5D
Aiming for at least – Two Pair
Out Cards –
Outs Total –
Ex 1.16
My Cards – 10S 8D
Flop – 9C 8H JD
Aiming for at least – Two Pair
Out Cards –
Outs Total –
Ex 1.17
My Cards – 7D KS
Flop – 4C 8C 6S
Aiming for at least – Two Pair
Out Cards –
Outs Total –
Ex 1.18
My Cards – 10D 5C
Flop – 4D JC 2H
Aiming for at least – Two Pair
Out Cards –
Outs Total –
Ex 1.19
My Cards – 10S KC
Flop – 8C JC 5D
Aiming for at least – Pair
Out Cards –
Outs Total –
Ex 1.20
My Cards – 5S 3C
Flop – 9H KH 8H
Aiming for at least – Straight
Out Cards –
Outs Total –
Ex 1.21
My Cards – 10H 5C
Flop – 10D 5H KD
Aiming for at least – Straight
Out Cards –
Outs Total –
Ex 1.22
My Cards – 6S 2C
Flop – 8S 10H 6D
Aiming for at least – Three of a Kind
Out Cards –
Outs Total –
Ex 1.23
My Cards – 8C 2C
Flop – 6S 5D 7H
Aiming for at least – Flush
Out Cards
Ex 1.24
My Cards – JH 5S
Flop – 5H 2S 8C
Aiming for at least – Full House
Out Cards –
Outs Total –
Ex 1.25
My Cards – KH QC
Flop – QD 7D 2D
Aiming for at least – Two Pair
Out Cards –
Outs Total –
Ex 1.26
My Cards – QH 6C
Flop – 5H 5S QS
Aiming for at least – Three of a Kind
Out Cards –
Outs Total –
Ex 1.27
My Cards – 9S 3H
Flop – AS 6H 4H
Aiming for at least – Straight
Out Cards –
Outs Total –
Ex 1.28
My Cards – 3S 5C
Flop – 7S KD 2D
Aiming for at least – Three of a Kind
Out Cards –
Outs Total –
Ex 1.29
My Cards – QC 2H
Flop – KD JC 6S
Aiming for at least – Pair
Out Cards –
Outs Total –
Ex 1.30
My Cards – 2H 2D
Flop – 7S 10H QD
Aiming for at least – Three of a Kind
Out Cards –
Outs Total –
Exercise 2 – Card Odds
Once you start to recognize the cards that will give you a winning hand, you need to know the card odds, or the probability of one of those cards coming up as the turn. This can be a percentage, or a ratio, and we suggest that you pick which ever of these comes easier to you.
Ratios and percentages are read in different ways. A card odds ratio of 1: 5 would mean that for every time you hit an out, you would have 5 times you missed. A card odds percentage of 10% means that you would hit an out 1 time out of 10. Knowing these figures will help you to understand just how much risk you are taking by staying in the hand.
Calculating ratios and percentages requires that we know how many outs we have out of the total possible cards left in the pack. If we were to have 6 outs, and know that we have 47 cards left in the pack, we can work out the card odds of one of the out cards appearing on the turn. We use the following formulas:
Ratio = (Cards in pack – Outs) / Outs
1 : 6.8 = (47 – 6) / 6
Percentage = (Outs / Cards in pack) x 100
[_ 12.8% = (6 / 47) x 100 _]
As we are just focusing on the post-flop stage in this book, there will always be 47 cards left in the pack that could be the card that appears on the turn. This is always the case no matter how many people are in your hand, as we do not know what cards the other players are holding, we must treat them as possible cards that could come up.
Below is a table with all of the ratios and percentages for different numbers of outs. Memorizing the card odds on this table for either the ratios or the percentages is important, and will make sure you quickly have the information you need when you’re at the table. You might want to print it off and have it beside you to refer back to while you’re learning.
Later, these card odds will be compared to the pot odds, which will help your decision of whether you should stay in the hand.
Number of Outs = Ratio = Percentage
1 Out = 1 : 46.0 = 2.1%
2 Outs = 1 : 22.5 = 4.3%
3 Outs = 1 : 14.7 = 6.4%
4 Outs = 1 : 10.8 = 8.5%
5 Outs = 1 : 8.4 = 10.6%
6 Outs = 1 : 6.8 = 12.8%
7 Outs = 1 : 5.7 = 14.9%
8 Outs = 1 : 4.9 = 17.0%
9 Outs = 1 : 4.2 = 19.1%
10 Outs = 1 : 3.7 = 21.3%
11 Outs = 1 : 3.3 = 23.4%
12 Outs = 1 : 2.9 = 25.5%
13 Outs = 1 : 2.6 = 27.7%
14 Outs = 1 : 2.4 = 29.8%
15 Outs = 1 : 2.1 = 31.9%
16 Outs = 1 : 1.9 = 34.0%
17 Outs = 1 : 1.8 = 36.2%
18 Outs = 1 : 1.6 = 38.3%
19 Outs = 1 : 1.5 = 40.4%
20 Outs = 1 : 1.4 = 42.6%
21 Outs = 1 : 1.2 = 44.7%
22 Outs = 1 : 1.1 = 46.8%
23 Outs = 1 : 1.0 = 48.9%
Example 1
My Cards – 7S 2H
Flop – KS 2S 7C
Outs to reach a Full House – 2C 7H 2D 7D
In total, you have 4 outs to hit Full House or higher, giving you a card odds ratio of 1 : 10.8 or an 8.5% percentage chance of hitting your cards.
Example 2
My Cards – 9H 10C
Flop – 7H 6C 10S
Outs to reach a Straight – 8C 8D 8S 8H
Outs to reach Three of a Kind – 10H 10D
In total, you have 6 outs to hit a Straight or higher, giving you a card odds ratio of 1 : 6.8 or a 12.8% percentage chance of hitting your cards.
