The Free, Online, Concise Guide to No Limit Texas Holdem Poker
By PokerAnon
Copyright PokerAnon 2010
Smashwords Edition, License Notes
Thank you for downloading this free ebook. You are welcome to share it with your friends. This book may be reproduced, copied and distributed for non-commercial purposes, provided the book remains in its complete original form. If you wish to use portions of this book only, please contact the author at pokeranon@gmail.com
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Index
Player Style descriptions
Tight/Aggressive style
Starting Hands
Playing the flop
Playing the turn and river
Odds and Outs
Count your Outs
Pot Odds
Odds on the Turn and River
Using Percentages
Bet sizing, expressed versus implied odds
Rules and terms
How to play a game
Poker hand rankings
Terminology and definitions
The Free, Online, Concise Guide to No Limit Texas Holdem Poker
Whether
you play poker for fun, play for real money or are preparing for a
poker tournament fundraiser this guide will tutor you on the basics
of poker and beyond.
And it's free.
This book is
structured under the assumption that you already know the basics and
the rules of the game. If not, you can find them in the Rules and
Terms section which is located at the end of the book.
This guide begins with:
Playing styles; their advantages and vulnerabilities, how to play against each style and some recommended starting hands to play, and then
the mathematics of poker including outs, odds, percentages, pot odds, and implied odds. At the end I include
additional suggested readings once you are comfortable with the basic material.
This book evolved from a blog that I started years ago as I learned the basics of poker. About half of the chapters originated as blog posts and then I wrote additional chapters to fill in the rest of the information that is needed for a beginner to become a winning microstakes poker player.
There is an online HTML version of this book available here:
www.anon-poker-blog.com/pokerbook
The online version includes something that is not included in this book; a 40 minute video that I recorded as a demonstration of starting hands to play.
~ ~ ~
Player Styles
There are various ways to describe the styles of poker players. The most common segregation is to split them into extremes such as:
Loose versus Tight: How often does the player see the flop
Passive versus Aggressive: Do they usually call or do they usually raise?
A Loose player plays lots of hands and a Tight player plays very few hands. A Passive player tends to play by checking or by calling bets and an Aggressive player tends to play by betting and raising. Since these two characteristics are not mutually exclusive they can be combined into a matrix, giving you four basic player types:
Loose/Passive: Plays lots of hands, usually by calling or checking
Loose/Aggressive: Plays lots of hands, usually betting or raising
Tight/Passive: Plays few hands, usually by calling or checking
Tight/Aggressive: Plays few hands, usually betting or raising
What
does this tell you? Over time every player gets AA and 72 as
often as anyone else. This means that if a player is loose and
plays often he must be playing more poor quality hands than a player
who is picky and is playing very few hands.
A Loose/Aggressive player is betting and raising with poorer quality hands than a player who is tight but also aggressive, so he's either intentionally trying to pressure his opponents into folding, or he overvalues the strength of his hands.
A player who is Loose/Passive likes to play often and calls a lot and hopes that it turns out that he has the best hand, though he's not sure enough to bet for himself. He will also chase a lot, calling in hopes that his flush or his one card straight draw will get there.
A Tight/Passive player is playing quality hands but is afraid that someone may have a better hand. He may just call preflop with a pair of Jacks, then just call bets after the flop hoping that his Jacks turn out to have been the best hand.
You
might hear these player types referred to by names: Loose/Aggressive
= Maniac, Loose/Passive = Calling Station, Tight/Passive = Rock, or
other equivalent names. Don't worry about the names, what's important
is how the person plays and what that style means.
By
categorizing players by playing style we can draw a guess as to how
strong their hand is as well as a guess as to how we expect them to
act or react. We then use this information to help determine how to
play against each type of player.
Against a Loose/Aggressive player we may decide not to bet with our strong hands and let him do the betting for us, or, because he is betting and raising often we may choose to re-raise his bets hoping that he will realize that his hand is not so strong. We should also tend to call his bets with marginal hands because he will be often bluffing or overvaluing the strength of his hand. Often we'll win, but sometimes we'll lose. A loose/aggressive player experiences wild swings as they win and lose many sizable pots, and take the rest of the table with them.
A Loose/Passive may have any two cards so we should bet our decent strength hands to get money into the pot when we are likely beating their hand. Be concerned if they suddenly become aggressive on the turn or river because this runs against their nature and likely means that they have a very strong hand.
But if a Tight/Passive player is calling he may have a strong hand that he's just afraid to bet. Against this type of player we need to be more judicious about how large and how frequently we bet because he may have us beat and just be afraid to bet it himself. As with the loose/passive we should be careful when the tight/passive player suddenly starts betting.
Note that I haven't made any comments about the Tight/Aggressive playing style yet. This is because Tight/Aggressive is the ideal style for beginners to adopt. Tight/Aggressive means choosing to play only good quality hands and not just hoping to get a miracle flop. Tight/Aggressive also means recognizing that we want to bet and raise with good hands in order to get more money into the pot when we are likely to be winning, and to make it expensive for the passive players to chase their longshot draws. When you play against a Tight/Aggressive opponent you know that they have a good hand and that they will make it expensive for you to see more cards. You will be forced to decide whether your hand is better, or whether the cost that he's going to charge you to see more cards is going to be worth it or not.
