Poker Hand Odds Calculation for Texas Hold'em
Learning how to properly count your outs and calculate poker odds is a
fundamental requirement of Texas Hold'em. While the math used to calculate odds
might sound scary and over the head of a new player, it really isn't as hard as
it looks. In fact, most of the time, you only need to know elementary arithmetic
to figure out your odds.
Why are Odds Important in Poker
Why are poker odds so important anyhow? Knowing odds is important because it
gives you an idea when you are in a good or bad situation. To illustrate:
Let's say you and a friend are flipping a quarter and he gives you 1:1 odds
that the next flip will land on heads. You already know that it will land on
heads 50% of the time, and it'll land on tails the rest of the time. In this
case, he's giving you an even bet, because nobody has a statistical
advantage.
Instead, let's say your friend just won $500 playing poker online and is on a
lucky streak. He offers you 2:1 odds that the next coin flip will be heads.
Would you take this bet? Hopefully you would, because the chances of heads or
tails coming up are still 1:1, while he's paying you at the 2:1 rate. Your
friend is hoping to ride his luck a little longer, but if he gambles with you
long enough, he'll be losing his shirt with these kinds of odds.
The above example is a simplified version of what goes on in Texas Hold'em
all the time. This is summed up in this short principle:
In poker, there are two types of players. The first group are players who
take bad odds in hopes of getting lucky. The second group are players who cash
in on the good odds that are left by the first group.
Hand Odds and Poker Odds
Hand odds are your chances of making a hand in Texas Hold'em poker. For
example: if you hold two hearts and there are two hearts on the flop, your hand
odds for making a flush are about 2 to 1. This means that for approximately
every 3 times you play this hand, you can expect to hit your flush one of those
times. If your hand odds were 3 to 1, then you would expect to hit your hand 1
out of every 4 times.
Odds are given below for hitting a draw by the river with a given number of
outs after the flop and turn, and examples of draws with specified numbers of
outs are given.
Example: if you hold [22] and the flop does not contain a [2], the odds of
hitting a [2] on the turn is 22:1 (4%). If the turn is also not a [2], the odds
of hitting it on the river are again 22:1 (4%). However, the combined odds of
hitting a [2] on the turn or river is 12:1 (8%). For mathematical reasons, only
use combined odds (two card odds) when you are in a possible allin
situation.
Examples of drawing hands after the flop
Draw 
Hand 
Flop 
Specific Outs 
# Outs 
Pocket Pair to Set 
[4♠ 4♥] 
[6♣ 7♦ T♠] 
4♦, 4♣ 
2 
One Overcard 
[A♠ 4♥] 
[6♥ 2♦ J♣] 
A♦, A♥, A♣ 
3 
Inside Straight 
[6♣ 7♦] 
[5♠ 9♥ A♦] 
8♣, 8♦, 8♥, 8♠ 
4 
Two Pair to Full House 
[A♦ J♥] 
[5♠ A♠ J♦] 
A♥, A♣, J♠, J♣ 
4 
One Pair to Two Pair or Set 
[J♣ Q♦] 
[J♦ 3♣ 4♠] 
J♥, J♠, Q♠, Q♥, Q♣ 
5 
No Pair to Pair 
[3♦ 6♣] 
[8♥ J♦ A♣] 
3♣, 3♠, 3♥, 6♥, 6♠,
6♦ 
6 
Two Overcards to Over Pair 
[A♣ K♦] 
[3♦ 2♥ 8♥] 
A♥, A♠, A♦, K♥, K♣,
K♠ 
6 
Set to Full House or Quads 
[5♥ 5♦] 
[5♣ Q♥ 2♠] 
5♠ Q♠, Q♦, Q♣, 2♥,
2♦, 2♣ 
7 
Open Straight 
[9♥ T♣] 
[3♣ 8♦ J♥] 
Any 7, Any Q 
8 
Flush 
[A♥ K♥] 
[3♥ 5♠ 7♥] 
Any heart (2♥ to Q♥) 
9 
Inside Straight & Two Overcards 
[A♥ K♣] 
[Q♠ J♣ 6♦] 
Any Ten, A♠, A♦ A♣, K♠, K♥,
K♦ 
10 
Flush & Inside Straight 
[K♣ J♣] 
[A♣ 2♣ T♥] 
Any Q, Any heart 
12 
Flush and Open Straight 
[J♥ T♥] 
[9♣ Q♥ 3♥] 
Any heart;, 8♦, 8♠, 8♣, K♦, K♠,
K♣ 
15 
Keyword Definitions
 Backdoor: A straight or flush draw where you need two cards
to help your hand out.