Example 3
My Cards – JD 4D
Flop – 10D 5S 9D
Outs to reach a Flush – 6D 3D QD 7D KD 2D AD 8D 5D
In total, you have 9 outs to hit a Flush or higher, giving you a card odds ratio of 1: 4.2 or a 19.1% percentage chance of hitting your cards.
Example 4
My Cards – QD QH
Flop – 6D AD 7D
Outs to reach a Two Pair – 6S 7H AC 6H AS AH 7C 6C 7S
Outs to reach a Flush – 9D 4D 8D JD 5D 2D 10D 3D KD
Outs to reach Three of a Kind – QC QS
In total, you have 20 outs to hit Two Pair or higher, giving you a card odds ratio of 1 : 1.4 or a 42.6% percentage chance of hitting your cards.
Run through the exercises below as practice. See answers at the end of the book, and if you want more exercises to continue your practice, sign up to pokeretude.com.
Ex 2.01
Number of Outs – 6
Ratio – 1 :
Percentage –
Ex 2.02
Number of Outs – 3
Ratio – 1 :
Percentage –
Ex 2.03
Number of Outs – 9
Ratio – 1 :
Percentage –
Ex 2.04
Number of Outs – 23
Ratio – 1 :
Percentage –
Ex 2.05
Number of Outs – 14
Ratio – 1 :
Percentage –
Ex 2.06
Number of Outs – 10
Ratio – 1 :
Percentage –
Ex 2.07
Number of Outs – 18
Ratio – 1 :
Percentage –
Ex 2.08
Number of Outs – 7
Ratio – 1 :
Percentage –
Ex 2.09
Number of Outs – 9
Ratio – 1 :
Percentage –
Ex 2.10
Number of Outs – 12
Ratio – 1 :
Percentage –
Ex 2.11
Number of Outs – 23
Ratio – 1 :
Percentage –
Ex 2.12
Number of Outs – 21
Ratio – 1 :
Percentage –
Ex 2.13
Number of Outs – 18
Ratio – 1 :
Percentage –
Ex 2.14
Number of Outs – 11
Ratio – 1 :
Percentage –
Ex 2.15
Number of Outs – 13
Ratio – 1 :
Percentage –
Ex 2.16
Number of Outs – 9
Ratio – 1 :
Percentage –
Ex 2.17
Number of Outs – 6
Ratio – 1 :
Percentage –
Ex 2.18
Number of Outs – 7
Ratio – 1 :
Percentage –
Ex 2.19
Number of Outs – 12
Ratio – 1 :
Percentage –
Ex 2.20
Number of Outs – 18
Ratio – 1 :
Percentage –
Ex 2.21
Number of Outs – 3
Ratio – 1 :
Percentage –
Ex 2.22
Number of Outs – 1
Ratio – 1 :
Percentage –
Ex 2.23
Number of Outs – 6
Ratio – 1 :
Percentage –
Ex 2.24
Number of Outs – 10
Ratio – 1 :
Percentage –
Ex 2.25
Number of Outs – 12
Ratio – 1 :
Percentage –
Ex 2.26
Number of Outs – 13
Ratio – 1 :
Percentage –
Ex 2.27
Number of Outs – 22
Ratio – 1 :
Percentage –
Ex 2.28
Number of Outs – 4
Ratio – 1 :
Percentage –
Ex 2.29
Number of Outs – 20
Ratio – 1 :
Percentage –
Ex 2.30
Number of Outs – 10
Ratio – 1 :
Percentage –
Exercise 3 – Pot Odds
As well as knowing the card odds of hitting an out on the turn, you need to know what it is going to cost you, and how much you could win if you won the hand – known as pot odds.
Knowing how much you need to put in to stay in the hand as well as how much you could win means you can make an informed decision about whether staying in the hand is a profitable move.
To demonstrate the principle, if you needed to put $1000 into the hand to win $1000, but you only had a 5% (or 1 : 19) chance of hitting an out and winning, you would have negative EV, and it would not be a play worth making. You are far more likely to lose than to win, and if you win you are only doubling your money, so playing that hand is unprofitable in the long term.
To get the ratios and percentages of the spend and potential win, we use the following formulas:
Ratio = (Already in Pot / To Call)
1: 2.5 = ($250 / $100)
Percentage = (To Call / (To Call + Already in Pot)) x 100
[_ 28.6% = ($100 / ($100 + $250)) x 100 _]
The formulas will give you exact pot odds, but most of the time it’s much easier to estimate what the pot odds will be. We only need to know if the pot odds are higher or lower than the card odds, so a lot of the time an estimate of the pot odds will do just fine.
We’ve included the exact numbers in the book for reference, but don’t feel you need to have the exact number in order for the exercise to be useful!
Example 1
To Call – $50
Already in Pot – $500
The ratio of these pot odds would be 1 : 10, and a percentage amount would round to 9.1%.
Example 2
To Call – $2
Already in Pot – $13
The ratio of these pot odds would be 1 : 6.5, and a percentage amount would round to 13.3%.
Example 3
To Call – $382
Already in Pot – $980
The ratio of these pot odds would be 1 : 2.6, and a percentage amount would round to 28.0%.
Example 4
To Call – $75
Already in Pot – $355
The ratio of these pot odds would be 1 : 4.7, and a percentage amount would round to 17.4%.
Have a go at the exercises on the next few pages. See answers at the end of the book, and if you want more exercises to continue your practice, sign up to pokeretude.com.