~ ~ ~
Playing a Tight/Aggressive poker style
Playing
in a Tight/Aggressive style will not come naturally to most
beginners. Most beginners don't want to fold 75% to 85% of their
hands (depending on the table size) that they should be folding
in order to play tight. It's more entertaining to call and see what
the flop brings. It's natural to want to play too many hands, and
besides, you didn't come to the game wanting to sit out. And
beginners hate to fold their A5 and see an Ace come on the
flop, or that their 85 hand that they almost decided to play would
have flopped 55K and someone with a King wins instead.
It's
also difficult to play aggressively. It can seem impolite,
or like you are trying to bully the other players. In board games
like Scrabble or chess you use what options the board and your
opponents give you but you don't challenge someone directly by
raising the stakes. In backgammon you can double the stakes, but in
backgammon there are no hidden cards and the whole board is directly
in front of both you and your opponent.
Poker has a mix of
skill and chance, known and unknown, that requires a leap of
confidence to be able to raise or bet when there is so much chance
involved and so much unknown to you. By betting or raising you
increase your risk without ever being certain of your exact chances
of winning. That's not easy to do. But if you only play quality hands
it makes it easier to decide what to do when the community cards are
dealt. This is important for the less experienced player and will
help keep you from losing more in difficult-to-play situations. And
by playing aggressively with quality hands you make it inappropriate
for strange, weak hands to continue to play and perhaps unexpectedly
catch on a 22Q flop, or to draw to a runner-runner flush or
runner-runner straight for free.
Okay, but what does playing
Tight/Aggressive mean at the tables? It means playing only certain
hole cards in certain situations, and raising when you do decide to
play. It also means betting the flop, turn and river appropriately to
put pressure on your opponents to continue and to make sure that they
can't draw for cheap. On the next page we will look at the Starting
Hands for what
and when to play preflop then you should do so. Also, watch the video
to see how I might recommend a beginner choose starting hands and how
to play them.
Tight/Aggressive is not the only way to play.
It's not even the only winning way to play poker. But it is the
easiest style for a beginner to target to help them to minimize the
difficult decisions and to protect their losses.
~ ~ ~
Preflop Hand Selection
First,
seating position and their names.
This changes every hand because position is labeled relative to who
is the dealer.
The small blind (SB) and big blind (BB) are
immediately to the left of the dealer and have to post their blinds
before the dealing begins.
The spots immediately after the
blinds are called under-the-gun (UTG) and under-the-gun plus one
(UTG+1).
Next are the middle position spots, MP1, MP2 and MP3.
These are followed by the late positions, the cutoff (CO, the
position immediately to the right of the dealer) and the button (the
dealer).
SB, BB, UTG and UTG+1 are considered "early
position". UTG and
UTG+1 have the disadvantage of having to make the first plays
preflop, as well as first after the SB and BB on the flop, turn, and
river. This
disadvantage means you can only play the best hands
from UTG and UTG+1. Moving to
middle and then to late positions you
can play progressively
weaker and weaker starting cards because 1)
there are fewer players after you that might have even bigger hands,
and 2)
you get to bet after the earlier positions so you get to see what
they do before you have to decide.
SB and BB are special early positions because you already have some
money committed to the pot, and we'll consider them separately.
So,
from early position
(UTG and UTG+1) play only: AA / KK / QQ / AK
From middle
position play all the
early position hands, plus:
JJ / TT / AQ / AJ / KQ
From late
position, all the early
and middle position hands,
plus: 99 / 88 / 77 / AT
/ KJ / QJ
(Note
that for simplicity I have not considered whether or not the cards
are of the same suit or not. In reality, being suited adds only a
small winning percentage to the relative value of the cards, but
worse yet is often overvalued by beginners.)
All of
these starting hands
assume
that 1)
no one else other than the blinds have put any money into the pot,
and 2)
you are going to raise with your hand.
You should raise
to 3 or 4 times the big blind,
so if the big blind is 0.10, put in 0.30 or 0.40. By doing so, you
1)
make it costly for weak hands after you to play, 2)
announce
to the table that you have a good hand and a high expectation of
winning this hand.
This puts the pressure on anyone deciding to play; you have the hand
to beat.
Gap
Concept
What
if someone else ahead of you has already raised? The gap concept says
that in order for you to play, you need to have at least as good a
hand or better than you would have raised with had you been in
the raiser's position. In other words, if a player in MP+1 raises, he
should be only raising with early position cards (AA/KK/QQ/AK) or
middle position cards (JJ/TT/AQ/AJ/KQ) and in order for you to call
you have to have cards that you would play only from that same
position. This is because he has announced that he has a good hand,
so if you are going to play, you need to be able to compete with this
hand. Makes sense, if the opponent raises from MP1, that means he's
saying he has AA/KK/QQ/AK/JJ/TT/AQ/AJ/KQ, so if you are in late
position, you should not call his raise if you have AT because you're
likely to lose. Just imagine that an Ace is the high card on the flop
and you are thinking, good, I hit top pair, but your opponent is
betting with AK thinking, why does this person not understand he's
beat?
Limped
pots
In
live poker or low limit on-line poker games most of your
opponents will play very loose (meaning they play more hands than
I've listed) and weak (meaning they almost never raise). This means
that often when in middle or late position you'll be faced with 2, 3,
4 or more people already on the pot who haven't raised but instead
just called the big blind. This is called limping. When this happens,
I recommend that if you have a first position hand (AA/KK/QQ/AK),
raise, but instead
of raising 3 - 4 times the blind, raise 4 plus one more for each
limper. If you
have 2 limpers ahead of you, raise 4 + 2 = 6 times the blind. The
reason for this is that each limper has increased the size of the
pot, so in order for you to create a situation that they are not
getting good odds to call, you have to make the bet higher. If you
have middle or late position types of hands and there are 2 or more
limpers ahead of you, just call. I find that in these situations
raising often does not chase all the weak hands from the pot, which
is fine if you have one of the top hands, but can be tricky when you
have a slightly lesser hand. Just call and see what action takes
place on the flop.