You have [A K]. Flop shows [T 2 5]. You need both
a [J] and [Q] for a straight.
 Overcard Draw: When you have a card above the flop.
You have [A 3]. Flop shows [K 5 2]. You need a [A] overcard to make top
pair. 3 total outs.
 Inside Straight Draw (aka 'Gutshot'): When you have one way
to complete a straight.
You have [J T]. Flop shows [A K 5]. You need a
[Q] to complete your straight. 4 total outs.
 Open Straight Draw: When you have two ways to complete a
straight.
You have [5 6]. Flop shows [7 8 A]. You need a [4] or [9] to
complete your straight. 8 total outs.
 Flush Draw: Having two cards to a suit with two suits
already on the flop.
You have [A♥ K♥]. Flop shows [7♥ 8♥ J♣]. You need any heart to make a
flush. 9 total outs.
To calculate your hand odds, you first need to know how many outs
your hand has. An out is defined as a card in the deck that helps you make your
hand. If you hold [A♠ K♠] and
there are two spades on the flop, there are 9 more spades in the deck (since
there are 13 cards of each suit). This means you have 9 outs to complete your
flush  but not necessarily the best hand! Usually you want your outs
to count toward a nut (best hand) draw, but this is not always possible.
The quick amongst you might be wondering "But what if someone else is holding
a spade, doesn't that decrease my number of outs?". The answer is yes (and no!).
If you know for sure that someone else is holding a spade, then you
will have to count that against your total number of outs. However, in most
situations you do not know what your opponents hold, so you can only calculate
odds with the knowledge that is available to you. That knowledge is your pocket
cards and the cards on the table. So, in essence, you are doing the calculations
as if you were the only person at the table  in that case, there are 9 spades
left in the deck.
When calculating outs, it's also important not to overcount your odds. An
example would be a flush draw in addition to an open straight draw.
Example: You hold [J♦ T♦] and the board shows [8♦ Q♦ K♠]. A
Nine or Ace gives you a straight (8 outs), while any diamond gives you the flush
(9 outs). However, there is an [A♦] and a [9♦], so you don't want to count these twice toward your
straight draw and flush draw. The true number of outs is actually 15 (8 outs + 9
outs  2 outs) instead of 17 (8 outs + 9 outs).
In addition to this, sometimes an out for you isn't really a true out. Let's
say that you are chasing an open ended straight draw with two of one suit on the
table. In this situation, you would normally have 8 total outs to hit your
straight, but 2 of those outs will result in three to a suit on the table. This
makes a possible flush for your opponents. As a result, you really only have 6
outs for a nut straight draw. Another more complex situation follows:
Example:You hold [J♠ 8♣]o (offsuit, or not of the same
suit) and the flop comes [9♠ T♥
J♣] rainbow (all of different suits). To make a
straight, you need a [Q] or [7] to drop, giving you 4 outs each or a total of 8
outs. But, you have to look at what will happen if a [Q♥]
drops, because the board will then show [9♠ T♥ J♣ Q♥]. This
means that anyone holding a [K] will have made a Kinghigh straight, while you
hold the secondbest Queenhigh straight. So, the only card that can really
help you is the [7], which gives you 4 outs, or the equivalent of a gutshot
draw. While it's true that someone might not be holding the [K] (especially in a
short or headsup game), in a big game, it's a very scary position to be
in.
To calculate your hand odds, you first need to know how many outs
your hand has. An out is defined as a card in the deck that helps you make your
hand. If you hold [A♠ K♠] and
there are two spades on the flop, there are 9 more spades in the deck (since
there are 13 cards of each suit). This means you have 9 outs to complete your
flush  but not necessarily the best hand! Usually you want your outs
to count toward a nut (best hand) draw, but this is not always possible.
The quick amongst you might be wondering "But what if someone else is holding
a spade, doesn't that decrease my number of outs?". The answer is yes (and no!).
If you know for sure that someone else is holding a spade, then you
will have to count that against your total number of outs. However, in most
situations you do not know what your opponents hold, so you can only calculate
odds with the knowledge that is available to you. That knowledge is your pocket
cards and the cards on the table. So, in essence, you are doing the calculations
as if you were the only person at the table  in that case, there are 9 spades
left in the deck.
When calculating outs, it's also important not to overcount your odds. An
example would be a flush draw in addition to an open straight draw.