Ex 3.01
To Call – $20
Already in Pot – $420
Ratio – 1 :
Percentage –
Ex 3.02
To Call – $1000
Already in Pot – $12200
Ratio – 1 :
Percentage –
Ex 3.03
To Call – $50
Already in Pot – $740
Ratio – 1 :
Percentage –
Ex 3.04
To Call – $60
Already in Pot – $660
Ratio – 1 :
Percentage –
Ex 3.05
To Call – $150
Already in Pot – $855
Ratio – 1 :
Percentage –
Ex 3.06
To Call – $50
Already in Pot – $905
Ratio – 1 :
Percentage –
Ex 3.07
To Call – $300
Already in Pot – $5190
Ratio – 1 :
Percentage –
Ex 3.08
To Call – $250
Already in Pot – $5250
Ratio – 1 :
Percentage –
Ex 3.09
To Call – $50
Already in Pot – $550
Ratio – 1 :
Percentage –
Ex 3.10
To Call – $150
Already in Pot – $1500
Ratio – 1 :
Percentage –
Ex 3.11
To Call – $10
Already in Pot – $80
Ratio – 1 :
Percentage –
Ex 3.12
To Call – $150
Already in Pot – $2055
Ratio – 1 :
Percentage –
Ex 3.13
To Call – $10
Already in Pot – $226
Ratio – 1 :
Percentage –
Ex 3.14
To Call – $500
Already in Pot – $10600
Ratio – 1 :
Percentage –
Ex 3.15
To Call – $250
Already in Pot – $6100
Ratio – 1 :
Percentage –
Ex 3.16
To Call – $125
Already in Pot – $1850
Ratio – 1 :
Percentage –
Ex 3.17
To Call – $150
Already in Pot – $2760
Ratio – 1 :
Percentage –
Ex 3.18
To Call – $60
Already in Pot – $1578
Ratio – 1 :
Percentage –
Ex 3.19
To Call – $10
Already in Pot – $70
Ratio – 1 :
Percentage –
Ex 3.20
To Call – $125
Already in Pot – $1000
Ratio – 1 :
Percentage –
Ex 3.21
To Call – $50
Already in Pot – $750
Ratio – 1 :
Percentage –
Ex 3.22
To Call – $10
Already in Pot – $181
Ratio – 1 :
Percentage –
Ex 3.23
To Call – $100
Already in Pot – $1100
Ratio – 1 :
Percentage –
Ex 3.24
To Call – $60
Already in Pot – $912
Ratio – 1 :
Percentage –
Ex 3.25
To Call – $25
Already in Pot – $300
Ratio – 1 :
Percentage –
Ex 3.26
To Call – $20
Already in Pot – $200
Ratio – 1 :
Percentage –
Ex 3.27
To Call – $10
Already in Pot – $244
Ratio – 1 :
Percentage –
Ex 3.28
To Call – $20
Already in Pot – $180
Ratio – 1 :
Percentage –
Ex 3.29
To Call – $25
Already in Pot – $25
Ratio – 1 :
Percentage –
Ex 3.30
To Call – $50
Already in Pot – $905
Ratio – 1 :
Percentage –
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Exercise 4 – Expected Value
Now you have the building blocks, we put all of the previous exercises together to practice calculating the expected value from start to finish. We will give you your hand, flop and chips – all you need to do is decide if the expected value is positive so you can go in on the hand!
We will give you your hand, the number of chips to call, and the number of chips currently in the pot. You need to calculate your card odds (exercises 1 and 2), and your pot odds (exercise 3). If your card odds are greater than your pot odds (e.g. if the probability of hitting an out and winning is greater than the proportion of money you would lose) then make the bet, otherwise, fold.
Example 1
My Cards – 4H KC
Flop – QS JC AD
Aiming for or Higher – Straight
You have 4 outs to reach a straight or higher, giving you card odds of 1:10.8 or 8.5%.
To Call – $50
Already in Pot – $1200
The ratio of these pot odds would be 1 : 24, and a percentage amount would round to 4%.
Bet or Fold – Bet
In this example, your card odds are greater than your pot odds. In the long run it’s worth betting on this hand.
Example 2
My Cards – JS KC
Flop – 3D 2C JC
Aiming for or Higher – Three of a Kind
You have 2 outs to reach a straight or higher, giving you card odds of 1: 22.5 or 4.3%.
To Call – $100
Already in Pot – $350
The ratio of these pot odds would be 1 : 3.5, and a percentage amount would round to 22.2%.
Bet or Fold – Fold
In this example, your card odds are less than your pot odds. In the long run it’s worth folding on this hand.
The method above is simpler way of telling you if your expected value is positive or negative, which tells you if you should bet or fold. But if you want to understand the hand in more detail and understand exactly how much you are likely to win (or lose) in the long run by playing a hand, you can use the expected value formula.
To work out the expected values:
EV = (Hit Hand x Chips to Win) + (Miss Hand x Chips to Lose)
Example 3
If you have 6 outs, the probability of hitting it is 12.8% on the turn; and if you have to call with $20 chips, and $150 already in the pot.
EV = (Hit Hand x Chips to Win) + (Miss Hand x Chips to Lose)
EV = (0.128 × $170) + (1 – 0.128 × $20)
[_ EV = +$4.32 => Bet _]
In the long run you are likely to win 4.32 chips by playing this hand.
Example 4
If you have 12 outs, the probability of hitting it is 25.5% on the turn; and if you have to call with $250 chips, and $270 already in the pot.
EV = (Hit Hand x Chips to Win) + (Miss Hand x Chips to Lose)
EV = (0.255 × $520) + (1 – 0.255 × $250)
[_ EV = -$53.65 => Fold _]
In the long run you are likely to lose $53.65 chips by playing this hand.
Use the final set of exercises to consolidate everything you’ve learnt so far. See answers at the end of the book, and if you want more exercises to continue your practice, sign up to pokeretude.com.