Playing
from the blinds
I've left this section until now because some concepts from
the intervening sections apply to playing from the blinds. From the
BB, obviously if no-one raises you can check and see the flop cards
for no additional cost. From the SB, if you have 2 or more limpers in
before you, then it only costs you 1/2 a big blind more to see the
flop, and you could do so with almost any except the worst hands. If
you have decent hand, say one that is in the list of hands to play
from late position, you can call with one limper. If you have a hand
that should be played from early or middle position and there's no or
maybe one limper, raise, and hope to take down the hand preflop, but
remember the rule for raising when there are limpers; 4 times the big
blind plus one for each limper. What if someone raises, and you have
a good hand? Remember that the blinds will be first to act on the
flop, turn, and river, so all the other players with have an
advantage over you. Use the recommended hands for the early position
hands and don't call a raise from someone without AA/KK/QQ/AK. In
fact, re-raise their bet with these hands, because you have a premium
hand plus you will be out of position during subsequent betting.
Hopefully they will realize that they are at risk and will fold.
Playing
tight
All
of this advice is all based on the concept of playing tight,
positional poker preflop. This is by far the easiest way for a
beginner to start, for the simple reason that you play only good
value hands relative to your position. By playing only good value
starting hands in good position you keep yourself from getting into
too many difficult situations later on.
This might be a good
time to watch the video
of me playing these starting hands, although in the video I also play
some hands according to some concepts that are covered in later
sections.
~ ~ ~
Playing the Flop
The
options that you have on the flop are similar to preflop:
Bet
Raise
Fold
possibly Call or Check, depending on the action in front of you
But there are a lot of considerations that determine the best of these options:
The number of players seeing the flop
If the pot was raised preflop or not
If it was raised preflop, who made the raise and who called
Your position relative to the other players still in the hand
The texture of the flop
What you guess that your opponents might hold, and how that might connect with the flop
Your cards relative to the flop
Your interpretation of your opponent's playing styles and tendencies
In a tournament setting or if you have varied stack sizes in a cash game, the stack sizes of you and your opponents
Notice
where your cards are in this list; not the first, not even in the
first half of this list of considerations. If you ever listen to a
good player as they discuss how they play or think through a hand,
the first four will often not even be mentioned. This is not
because they don't consider these items but it is because
these things are already known, so the experienced player has
taken these elements into consideration as the flop is being dealt.
Even so, one or more of these first four considerations will be
particularly important and will bear mentioning while evaluating the
flop.
1)
The more players there are in the pot, the stronger the hand
you need to continue. If you had AA preflop, the chances that your AA
is still the best hand decreases further and further the more
opponents there are that are still playing. Similarly even top pair
on the flop is a good hand against one opponent, but against 3 it may
be second or even third best.
2) If the pot was raised
preflop, any active players likely have stronger
starting hands, or at least fewer garbage hands, and you may need
a stronger hand to continue, depending upon the flop texture and your
opponents' styles.
3) If you raised preflop, then you
should be betting the flop 70-80% of the time. You showed
strength preflop, and you need to continue to do so, depending on the
number of players, the texture of the flop, and your interpretation
of your opponents. Betting in this situation is so common that it has
a name; Continuation Betting, because you are continuing your
representation of a strong hand.
If, however, you have
more than one opponent still in the hand, then continuation betting
is much less useful. This is because as soon as you have two
opponents instead of one, there are automatically twice as many
chances that someone now has a good enough hand to continue playing.
Unless you have a "made" hand such as an overpair or top
pair, or you have a good read on your opponents and you expect them
both to fold easily, you should be less inclined to make a
continuation bet when you have more than one opponent.
If you
called someone else's raise preflop, you will not be expected to bet
the flop but you might call or check and then call a bet if you have
a good drawing hand or you think that the player who raised may not
have a strong hand. You also might raise or check-raise with a good
hand or as a semi-bluff.
4) If you are one of the first
players to act, you might tend to check and possibly call a bet if
you have something like J9 on a flop of J72; top pair without a
strong second card. If you are the last to act and no one has bet,
you might bet with anything because no one has shown interest. As in
3) you might also check-raise from early position against a player
who habitually bets or raise from late position against a player who
habitually bets.
5) and 6) work together and in
conjunction with the other considerations. If the flop comes J22 and
it was raised preflop, then it's unlikely that the flop helped anyone
and a bet may take it down uncontested. If on the other hand the flop
comes JT8 with two cards of the same suit, then there are all kinds
of one pair with straight draws/two pair/pair with flush draw hands
that may not fold. This is a difficult/dangerous flop if you raised
with AA and have two callers.
7) Finally we come to your
cards and the flop. 2 out of every 3 times any two unpaired
cards are not going to connect with the flop. Keep that in mind when
you raise AK and get flops like 36Q, or 67J. When you continuation
bet flops like these you may very well have the best hand even
though all you have is Ace high with overcards to the flop. Keep that
in mind too when someone else raises preflop and you call with 99 and
then they bet the flop. Your 99 may be the best hand.