Example: You hold [J♦ T♦] and the board shows [8♦ Q♦ K♠]. A
Nine or Ace gives you a straight (8 outs), while any diamond gives you the flush
(9 outs). However, there is an [A♦] and a [9♦], so you don't want to count these twice toward your
straight draw and flush draw. The true number of outs is actually 15 (8 outs + 9
outs  2 outs) instead of 17 (8 outs + 9 outs).
In addition to this, sometimes an out for you isn't really a true out. Let's
say that you are chasing an open ended straight draw with two of one suit on the
table. In this situation, you would normally have 8 total outs to hit your
straight, but 2 of those outs will result in three to a suit on the table. This
makes a possible flush for your opponents. As a result, you really only have 6
outs for a nut straight draw. Another more complex situation follows:
Example:You hold [J♠ 8♣]o (offsuit, or not of the same
suit) and the flop comes [9♠ T♥
J♣] rainbow (all of different suits). To make a
straight, you need a [Q] or [7] to drop, giving you 4 outs each or a total of 8
outs. But, you have to look at what will happen if a [Q♥]
drops, because the board will then show [9♠ T♥ J♣ Q♥]. This
means that anyone holding a [K] will have made a Kinghigh straight, while you
hold the secondbest Queenhigh straight. So, the only card that can really
help you is the [7], which gives you 4 outs, or the equivalent of a gutshot
draw. While it's true that someone might not be holding the [K] (especially in a
short or headsup game), in a big game, it's a very scary position to be
in.
Pot Odds and Poker Odds:
Now that you know how to calculate poker odds in terms of hand odds, you're
probably wondering "what am I going to need it for?" That's a good question 
this is where pot odds come into play.
Pot odds are simply the ratio of the amount of money in the pot to how much
money it costs to call. If there is $100 in the pot and it takes $10 to call,
your pot odds are 100:10, or 10:1. If there is $50 in the pot and it takes $10
to call, then your pot odds are 50:10 or 5:1. The higher the ratio, the better
your pot odds are.
Pot odds ratios are a very useful tool to see how often you need to win the
hand to break even. If there is $100 in the pot and it takes $10 to call, you
must win this hand 1 out of 11 times in order to break even. The thinking goes
along the lines of: if you play 11 times, it'll cost you $110, but when you win
once, you will get $110 ($100 + your $10 call).
The usefulness of hand odds and pot odds becomes very apparent when you start
comparing the two. As we now know, in a flush draw, your hand odds for
making your flush are 1.9 to 1. Let's say you're in a hand with a nut flush draw
and it's $5 to you on the flop to call. Do you call? Your answer should be:
"What are my pot odds?"
If there is $15 in the pot plus a $5 bet from an opponent, then you are
getting 20:5 or 4:1 pot odds. This means that, in order to break even, you must
win 1 out of every 5 times. However, with your flush draw, your odds of winning
are 1 out of every 3 times! You should quickly realize that not only are you
breaking even, but you're making a nice profit on this in the long run. Let's
calculate the profit margin on this by theoretically playing this hand 100 times
from the flop, which is then checked to the river.
Net Cost to Play = 100 hands * $5 to call = $500 Pot Value = $15 + $5 bet
+ $5 call
Odds to Win = 1.9:1 or 35% (From the flop) Total Hands Won =
100 * Odds to Win (35%) = 35 wins
Net Profit = Net Cost to Play + (Total
Times Won * Pot Value) = $500 + (35 * $25) = $500 +
$875 = $375 Profit
As you can see, you have a great reason to play this flush draw, because
you'll be making moneyin the long run according to your hand odds and pot odds.
The most fundamental point to take from this is:
If your Pot Odds are greater than your Hand Odds, then you are making a
profit in the long run.
Even though you may be faced with a gut shot straight draw at times  which
is a terrible draw at 5 to 1 hand odds  it can be worth it to call if you are
getting pot odds greater than 5 to 1. Other times, if you have an excellent draw
such as the flush draw, but someone has just raised a large amount so that your
pot odds are 1:1, then you obviously should not continue trying to draw to a
flush, as you will lose money in the long run. In this situation, a fold or
semibluff is your only solution, unless you know there will be callers behind
you that improve your pot odds to better than breakeven.
Your ability to memorize or calculate your hand odds and pot odds will lead
you to make many of the right decisions in the future  just be sure to remember
that fundamental principle of profitably playing drawing hands requires that
your pot odds are greater than your hand odds.