Ex 4.01
My Cards – 9S AH
Flop – 8C 6S 5H
Aiming for at least – Pair
Card Odds –
Chips to Call – $10
Chips still in Pot – $65
Pot Odds –
Bet or Fold –
Ex 4.02
My Cards – 9C 10H
Flop – 2H 4H 6D
Aiming for at least – Pair
Card Odds –
Chips to Call – $60
Chips still in Pot – $1440
Pot Odds –
Bet or Fold –
Ex 4.03
My Cards – 9S 7S
Flop – 5S 9D 2C
Aiming for at least – Three of a Kind
Card Odds –
Chips to Call – $60
Chips still in Pot – $912
Pot Odds –
Bet or Fold –
Ex 4.04
My Cards – 6C QD
Flop – 10D 9C 7D
Aiming for at least – Two Pair
Card Odds –
Chips to Call – $1000
Chips still in Pot – $14800
Pot Odds –
Bet or Fold –
Ex 4.05
My Cards – 8H 5C
Flop – KD QD 6H
Aiming for at least – Three of a Kind
Card Odds –
Chips to Call – $100
Chips still in Pot – $720
Pot Odds –
Bet or Fold –
Ex 4.06
My Cards – 8H 5H
Flop – 2C JH 7S
Aiming for at least – Straight
Card Odds –
Chips to Call – $200
Chips still in Pot – $2740
Pot Odds –
Bet or Fold –
Ex 4.07
My Cards – JH 9D
Flop – 4S 6S 3C
Aiming for at least – Flush
Card Odds –
Chips to Call – $300
Chips still in Pot – $7410
Pot Odds –
Bet or Fold – Fold
Ex 4.08
My Cards – 2S 6S
Flop – QC 2D JS
Aiming for at least – Two Pair
Card Odds –
Chips to Call – $200
Chips still in Pot – $3520
Pot Odds –
Bet or Fold –
Ex 4.09
My Cards – KC 7H
Flop – 4H AD 8C
Aiming for at least – Flush
Card Odds –
Chips to Call – $1000
Chips still in Pot – $22600
Pot Odds –
Bet or Fold –
Ex 4.10
My Cards – JS KS
Flop – 4C 7H 9C
Aiming for at least – Three of a Kind
Card Odds –
Chips to Call – $50
Chips still in Pot – $750
Pot Odds –
Bet or Fold –
Ex 4.11
My Cards – 6S 2D
Flop – 7D 3C AD
Aiming for at least – Straight
Card Odds –
Chips to Call – $50
Chips still in Pot – $610
Pot Odds –
Bet or Fold –
Ex 4.12
My Cards – 3C AC
Flop – QH 4H 6D
Aiming for at least – Straight
Card Odds –
Chips to Call – $10
Chips still in Pot – $263
Pot Odds –
Bet or Fold –
Ex 4.13
My Cards – 4H 8S
Flop – 9D 10S KC
Aiming for at least – Flush
Card Odds –
Chips to Call – $250
Chips still in Pot – $3250
Pot Odds –
Bet or Fold –
Ex 4.14
My Cards – 3H 5S
Flop – 10D 4S KC
Aiming for at least – Straight
Card Odds –
Chips to Call – $25
Chips still in Pot – $250
Pot Odds –
Bet or Fold –
Ex 4.15
My Cards – JD 5S
Flop – 8H 10S 9H
Aiming for at least – Pair
Card Odds –
Chips to Call – $250
Chips still in Pot – $4400
Pot Odds –
Bet or Fold –
Ex 4.16
My Cards – 4H 5H
Flop – KD 6D 3H
Aiming for at least – Pair
Card Odds –
Chips to Call – $50
Chips still in Pot – $905
Pot Odds –
Bet or Fold –
Ex 4.17
My Cards – 6C 4H
Flop – 6S 6H JC
Aiming for at least – Full House
Card Odds –
Chips to Call – $500
Chips still in Pot – $7600
Pot Odds –
Bet or Fold –
Ex 4.18
My Cards – QD KS
Flop – 9D 9S JC
Aiming for at least – Two Pair
Card Odds –
Chips to Call – $500
Chips still in Pot – $5500
Pot Odds –
Bet or Fold –
Ex 4.19
My Cards – 5S QH
Flop – 10S KH 4S
Aiming for at least – Two Pair
Card Odds –
Chips to Call – $10
Chips still in Pot – $122
Pot Odds –
Bet or Fold –
Ex 4.20
My Cards – 6C 3S
Flop – KD AC QD
Aiming for at least – Three of a Kind
Card Odds –
Chips to Call – $20
Chips still in Pot – $408
Pot Odds –
Bet or Fold –
Ex 4.21
My Cards – 6S 4S
Flop – 3S AS 10C
Aiming for at least – Flush
Card Odds –
Chips to Call – $125
Chips still in Pot – $3212.50
Pot Odds –
Bet or Fold –
Ex 4.22
My Cards – 6S AS
Flop – AH 6H 9H
Aiming for at least – Three of a Kind
Card Odds –
Chips to Call – $100
Chips still in Pot – $1000
Pot Odds –
Bet or Fold –
Ex 4.23
My Cards – 8C QH
Flop – 5S 3S 2H
Aiming for at least – Three of a Kind
Card Odds –
Chips to Call – $125
Chips still in Pot – $2437.50
Pot Odds –
Bet or Fold –
Ex 4.24
My Cards – 9C 6H
Flop – AS 2H 4D
Aiming for at least – Pair
Card Odds –
Chips to Call – $150
Chips still in Pot – $525
Pot Odds –
Bet or Fold –
Ex 4.25
My Cards – 5C 7D
Flop – 5D KD 7C