8)
We've already talked about playing opponents who habitually bet, but
there are also tight opponents who habitually fold so against them
you should bet most hands. There are also opponents who habitually
call with low pairs or weak draws, so you should bet if you have a
decent hand to make sure that they pay to see additional cards, and
not bet with just overcards or pocket pairs lower than the cards in
the flop since they won't fold.
9) In a tournament when
your chip stack is very low, or if you decide to try to play cash
games with the minimum buy in (called "short stacking"),
all of your decisions should be made preflop. Either you raise and
are prepared to go all in, or you fold. I didn't cover this in the
Starting Hands section, but if you are playing with a chip stack of
less than 10 big blinds, you should be pushing all in with any hands
that you chose to play.
When to bet
I've
already mentioned some of the situations where you might choose to
bet at the flop.
You raised preflop and you have one opponent, you should usually continuation bet
No one else has bet and you think that a bet will cause your opponents to fold
You think that your opponents are the type that usually fold when someone bets
You think that you have the best hand and want to get more money in the pot
The other way of looking at betting is to look at it in terms of what you hope to accomplish by betting or raising.
You might cause an opponent with a better hand than you to fold
You might cause an opponent that has a draw that could beat you to fold
You might build the size of the pot when you have a better hand and are likely to win, and in the same vein you bet when you want to give your opponent incorrect odds to try to improve to beat your hand.
There
are also more situation-specific objectives for betting, such as
betting in hopes that your opponent will raise so that you can push
all-in, or betting or raising a bet when you are in position so that
you can see the turn and river cards for no additional cost. For
example, you are the dealer, the flop comes, one person bets
small and you have a flush draw. You raise. If the person folds, you
win. If he calls, the person will often check on the turn to wait to
see if you bet again. If you didn't fill your flush on the turn you
can just check and now you get to see if the river card helps
you.
How much to bet?
Okay, you've decided that
you should bet, so the question is, how much? Complete answer: it
depends.
In tournaments, especially when chip stacks get
smaller relative to the blind size a bet of about 1/3 - 2/3 of the
pot can be reasonable. Bet less and you give your opponent(s) little
reason to fold, bet more and it can look suspicious or weak. In cash
games the chip stacks size relative to blind size are usually deeper
so 1/2 to full pot is reasonable. See the later section on outs and
odds for more mathematics relating to pot to bet size ratios. If you
have more than one opponent you should size your bet on the larger
side because if one opponent calls then the next opponent has even
more incentive to call because the pot is bigger compared to the bet
size. The larger bet will help to deter the first opponent from
calling and then if he does call your bet the next opponent doesn't
get quite as good odds because you made the bet size larger to
begin.
When you are playing against beginners you can adjust
the size of your bets slightly because they probably won't notice.
When you have a hand that you will fold if raised, make the bet on
the smaller side. If you have a strong hand and the flop is
dangerous, bet larger. If you have a monster and you want callers,
bet smaller. Keep in mind that over time adjusting bet sizes in this
way will telegraph information if anyone is paying attention, so you
may want to mix up your sizing if you are playing the same players
over a long period of time.
When to call
So
someone before you bets, or you checked and someone after you has
bet. When should you call?
Do you likely have the best hand? If you're unsure you may choose to call and see what happens on the turn. If you're pretty sure that you have the best hand you should probably bet or raise rather than call, unless you have a really big hand and then you might choose to slowplay.
If it's unlikely that you have the best hand, what are your chances of improving to be the best hand?
What pot odds are you being given by the bet?
What are your implied odds?
Might you be able to take the pot away on the turn with a bet?
Questions 2. to 4. are covered more completely in the Outs and Odds section. The last is a move called floating. It's normally done by calling a preflop raise, calling the flop bet and then betting the turn, but it's best reserved until you develop a good ability to read players and to read board textures.
~ ~ ~
Playing the Turn and River
Most of the time you will fold your hands before the flop. Then much of the time you or all your opponents will fold on the flop when there is betting action. As a result you won't see the turn or river very often (unless you play a loose style, or the table is shorthanded which means that the relative value of any hand increases). When you actually make it to the turn and river either you
don't have a very strong hand but neither does anyone else so no one has bet or raised, or
you have a decent hand or a good draw.
I'm only going to provide some generalities here as there are substantial mathematical details to be considered and these are covered in the Odds and Outs section.
if no one else is showing interest, a bet may take the pot down. This also may work on the flop if you are in late position
if a scare card such as an Ace or the third card of a flush comes (especially when it comes on the river), a bet may take the pot down. This is more likely to work if you have only one opponent, or you have thinking opponents who realize that it's more difficult to bluff multiple opponents so therefore you must not be bluffing
when you have a big hand, the turn and river are the time to really work on building the pot with raises or check-raises
because we should always be making our bet sizes relative to the size of the pot, the turn and river bets will be large because the pot keeps getting multiplied.
When you have a medium strength hand (see here in the blog for more discussion on hand strength) you need to guess which scenario is most likely. You:
probably have the best hand (bet or call or raise)
probably don't have the best hand but can make your opponent fold (bluff, or semi-bluff the flop or turn with draws)
maybe have the best hand and your opponent probably won't fold (check, call, or possibly make a small blocking bet)
Some things to remember from other sections:
be concerned if a passive player bets or raises
be sometimes willing to call an aggressive player down since they will often have a weak hand that they are overvaluing or they will be bluffing
bet large enough to charge players who have draws if they want to chase
don't chase draws yourself unless your opponent gives you odds to continue, or you believe that they will always give you lots of chips if you do make your draw
~ ~ ~
Count your Outs
For some reason there often seems to be confusion about odds in poker. I think partly this is due to the fact that there are a variety of different aspects to odds as well as different methods of for calculating or viewing them. As a bit of a project I thought that I'd try to organize and summarize the various aspects that I've come across. But before looking at odds, we have to be able to count your chances.