Poker Odds from the Flop to Turn and Turn to River
An important note I have to make is that many players who understand Hold'em
odds tend to forget is that much of the theoretical odds calculations from the
flop to the river assume there is no betting on the turn. So while it's
true that for a flush draw, the odds are 1.9 to 1 that the flush will complete,
you can only call a 1.9 to 1 pot on the flop if your opponent will let you see
both the turn and river cards for one call. Unfortunately, most of the time,
this will not be the case, soyou should not calculate pot odds
from the flop to the river and instead calculate them one card at a time.
To calculate your odds one card at a time, simply use the same odds that you
have going from the turn to the river. So for example, your odds of hitting a
flush from the turn to river is 4 to 1, which means your odds of hitting a flush
from the flop to the turn is 4 to 1 as well.
To help illustrate even further, we will use the flush calculation example
that shows an oftenused (but incorrect) way of thinking
Example of Incorrect Pot Odds Math You Hold: Flush
Draw Flop: $10 Pot + $10 Bet You Call: $10 (getting 2 to 1
odds)
Turn: $30 Pot + $10 Bet You Call: $10 (getting 4 to 1
odds)
LongTerm Results Over 100 Hands Cost to Play =
100 Hands * ($10 Flop Call + $10 Turn Call) = $2,000 Total Won = 100 Hands *
35% Chance to Win * $50 Pot = $1,750
Total Net = $1,750 (Won)  $2,000
(Cost) = $250 Profit =
$2.5/Hand
Example of Correct Pot Odds Math You Hold:
Flush Draw Flop: $30 Pot + $10 Bet You Call: $10 (getting 4 to 1
odds)
Turn: $50 Pot + $16 Bet You Call: $16 (getting about 4 to 1
odds)
LongTerm Results Over 100 Hands Cost to Play =
100 Hands * ($10 Flop Call + $16 Turn Call) = $2,600 Total Won = 100 Hands *
35% Chance to Win * $82 Pot = $2,870
Total Net = $2,870 (Won)  $2,600
(Cost) = $270 Profit = $2.7/Hand
As you can see from these example calculations, calling a flush draw with 2
to 1 pot odds on the flop can lead to a long term loss, if there is additional
betting past the flop. Most of the time, however, there is a concept called
Implied Value (which we'll get to next) that is able to help flush draws and
openended straight draws still remain profitable even with seemingly 'bad'
odds. The draws that you want to worry about the most are your long shot draws:
overcards, gut shots and twoouters (hoping to make a set with your pocket
pair). If you draw these hands using incorrect odds (such as flop to river
odds), you will be severely punished in the long run.
Implied Value
Implied Value is a pretty cool concept that takes into account future
betting. Like the above section, where you have to worry about your opponent
betting on the turn, implied value is most often used to anticipate your
opponent calling on the river. So for example, let's say that you have yet
another flush draw and are being offered a 3 to 1 pot odds on the turn. Knowing
that you need 4 to 1 pot odds to make this a profitable call, you decide to
fold.
Aha, but wait! Here is where implied value comes into play. So, even though
you're getting 3 to 1 pot odds on the turn, you can likely anticipate your
opponent calling you on the river if you do hit your flush draw. This means that
even though you're only getting 3 to 1 pot odds, since you anticipate your
opponent calling a bet on the river, you are anticipating 4 to 1 pot odds  so
you are able to make this call on the turn.
So in the most practical standpoint, implied value usually means that you can
subtract one bet from your drawing odds on the turn, as it anticipates your
opponents calling at least one bet. In some more advanced areas, you can use
implied odds as a means of making some draws that might not be profitable a
majority of the time, but stand to make big payouts when they do hit. Some
examples of this would be having a tight image and drawing to a gut shot against
another tight player. Even though this is a horribly bad play (and hopefully you
don't have to pay much for it), it can possibly be a positive play if you know
your opponent will pay you off if you hit your draw  because he won't believe
you played a gut shot draw. For many reasons, I do not recommend fancy implied
odds plays like these, but mentioned it more so that you can recognize some
players who pull these 'tricky' plays on you as well.
Conclusion  Poker Odds
Knowing how to figure out your odds in Texas Hold'em is one of the most
fundamental points in becoming a solid poker player. If this poker odds page was
a bit difficult to understand, don't worry. Keep playing, bookmark this page and
come back when you need another brushup on how to properly apply odds. It takes
a while to learn how to calculate them properly and to memorize them as well.
Practice makes perfect.
Never forget to Bluffnaked either, that's always fun!!!