Aiming for at least – Straight
Card Odds –
Chips to Call – $250
Chips still in Pot – $4600
Pot Odds –
Bet or Fold –
Ex 4.26
My Cards – 6D 2C
Flop – AC AH KH
Aiming for at least – Straight
Card Odds –
Chips to Call – $10
Chips still in Pot – $184
Pot Odds –
Bet or Fold –
Ex 4.27
My Cards – 7S 4D
Flop – 3S 9C 4H
Aiming for at least – Flush
Card Odds –
Chips to Call – $1000
Chips still in Pot – $24900
Pot Odds –
Bet or Fold –
Ex 4.28
My Cards – 8C 3C
Flop – JS 3D 6H
Aiming for at least – Flush
Card Odds –
Chips to Call – $150
Chips still in Pot – $2205
Pot Odds –
Bet or Fold –
Ex 4.29
My Cards – KH 6C
Flop – 2S 4D KD
Aiming for at least – Three of a Kind
Card Odds –
Chips to Call – $250
Chips still in Pot – $1125
Pot Odds –
Bet or Fold –
Ex 4.30
My Cards – 3S 2D
Flop – 9H 3D 2C
Aiming for at least – Three of a Kind
Card Odds –
Chips to Call – $1000
Chips still in Pot – $21000
Pot Odds –
Bet or Fold –
Final Note…
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Answers
[]Exercise 1
Ex 1.01
My Cards – 4S 4H
Flop – AD KS 9C
Aiming for at least – Two Pair
Out Cards – 9H 9S KC AS AH KD AC 9D KH 4D 4C
Outs Total – 11
Ex 1.02
My Cards – 6D AD
Flop – 4H 2H 2D
Aiming for at least – Three of a Kind
Out Cards – None
Outs Total – 0
Ex 1.03
My Cards – AH 8S
Flop – 5H 6S 9D
Aiming for at least – Straight
Out Cards – 7C 7H 7S 7D
Outs Total – 4
Ex 1.04
My Cards – 3D 10H
Flop – 9S QD QH
Aiming for at least – Full House
Out Cards – None
Outs Total – 0
Ex 1.05
My Cards – KS 2H
Flop – 3D 10H JC
Aiming for at least – Straight
Out Cards – None
Outs Total – 0
Ex 1.06
My Cards – 8D 5S
Flop – 3S JC 4C
Aiming for at least – Pair
Out Cards – 8S 5H 5C 8H 8C 5D
Outs Total – 6
Ex 1.07
My Cards – AH 9H
Flop – 6H 5H 7S
Aiming for at least – Two Pair
Out Cards – 3H KH 8H JH 2H 4H 10H 7H QH 8S 8C 8D
Outs Total – 12
Ex 1.08
My Cards – KD 7H
Flop – 9C 8C 5C
Aiming for at least – Pair
Out Cards – KC 7D KS 7S KH 7C 6S 6D 6H 6C
Outs Total – 10
Ex 1.09
My Cards – 7C 5H
Flop – JD 4D QC
Aiming for at least – Pair
Out Cards – 7H 5S 5C 7D 5D 7S
Outs Total – 6
Ex 1.10
My Cards – 7C 4C
Flop – 8C AS 5H
Aiming for at least – Straight
Out Cards – 6D 6C 6S 6H
Outs Total – 4
Ex 1.11
My Cards – 10D 5D
Flop – 5S QH 10C
Aiming for at least – Three of a Kind
Out Cards – 5H 10H 10S 5C
Outs Total – 4
Ex 1.12
My Cards – 7D 10S
Flop – 7H 7S 6H
Aiming for at least – Straight
Out Cards – 6C 10C 6S 6D 10D 10H 7C
Outs Total – 7
Ex 1.13
My Cards – AH KH
Flop – KS 8D 9C
Aiming for at least – Two Pair
Out Cards – 8S AC AS 9D AD 8C 9H 9S 8H KD KC
Outs Total – 11
Ex 1.14
My Cards – 2S 6H
Flop – 7D 7C 3C
Aiming for at least – Straight
Out Cards – None
Outs Total – 0
Ex 1.15
My Cards – JD 8D
Flop – 3D 10C 5D
Aiming for at least – Two Pair
Out Cards – 10D KD 4D 9D AD 2D 7D 6D QD
Outs Total – 9
Ex 1.16
My Cards – 10S 8D
Flop – 9C 8H JD
Aiming for at least – Two Pair
Out Cards – QC QD QH QS 7D 7C 7H 7S 8S 8C 9D 10C 10D 9S JH JC 10H JS 9H
Outs Total – 19
Ex 1.17
My Cards – 7D KS
Flop – 4C 8C 6S
Aiming for at least – Two Pair
Out Cards – 5D 5S 5C 5H
Outs Total – 4
Ex 1.18
My Cards – 10D 5C
Flop – 4D JC 2H
Aiming for at least – Two Pair
Out Cards – None
Outs Total – 0
Ex 1.19
My Cards – 10S KC
Flop – 8C JC 5D
Aiming for at least – Pair
Out Cards – KS 10D KH KD 10C 10H
Outs Total – 6
Ex 1.20
My Cards – 5S 3C
Flop – 9H KH 8H
Aiming for at least – Straight
Out Cards – None
Outs Total – 0
Ex 1.21
My Cards – 10H 5C
Flop – 10D 5H KD
Aiming for at least – Straight
Out Cards – 10S 5D 5S 10C
Outs Total – 4
Ex 1.22
My Cards – 6S 2C
Flop – 8S 10H 6D
Aiming for at least – Three of a Kind
Out Cards – 6H 6C
Outs Total – 2
Ex 1.23
My Cards – 8C 2C
Flop – 6S 5D 7H
Aiming for at least – Flush
Out Cards – None
Outs Total – 0
Ex 1.24
My Cards – JH 5S
Flop – 5H 2S 8C
Aiming for at least – Full House
Out Cards – None
Outs Total – 0
Ex 1.25
My Cards – KH QC
Flop – QD 7D 2D