Outs, what are they and how do you count them?
Outs are chances or different possibilities that your hand might improve. You hold
A
8,
the flop comes K65
.
What are your chances of getting a flush? To get a flush you need one more spade. There are 13 spades in a deck, 4 are known (you have two and two are in the flop) so there are 13 - 4 = 9 remaining spades. Each chance is called an "out", so you have 9 outs to make the flush. It doesn't matter whether someone else had or has a spade in their hand. Unless someone tells you that they folded a spade or you're watching televised poker you won't know if another spade has been seen, so for calculating your outs it doesn't matter. (Obviously if you're playing Stud or some other game where you can see other cards that are gone then those cards have to be deducted from your total outs)
What if you suspect your that opponent has paired the king? In that case if an Ace comes you will be beating him with your higher pair. There are 4 Aces in the deck, and you have one so 4 - 1 = 3 aces as outs. If, as you suspect, your opponent has paired the King, then if you get an Ace or if you get a spade, you will be beating him so you can add the outs, 9 spades + 3 Aces = 12 outs.
Let's look at straights. You hold
98
and the flop is A
76
.
Now if a 10 or 5 of any suit comes, you will have a straight. There are four 10s and four 5s so 4 + 4 = 8 outs to get a straight.
Say you hold
98
again but the flop this time is A65.
Now only a 7 fills your straight (these are called "inside" or "gut shot" straight draws). Four 7s = 4 outs to fill the gut shot straight.
Or, you hold
98
the flop is J75.
Now, a 7 fills your 56789 straight, but a T fills your 789TJ straight. This is the "double gutshot" or "double belly buster" straight draw with four 7s and four Ts to fill a straight so 4 + 4 = 8 outs.
~
Try
one more.
This time you have 98
and the flop is A76.
You think you will win if you hit a flush or a straight. To
get there, you have nine outs for the flush draw
(KQJT65432).
Then any 10 or 5 will give you a straight. However, you have already
counted T
and 5
in your flush outs, so now you can only count TTT
for three more 10s and 555
for three more 5s as outs. Nine flush outs plus three other 10s and
three other 5s gives you 9 + 3 + 3 = 15 outs in total.
Clean outs, Tainted outs
Sometimes
not all of your outs are always going to win for you if they hit.
Say you have 98
and the flop is A76.
This time, your opponent knocks over his cards in his
excitement and you see that he holds two more Aces for a set of Aces.
Now the 6
is not an out; do you see why? In fact, if you didn't know your
opponent had AA (or 77 for that matter) you would be in big trouble
if the 6
hit because your big hand is almost dead to his bigger hand. Your
only hope in that event is a straight flush.
More often,
something like 98
on a A76
flop will come up. Of your eight outs for making a straight, only six
are clean outs as the T
and 5
would give someone a flush if they do indeed hold the flush draw.
Sometimes these are referred to as "tainted" outs. They can
be counted as partial outs, so you could value them as 1/2 outs each.
Six clean outs plus two tainted outs for a total of seven outs.
Say
instead you hold the 54
on the A76
flop. Your opponent has T9.
Here an 8 or 3 will give you a straight so there are eight possible
useful cards. However an 8
gives your opponent a diamond flush. If the one of the other 8s
comes, your opponent will hit a T9876 straight which will beat your
87654 straight. Even if you don't know exactly what your opponent
holds, the uncertainty of having the winning hand if an 8 comes means
that it is dangerous to consider any 8 as a full out. I would ignore
the 8
entirely and value the 88
or 8
as 1/2 outs. Four 3s as outs, three 8s as 1/2 outs = 4 + 1.5 = 5.5
outs.
As it turns out, your opponent has nine outs with the
flush draw, plus the other three 8s for a gut shot straight draw or 9
+ 3 = 12 outs. He's also ahead of you at the moment, though neither
of you know that at the time. If you did know each other's cards (if
one of you is all in and the cards have been turned over) you would
see that a 5,
5,
4
or 4
will give you a pair which is currently enough to beat his hand. The
5
or 4
gives him the flush so they are not outs for you, but the others give
you four more outs. That's unless he gets a T or a 9 to beat your
lower pair.
Partial Outs
In the last examples the tainted outs were counted as 1/2 outs because their value may be questionable. There are other situations where you will encounter partial outs.
This will happen often on the flop because you have the turn and river cards yet to come. For example, you have
98
and the flop is A72.
This time if both the turn and river cards are spades you can still hit a runner-runner flush. How often does a runner-runner flush come in? There are ten remaining spades. On the turn there are 52 total cards - 5 known cards = 47 cards remaining. Assuming that you caught a spade on the turn, at the river there are 9 more spades remaining and 52 total - 6 known cards = 46 remaining cards. Therefore, the chances of the turn being a spade are 10 in 47, and if it is, the chance of the river also being a spade is 9 in 46. The math calculation is (10/47)(9/46) = 4.16% or slightly better than a 1 in 25 chance (actually closer to 1 in 24). Not particularly good odds; runner-runner flushes are usually valued as one or perhaps 1.5 outs.