Aiming for at least – Two Pair
Out Cards – QS QH KS 7C 7H 2H 2C KD 2S KC 7S
Outs Total – 11
Ex 1.26
My Cards – QH 6C
Flop – 5H 5S QS
Aiming for at least – Three of a Kind
Out Cards – QD QC 5C 5D
Outs Total – 4
Ex 1.27
My Cards – 9S 3H
Flop – AS 6H 4H
Aiming for at least – Straight
Out Cards – None
Outs Total – 0
Ex 1.28
My Cards – 3S 5C
Flop – 7S KD 2D
Aiming for at least – Three of a Kind
Out Cards – None
Outs Total – 0
Ex 1.29
My Cards – QC 2H
Flop – KD JC 6S
Aiming for at least – Pair
Out Cards – QD 2S QH 2D 2C QS
Outs Total – 6
Ex 1.30
My Cards – 2H 2D
Flop – 7S 10H QD
Aiming for at least – Three of a Kind
Out Cards – 2C 2S
Outs Total – 2
Exercise 2
Ex 2.01
Number of Outs – 6
Ratio – 1 : 6.8
Percentage – 12.8%
Ex 2.02
Number of Outs – 3
Ratio – 1 : 14.7
Percentage – 6.4%
Ex 2.03
Number of Outs – 9
Ratio – 1 : 4.2
Percentage – 19.1%
Ex 2.04
Number of Outs – 23
Ratio – 1 : 1
Percentage – 48.9%
Ex 2.05
Number of Outs – 14
Ratio – 1 : 2.4
Percentage – 29.8%
Ex 2.06
Number of Outs – 10
Ratio – 1 : 3.7
Percentage – 21.3%
Ex 2.07
Number of Outs – 18
Ratio – 1 : 1.6
Percentage – 38.3%
Ex 2.08
Number of Outs – 7
Ratio – 1 : 5.7
Percentage – 14.9%
Ex 2.09
Number of Outs – 9
Ratio – 1 : 4.2
Percentage – 19.1%
Ex 2.10
Number of Outs – 12
Ratio – 1 : 2.9
Percentage – 25.5%
Ex 2.11
Number of Outs – 23
Ratio – 1 : 1
Percentage – 48.9%
Ex 2.12
Number of Outs – 21
Ratio – 1 : 1.2
Percentage – 44.7%
Ex 2.13
Number of Outs – 18
Ratio – 1 : 1.6
Percentage – 38.3%
Ex 2.14
Number of Outs – 11
Ratio – 1 : 3.3
Percentage – 23.4%
Ex 2.15
Number of Outs – 13
Ratio – 1 : 2.6
Percentage – 27.7%
Ex 2.16
Number of Outs – 9
Ratio – 1 : 4.2
Percentage – 19.1%
Ex 2.17
Number of Outs – 6
Ratio – 1 : 6.8
Percentage – 12.8%
Ex 2.18
Number of Outs – 7
Ratio – 1 : 5.7
Percentage – 14.9%
Ex 2.19
Number of Outs – 12
Ratio – 1 : 2.9
Percentage – 25.5%
Ex 2.20
Number of Outs – 18
Ratio – 1 : 1.6
Percentage – 38.3%
Ex 2.21
Number of Outs – 3
Ratio – 1 : 14.7
Percentage – 6.4%
Ex 2.22
Number of Outs – 1
Ratio – 1 : 46
Percentage – 2.1%
Ex 2.23
Number of Outs – 6
Ratio – 1 : 6.8
Percentage – 12.8%
Ex 2.24
Number of Outs – 10
Ratio – 1 : 3.7
Percentage – 21.3%
Ex 2.25
Number of Outs – 12
Ratio – 1 : 2.9
Percentage – 25.5%
Ex 2.26
Number of Outs – 13
Ratio – 1 : 2.6
Percentage – 27.7%
Ex 2.27
Number of Outs – 22
Ratio – 1 : 1.1
Percentage – 46.8%
Ex 2.28
Number of Outs – 4
Ratio – 1 : 10.8
Percentage – 8.5%
Ex 2.29
Number of Outs – 20
Ratio – 1 : 1.4
Percentage – 42.6%
Ex 2.30
Number of Outs – 10
Ratio – 1 : 3.7
Percentage – 21.3%
Exercise 3
Ex 3.01
To Call – $20
Already in Pot – $420
Ratio – 1 : 21
Percentage – 4.5%
Ex 3.02
To Call – $1000
Already in Pot – $12200
Ratio – 1 : 12.2
Percentage – 7.6%
Ex 3.03
To Call – $50
Already in Pot – $740
Ratio – 1 : 14.8
Percentage – 6.3%
Ex 3.04
To Call – $60
Already in Pot – $660
Ratio – 1 : 11
Percentage – 8.3%
Ex 3.05
To Call – $150
Already in Pot – $855
Ratio – 1 : 5.7
Percentage – 14.9%
Ex 3.06
To Call – $50
Already in Pot – $905
Ratio – 1 : 18.1
Percentage – 5.2%
Ex 3.07
To Call – $300
Already in Pot – $5190
Ratio – 1 : 17.3
Percentage – 5.5%
Ex 3.08
To Call – $250
Already in Pot – $5250
Ratio – 1 : 21
Percentage – 4.5%
Ex 3.09
To Call – $50
Already in Pot – $550
Ratio – 1 : 11
Percentage – 8.3%
Ex 3.10
To Call – $150
Already in Pot – $1500
Ratio – 1 : 10
Percentage – 9.1%
Ex 3.11
To Call – $10
Already in Pot – $80
Ratio – 1 : 8
Percentage – 11.1%
Ex 3.12
To Call – $150
Already in Pot – $2055
Ratio – 1 : 13.7
Percentage – 6.8%
Ex 3.13
To Call – $10
Already in Pot – $226
Ratio – 1 : 22.6
Percentage – 4.2%
Ex 3.14
To Call – $500
Already in Pot – $10600
Ratio – 1 : 21.2
Percentage – 4.5%
Ex 3.15
To Call – $250
Already in Pot – $6100
Ratio – 1 : 24.4
Percentage – 3.9%
Ex 3.16
To Call – $125
Already in Pot – $1850
Ratio – 1 : 14.8
Percentage – 6.3%
Ex 3.17
To Call – $150
Already in Pot – $2760
Ratio – 1 : 18.4
Percentage – 5.2%
Ex 3.18
To Call – $60
Already in Pot – $1578
Ratio – 1 : 26.3
Percentage – 3.7%
Ex 3.19
To Call – $10
Already in Pot – $70
Ratio – 1 : 7
Percentage – 12.5%
Ex 3.20
To Call – $125
Already in Pot – $1000
Ratio – 1 : 8
Percentage – 11.1%
Ex 3.21
To Call – $50
Already in Pot – $750
Ratio – 1 : 15
Percentage – 6.3%
Ex 3.22
To Call – $10
Already in Pot – $181
Ratio – 1 : 18.1
Percentage – 5.2%
Ex 3.23
To Call – $100
Already in Pot – $1100
Ratio – 1 : 11
Percentage – 8.3%
Ex 3.24
To Call – $60
Already in Pot – $912
Ratio – 1 : 15.2
Percentage – 6.2%
Ex 3.25
To Call – $25
Already in Pot – $300
Ratio – 1 : 12
Percentage – 7.7%
Ex 3.26
To Call – $20
Already in Pot – $200
Ratio – 1 : 10
Percentage – 9.1%
Ex 3.27
To Call – $10
Already in Pot – $244
Ratio – 1 : 24.4
Percentage – 3.9%
Ex 3.28
To Call – $20
Already in Pot – $180
Ratio – 1 : 9
Percentage – 10%
Ex 3.29
To Call – $25
Already in Pot – $25
Ratio – 1 : 1
Percentage – 50%
Ex 3.30
To Call – $50
Already in Pot – $905
Ratio – 1 : 8.1
Percentage – 5.2%
Exercise 4
Ex 4.01
My Cards – 9S AH
Flop – 8C 6S 5H
Aiming for at least – Pair
Card Odds – 21.3% or 1 : 3.7
Chips to Call – $10
Chips still in Pot – $65
Pot Odds – 13.3% or 1:6.5
EV – +$6
Bet or Fold – Bet
Ex 4.02
My Cards – 9C 10H
Flop – 2H 4H 6D
Aiming for at least – Pair
Card Odds – 12.8% or 1 : 6.8
Chips to Call – $60
Chips still in Pot – $1440
Pot Odds – 4.% or 1:24
EV – +$132
Bet or Fold – Bet
Ex 4.03
My Cards – 9S 7S
Flop – 5S 9D 2C
Aiming for at least – Three of a Kind
Card Odds – 4.3% or 1 : 22.5
Chips to Call – $60
Chips still in Pot – $912
Pot Odds – 6.2% or 1:15.2
EV – -$18
Bet or Fold – Fold
Ex 4.04
My Cards – 6C QD
Flop – 10D 9C 7D
Aiming for at least – Two Pair
Card Odds – 8.5% or 1 : 10.8
Chips to Call – $1000
Chips still in Pot – $14800
Pot Odds – 6.3% or 1:14.8
EV – +$343
Bet or Fold – Bet
Ex 4.05
My Cards – 8H 5C
Flop – KD QD 6H
Aiming for at least – Three of a Kind
Card Odds – 0
Chips to Call – $100
Chips still in Pot – $720
Pot Odds – 12.2% or 1:7.2
EV – -$100
Bet or Fold – Fold
Ex 4.06
My Cards – 8H 5H
Flop – 2C JH 7S
Aiming for at least – Straight
Card Odds – 0
Chips to Call – $200
Chips still in Pot – $2740
Pot Odds – 6.8% or 1:13.7
EV – -$200
Bet or Fold – Fold
Ex 4.07
My Cards – JH 9D
Flop – 4S 6S 3C
Aiming for at least – Flush
Card Odds – 0
Chips to Call – $300
Chips still in Pot – $7410
Pot Odds – 3.9% or 1:24.7
EV – -$300
Bet or Fold – Fold
Ex 4.08
My Cards – 2S 6S
Flop – QC 2D JS
Aiming for at least – Two Pair
Card Odds – 23.4% or 1 : 3.3
Chips to Call – $200
Chips still in Pot – $3520
Pot Odds – 5.4% or 1:17.6
EV – +$670
Bet or Fold – Bet
Ex 4.09
My Cards – KC 7H
Flop – 4H AD 8C
Aiming for at least – Flush
Card Odds – 0
Chips to Call – $1000
Chips still in Pot – $22600
Pot Odds – 4.2% or 1:22.6
EV – -$1000
Bet or Fold – Fold
Ex 4.10
My Cards – JS KS
Flop – 4C 7H 9C
Aiming for at least – Three of a Kind
Card Odds – 0
Chips to Call – $50
Chips still in Pot – $750
Pot Odds – 6.3% or 1:15
EV – -$50
Bet or Fold – Fold
Ex 4.11
My Cards – 6S 2D
Flop – 7D 3C AD
Aiming for at least – Straight
Card Odds – 0
Chips to Call – $50
Chips still in Pot – $610
Pot Odds – 7.6% or 1:12.2
EV – -$50
Bet or Fold – Fold
Ex 4.12
My Cards – 3C AC
Flop – QH 4H 6D
Aiming for at least – Straight
Card Odds – 0
Chips to Call – $10
Chips still in Pot – $263
Pot Odds – 3.7% or 1:26.3
EV – -$10
Bet or Fold – Fold
Ex 4.13
My Cards – 4H 8S
Flop – 9D 10S KC
Aiming for at least – Flush
Card Odds – 0
Chips to Call – $250
Chips still in Pot – $3250
Pot Odds – 7.1% or 1:13
EV – -$250
Bet or Fold – Fold
Ex 4.14
My Cards – 3H 5S
Flop – 10D 4S KC
Aiming for at least – Straight
Card Odds – 0
Chips to Call – $25
Chips still in Pot – $250
Pot Odds – 9.1% or 1:10
EV – -$25
Bet or Fold – Fold
Ex 4.15
My Cards – JD 5S
Flop – 8H 10S 9H