The
7
also gives you three cards to a runner-runner straight draw. The
chances to hit the straight are similar to the flush, so you could
count the straight draw as another 1 or 1.5 outs. If however the flop
has a 6 instead of a 7 such as A62
you have a gap in the straight draw. As we saw with the gutshot draw
earlier on the chances of hitting drop. The chances of hitting are so
remote I wouldn't even consider the runner-runner gutshot draw as an
out unless you get to see the turn for free and the turn card is part
of your straight.
~ ~ ~
Pot Odds
Well,
we've figured out how to count chances or "outs". Now let's
see what to do with that information. "Odds" in poker
refers to a lot of different types of aspects. Unfortunately for the
beginner, any one of these aspects could be the subject of discussion
and could be referred to as just "odds", with the
assumption that everyone knows what type of odds is being discussed.
Outs and Odds
Flip a coin. The chances of
it coming up heads is 50%, the chances of tails is 50%. These are
even odds, or 1 to 1. 50% + 50% = 100%, or all the possible outcomes.
Roll a die. It has six sides. On average, every six times you roll
the die, five times you will not get the number one, and one time you
will get the number one. Roll it 318 times, on average 53 times it
comes up with a one, 265 times it doesn't. The chances of rolling a
one is 5 against, to 1 for, so 5 to 1 odds. Let's go back the some
examples from the "outs" post.
You
hold A
8,
the flop comes K65
.
To make the flush on the turn, there are 13 - 4 spades = 9 spades left, or 9 outs. There are 52 total cards less 5 known cards = 47 remaining unseen cards. If you take the unseen 47 cards, you have 9 chances to get a spade and 47 - 9 = 38 times you will not get a spade. Your odds are 38 to 9. Divide 38 by 9 and you get 4.2 to 1 odds of hitting the flush on the turn.
What about trying to just hit an Ace? 47 unseen cards, 3 remaining Aces, 47 less 3 = 44 non-Aces. 44 to 3 odds, or 14.7 to 1.
To hit the flush or an Ace, there are 9 flush outs plus 3 Ace outs for a total of 12 outs, so 47 less 12 = 35 or 35 to 12 odds, or 2.9 to 1 odds.
The
next example was an open ended straight draw, where you hold 98
and the flop is A
76
.
This time you're looking for any 10 or 5, so eight cards in total. 47
unseen cards less 8 straight-filling cards = 39. Divide 39 into 8 and
you get 4.9 to 1 odds of hitting the straight on the turn.
Obviously, this is easy to calculate in advance for any number of potential outs that you may have.
Okay, now there's two routes to go. Either look at what these odds tell you, or, look at how the odds change for the river and how the turn and river cards together can be evaluated. I think it's less confusing to look at what the odds tell you first.
Pot Odds
Say
the blinds are 5/10, you just called with your A8,
the small blind folds and the big blind checks. There's now $25 in
the pot. The flop comes K65
and the big blind bets $10, making the pot $35 total. In order to
call, you have to pay $10 to have a chance to win that $35. That's
$35 to $10, or 3.5 to 1 odds. (Note that you do not include the $10
to call in the winnings because you could have just kept the $10 by
folding each time. You are investing $10 with the hopes of winning
the $35 pot available to you.) Because these odds are being
calculated relative to the pot, these are called "pot odds".
Say you think that you need the flush to win. If you look at the chart above, when you have 9 flush outs you have 4.2 to 1 odds against making your flush on the turn. You are getting 3.5 to 1 pot odds. To make your call worthwhile in the long run, you need better pot odds than your cards are giving you.
There are a number of ways of proving this, but let's try this method.
In order to get to a common whole number I'm going to use 1,820 repetitions of the same situation. Run this scenario 1,820 times, and at 4.2 to 1 odds the flush hits once every 5.2 times so 350 times. In 1,820 repetitions you paid $10 at total of 1,820 times for a cost of $18,200, and in 350 instances you won the $35 pot. 350 multiplied by $35 = $12,250, plus 350 times your $10 that you get back when you win, so $12,250 + $3,500 = $15,750 total winnings. In other words, after running the scenario 1,820 times, you lose $2,450 or an average loss of $1.35 each time, so fold rather than call.
Now let's assume that your opponent has likely paired the King. In this case any of the three remaining Aces are outs for you as well. You have a total of 12 outs, 12 outs gives you 2.9 odds, the pot odds are 3.5 to 1, pot odds are greater than the odds the cards are giving you, so call as in the long run you will come out ahead.
Quick check using repetitions. 1,365 repetitions, you win 350 times. $10 x 1,365 = $13,650 cost. $35 per win times 350 wins = $12,250 plus $10 recovered 350 times, so $12,250 plus $3,500 for a total of $15,750 and net of plus $2,100 or $1.54 average. So, now it pays to call.
These calculations are just proofs. The thing to remember is that if you are getting better pot odds than the odds that the cards are offering to you, call. If not, probably fold, though we will cover some aspects later that may make it worthwhile to continue in the hand.
If someone says "you gave me pot odds to call", this is what they are referring to. If you have the best hand and you bet too small, someone who may be still drawing for their hand has the correct odds to call. That's why minimum betting at the flop or turn is so bad. The only people it scares away are the ones who have absolutely no hand and no draws, and even then it only works if no one is aggressive enough to raise you off the hand with a substantial re-raise.