Aiming for at least – Pair
Card Odds – 29.8% or 1 : 2.4
Chips to Call – $250
Chips still in Pot – $4400
Pot Odds – 5.4% or 1:17.6
EV – +$1136
Bet or Fold – Bet
Ex 4.16
My Cards – 4H 5H
Flop – KD 6D 3H
Aiming for at least – Pair
Card Odds – 29.8% or 1 : 2.4
Chips to Call – $50
Chips still in Pot – $905
Pot Odds – 5.2% or 1:18.1
EV – +$235
Bet or Fold – Bet
Ex 4.17
My Cards – 6C 4H
Flop – 6S 6H JC
Aiming for at least – Full House
Card Odds – 14.9% or 1 : 5.7
Chips to Call – $500
Chips still in Pot – $7600
Pot Odds – 6.2% or 1:15.2
EV – +$707
Bet or Fold – Bet
Ex 4.18
My Cards – QD KS
Flop – 9D 9S JC
Aiming for at least – Two Pair
Card Odds – 21.3% or 1 : 4.7
Chips to Call – $500
Chips still in Pot – $5500
Pot Odds – 8.3% or 1:11
EV – +$778
Bet or Fold – Bet
Ex 4.19
My Cards – 5S QH
Flop – 10S KH 4S
Aiming for at least – Two Pair
Card Odds – 0
Chips to Call – $10
Chips still in Pot – $122
Pot Odds – 7.6% or 1:12.2
EV – -$10
Bet or Fold – Fold
Ex 4.20
My Cards – 6C 3S
Flop – KD AC QD
Aiming for at least – Three of a Kind
Card Odds – 0
Chips to Call – $20
Chips still in Pot – $408
Pot Odds – 4.7% or 1:20.4
EV – -$20
Bet or Fold – Fold
Ex 4.21
My Cards – 6S 4S
Flop – 3S AS 10C
Aiming for at least – Flush
Card Odds – 19.1% or 1 : 4.2
Chips to Call – $125
Chips still in Pot – $3212.50
Pot Odds – 3.7% or 1:25.7
EV – +$512
Bet or Fold – Bet
Ex 4.22
My Cards – 6S AS
Flop – AH 6H 9H
Aiming for at least – Three of a Kind
Card Odds – 8.5% or 1 : 10.8
Chips to Call – $100
Chips still in Pot – $1000
Pot Odds – 9.1% or 1:10
EV – -$7
Bet or Fold – Fold
Ex 4.23
My Cards – 8C QH
Flop – 5S 3S 2H
Aiming for at least – Three of a Kind
Card Odds – 0
Chips to Call – $125
Chips still in Pot – $2437.50
Pot Odds – 4.9% or 1:19.5
EV – -$125
Bet or Fold – Fold
Ex 4.24
My Cards – 9C 6H
Flop – AS 2H 4D
Aiming for at least – Pair
Card Odds – 12.8% or 1 : 6.8
Chips to Call – $150
Chips still in Pot – $525
Pot Odds – 22.2% or 1:3.5
EV – -$64
Bet or Fold – Fold
Ex 4.25
My Cards – 5C 7D
Flop – 5D KD 7C
Aiming for at least – Straight
Card Odds – 8.5% or 1 : 10.8
Chips to Call – $250
Chips still in Pot – $4600
Pot Odds – 5.2% or 1:18.4
EV – +$162
Bet or Fold – Bet
Ex 4.26
My Cards – 6D 2C
Flop – AC AH KH
Aiming for at least – Straight
Card Odds – 0
Chips to Call – $10
Chips still in Pot – $184
Pot Odds – 5.2% or 1:18.4
EV – -$10
Bet or Fold – Fold
Ex 4.27
My Cards – 7S 4D
Flop – 3S 9C 4H
Aiming for at least – Flush
Card Odds – 0
Chips to Call – $1000
Chips still in Pot – $24900
Pot Odds – 3.9% or 1:24.9
EV – -$1000
Bet or Fold – Fold
Ex 4.28
My Cards – 8C 3C
Flop – JS 3D 6H
Aiming for at least – Flush
Card Odds – 0
Chips to Call – $150
Chips still in Pot – $2205
Pot Odds – 6.4% or 1:14.7
EV – -$150
Bet or Fold – Fold
Ex 4.29
My Cards – KH 6C
Flop – 2S 4D KD
Aiming for at least – Three of a Kind
Card Odds – 4.3% or 1 : 22.5
Chips to Call – $250
Chips still in Pot – $1125
Pot Odds – 18.2% or 1:4.5
EV – -$191
Bet or Fold – Fold
Ex 4.30
My Cards – 3S 2D
Flop – 9H 3D 2C
Aiming for at least – Three of a Kind
Card Odds – 8.5% or 1 : 10.8
Chips to Call – $1000
Chips still in Pot – $21000
Pot Odds – 4.5% or 1:21
EV – +$870
Bet or Fold – Bet
A Beginners Guide to Calculating Poker Expected Values (EV) with Speed
Do you want to improve your poker? Improvement comes through ongoing practice of a specific technique. Tennis players practice their serve, musicians practice their scales, and now it’s your turn to practice your poker skills in the same way.
The aim of this eBook is to help you improve your ability to recognise your expected value at speed, which is the key to your long term profitability. You will do this through exercises, which have been broken down in to each stage of an expected value assessment process.
- ISBN: 9781370667796
- Author: pokeretude
- Published: 2016-08-21 17:41:11
- Words: 10053