~
Simple? Ah, but we haven't looked at the river odds, or the turn and the river cards combined yet. :)
~ ~ ~
Odds on the Turn and River
So far we've counted our outs, looked at how to translate outs into odds of hitting those outs, calculated the pot odds that our opponent is giving us, and compared the pot odds to the odds of us hitting one of our outs. All on the flop, looking only at the turn card to come.
River odds
What about the river? There's still another card to come, how does that factor into the odds?
Let's
start by using the flush hand that we've looked at before. You're
holding A
8,
the flop comes K65
.
You
know that there are 9 remaining spades = 9 flush outs. Say the J
comes on the turn, and now we're at the river. Now of the 52 total
cards in the deck we know 6 so there are 52 - 6 = 46 remaining unseen
cards. 46 unseen cards less the 9 spades = 37 times you will not get
a spade. Your odds are 37 to 9. Divide 37 by 9 and you get 4.1 to 1
odds of hitting the flush on the river. Note that this is only
marginally lower than on the turn because the situation has only
changed by one card.
Because the situation has only changed marginally in terms of known/unknown cards, the odds of hitting one of your outs on the river as opposed to the turn is slightly better on the river than the turn, but not enough that it is going to make a significant difference in your situation.
Considering the Turn and River together
Here
we get into an area that is often misunderstood by beginners. We'll
go back to our flush draw hand. You've got A8,
the flop comes K65.
There are 9 outs to fill the flush. You know 9 outs gives you 4.2 odds of hitting the flush on the turn. If you miss, you will have 4.1 odds of hitting the flush on the river. But on the turn, with both the turn and river cards to come, your odds must be better than 4.2 to get one spade on the turn and/or the river.
Step-by-step, you have 52-5=47 unseen cards on the turn. 9 are spades, so 47-9=38 non-spades. On the river there are 46 cards and 9 spades remaining. 9/46*38 = 7.4 times the non-spade turn will be followed by a spade. Add those 7.4 to the 9 where you hit the spade on the turn, 9 + 7.4 = 16.4 times a spade hits out of 47 times on the turn so 47 - 16.4 = 30.6 to 16.4 or 1.86 to one odds.
So, rounded, the odds are 1.9 to 1 against getting a spade on either the turn or on the river.
1.9 to 1 are pretty good odds, so now you can call that flop bet, right? Not necessarily. Preflop you called the $10 blind, the small blind folded his $5 and the big blind checked his $10. $25 in the pot when the big blind bets $10 into you, giving you $35 to $10 to call pot odds, or 3.5 to 1. If you look at this and see the 3.5 to 1 pot odds as better than your 1.9 to 1 flush draw odds, you're missing the fact that you will likely have to call another bet on the turn if you miss the flush on the turn.
Say
you call the $10 turn bet and the turn is the J.
The pot is $45 to start, and the big blind bets $20. Now you have to
put in $20 to win $45, or 45 to 20 or 2.5 to 1 odds. There is only
the river card to come, and you know that your chance of hitting the
flush on the river is 4.1 to 1 so now you fold. In a strict
application of pot odds theory and assuming that you need the flush
to win, you should have folded on the turn but you were misled by
neglecting to consider that you may have to call a turn bet.
From your opponent's perspective, this is why you need to bet the turn as well as the flop, to charge your opponents for making the mistake of trying to draw to beat your hand if, in fact, they are chasing the draw. If on the other hand you happened to have a King with a better kicker than your opponent then your opponent is building the pot for you by trying to make draws pay, but neither of you know that for sure.
~ ~ ~
Using Percentages
Rather
than considering odds in terms of 3 to 1, you can look at them in
terms of percentages.
First, determine your outs as we did previously. 9 outs to a flush on
the turn, with 47 cards possible. Simply get the percentage of 9 to
47 which equals 19%. So, you have a 19% chance of hitting the flush
on the turn.
Phil Gordon claims to have named the "rule
of two and four". This is a method for approximating the
percentages of hitting your outs on either the river alone or the
turn and river combined. With 9 flush outs, you multiply by two to
get the river percentage; 18%. To get the odds for the turn and river
combined, you multiply the outs by 4; 36%. This is not exact, but is
a pretty fast and fairly close approximation of the likelihood of
hitting your outs. This method tends to get more inaccurate the more
outs you have. If you want your results to be more accurate, adjust
the rule of four by subtracting one percent for each out greater than
8. For 15 outs, 15 times 4 = 60. 15 - 8 = 7, so 60 - 7 = 53%.
Please note that the rule
of four applies to both the turn and river combined.
And as we saw earlier, this does not take into account the
possibility that you will have to call another bet on the turn. Where
this does apply is where one of you will be all in. This means that
there will be no bet on the turn and no bet on the river. Say you are
playing a tournament and you raise your A8
from late position to 3 big blinds. Other players fold, but the big
blind, who only has 7 big blinds left, just calls you. The flop is as
before, K65
and the big blind pushes in his last 4 big blinds. Now the pot is
your 3 BBs, the small blind's 1/2 BB that he folded, the big blind's
3 BBs to call plus his 4 BBs shove for a total of 10.5 BBs. You have
9 outs = 35% chance of hitting. You are being asked to call 4 BBs
into a 10.5 BB pot, so 10.5 + 4 =14.5. Your call of 4 as a percentage
of the total future pot of 14.5 = 28%. Your percentage of hitting is
better than the percentage that you have to put into the pot, so
call.
Comparing Odds with Percentages We've now come to the point of another confusing aspect for beginners. When you use percentages to determine whether or not to call as we just did, you must add your bet to the pot to get the pot percentage. Then, if your percentage is greater than the call bet to total pot percentage, you call. When you use odds, you don't include your bet in the pot size, and you call if your card odds are smaller than the odds the pot to bet ratio is giving you. This is because
percentages are calculated as a wins compared to the total of all wins and loses, whereas odds are ratios comparing wins against losses, and
better winning percentages are bigger numbers, whereas in ratios the wins are always 1, so the smaller the number of loses, the better your ratio is.
So
to calculate the flush example above, you have to call 4 BBs, so
you're getting 10.5 to 4 odds, or 2.6 to 1 pot odds. You have a 1.9
to 1 chance of hitting your flush on either the turn or the river,
and there will be no turn bet to call. Pot odds are better than your
card odds, so call.
One last thing to keep in mind that the number of outs can increase on the turn. In particular a runner-runner draw that you valued at 1 out may become a full value group of outs if one of your runners come in on the turn. Say you have two of a flush in your hand, and one appears on the flop. Because you need a two more of your suit which is a longshot, you value it for perhaps only one out. But if one of your suit comes on the turn, now your chances have improved and you can count the full 9 remaining flush outs.
But
a really interesting one is flopping a set, especially if there is
three to a flush in the flop. Say you call with 8
8
and the flop comes K82.
If someone has a made flush, you have 1 out to make quad 8s, 3 outs
to pair the K and 3 outs to pair the 2 to make a full house so a
total of 1+3+3=7. Say the turn misses you with a 6.
Now your outs actually increase. Your 7 outs on the flop are still
good but now you have gained 3 more outs if a 6,
6,
or 6
comes on the river for a total of 10 outs.
I'm finally just about ready to wrap this up. As usual, it was more work than I expected and took more words and more posts than I had anticipated.
~ ~ ~
Bet sizing
We've
looked at when to call bets relative to your draws, and I mentioned
briefly how terrible small bets are since they give anyone with draws
the proper odds to call. We need to look at the other side; how to
size your bets so as to give you opponent the incorrect odds to call.
Essentially this is just the inverse of pot odds calculations.
You
are in the big blind. One limper calls $10, the small blind folds.
You check your K9
and the flop comes K65.
You have top pair with a so-so kicker. Immediately you should see
that there is a spade flush draw as well as possible straight draws
with the 65.
If you bet too small, you will give your opponent the correct odds to
call. You know the flush draw is 4.2 to 1 to hit on the turn, and the
open ended straight draw is 4.9 to 1. The flush draw has better odds,
so if you give the flush draw incorrect odds you will also give him
incorrect pot odds in case he has the OESD.
How much do you
bet to make it incorrect for your opponent to call if he has a flush
draw? The pot is $35. A standard bet here might be 1/2 pot, so
bet $20. If you do so, the pot becomes $55 and your opponent has to
put in $20 to continue. This means he has 55/20 odds, or 2.75 to 1
odds, not enough for either the flush draw or the straight draw. What
if he happens to have the flush draw and one card is the A?
That gives him 12 outs, requiring 2.9 to 1 odds; still not enough.
What about the if he's holding the 78?
In that event he has 9 flush outs plus three 4s and three Ts for 15
outs and 2.1 to 1 odds to continue. To make it incorrect for him to
call, you have to bet the pot, $35, to give him $70 to $35 odds or 2
to 1. In reality it's very unlikely that this or some other
straight/flush combination this strong is what he is holding, and if
so he's probably not going to fold no matter how much you bet.
Notice that the larger you bet, the larger the pot becomes,
but that the ratio of the pot odds does not increase as fast as you
increase your bet size is increasing. A 10% pot sized bet gives off
11 to 1 odds, a 50% pot sized bet gives 3 to 1 odds, but a 100% pot
sized bet only brings the odds down to 2 to 1.
Other factors
There's more to playing poker than odds. Some to consider include:
stack sizes relative to pot sizes - ie. if on the flop your stack size is not much larger than the pot, just push all in because you won't have enough left to bet at the turn or river anyways
bubbles in tournament settings - the balance between aggression and survival is more important than pot odds
fold equity, semi-bluffing your draws - especially out of position it can be a better option to bet into your opponent rather than waiting to see what odds they will give to chase your draw
opponent reads - if your opponent bets at most flops, you can happily call with your draws (or raise them) even if you're not getting correct pot odds simply because there's a good chance he has nothing
Expressed odds and Implied odds
What
we've looked at so far come under the heading of "expressed
odds"; numbers based on the bets, card odds and pot sizes. Lets
say you have 98
and the flop is A76.
The pot is $35, and your opponent in the big blind bets $20 making
the pot $55. You are getting 55 to 20 pot odds, or 2.75 to one. Your
open ended straight draw has a 4.9 to 1 chance of hitting on the
turn. Fold? But say you called and the turn is a Ten. You've made the
straight. Now you've got the turn and the river to make more money
from your opponent. Or, say the turn is a 5 of some kind. A 5 is a
little more obvious since it gives a 567 on the table, so maybe you
won't be able to get quite as much money from your opponent. This
extra money that you collect when you hit your hand is what is
referred to as "implied odds". Implied odds are very
imprecise, but very real, odds that you will collect money when you
hit your draw. But, they are affected by
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