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In our poker math and probability lesson it was stated that when it comes to poker; “the math is essential“. Although you don’t need to be a math genius to play poker, a solid understanding of probability will serve you well and knowing the odds is what it’s all about in poker. It has also been said that in poker, there are good bets and bad bets. The game just determines who can tell the difference. That statement relates to the importance of knowing and understanding the math of the game.

1. Poker Hand Odds Calculator Preflop
2. Poker Hands Odds Of Winning
3. Poker Hand Odds Chart

In this lesson, we’re going to focus on drawing odds in poker and how to calculate your chances of hitting a winning hand. We’ll start with some basic math before showing you how to correctly calculate your odds. Don’t worry about any complex math – we will show you how to crunch the numbers, but we’ll also provide some simple and easy shortcuts that you can commit to memory.

If you flop an open-ended straight draw this gives you eight outs (eight possible cards that will complete the hand), so you'll hit your hand by the river 31.5% of the time. Just make sure you're getting pot odds (the value of the pot versus the value of your bet) to see the next card. Experienced players will be better at playing post-flop, and therefore will be able to play a wider range of hands successfully. However, we recommend that beginning poker players play a tighter.

Texas Holdem Heads-Up Preflop Odds. This table was created by enumerating through every possible board and opponent hole card combination for each of the 169 texas holdem preflop starting hands.

Basic Math – Odds and Percentages

Odds can be expressed both “for” and “against”. Let’s use a poker example to illustrate. The odds against hitting a flush when you hold four suited cards with one card to come is expressed as approximately 4-to-1. This is a ratio, not a fraction. It doesn’t mean “a quarter”. To figure the odds for this event simply add 4 and 1 together, which makes 5. So in this example you would expect to hit your flush 1 out of every 5 times. In percentage terms this would be expressed as 20% (100 / 5).

Here are some examples:

• 2-to-1 against = 1 out of every 3 times = 33.3%
• 3-to-1 against = 1 out of every 4 times = 25%
• 4-to-1 against = 1 out of every 5 times= 20%
• 5-to-1 against = 1 out of every 6 times = 16.6%

Converting odds into a percentage:

• 3-to-1 odds: 3 + 1 = 4. Then 100 / 4 = 25%
• 4-to-1 odds: 4 + 1 = 5. Then 100 / 5 = 20%

Converting a percentage into odds:

• 25%: 100 / 25 = 4. Then 4 – 1 = 3, giving 3-to-1 odds.
• 20%: 100 / 20 = 5. Then 5 – 1 = 4, giving 4-to-1 odds.

Another method of converting percentage into odds is to divide the percentage chance when you don’t hit by the percentage when you do hit. For example, with a 20% chance of hitting (such as in a flush draw) we would do the following; 80% / 20% = 4, thus 4-to-1. Here are some other examples:

• 25% chance = 75 / 25 = 3 (thus, 3-to-1 odds).
• 30% chance = 70 / 30 = 2.33 (thus, 2.33-to-1 odds).

Some people are more comfortable working with percentages rather than odds, and vice versa. What’s most important is that you fully understand how odds work, because now we’re going to apply this knowledge of odds to the game of poker.

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Poker Hand Odds Calculator Preflop

Counting Your Outs

Before you can begin to calculate your poker odds you need to know your “outs”. An out is a card which will make your hand. For example, if you are on a flush draw with four hearts in your hand, then there will be nine hearts (outs) remaining in the deck to give you a flush. Remember there are thirteen cards in a suit, so this is easily worked out; 13 – 4 = 9.

Another example would be if you hold a hand like and hit two pair on the flop of . You might already have the best hand, but there’s room for improvement and you have four ways of making a full house. Any of the following cards will help improve your hand to a full house; .

The following table provides a short list of some common outs for post-flop play. I recommend you commit these outs to memory:

Table #1 – Outs to Improve Your Hand

The next table provides a list of even more types of draws and give examples, including the specific outs needed to make your hand. Take a moment to study these examples:

Table #2 – Examples of Drawing Hands (click to enlarge)

Counting outs is a fairly straightforward process. You simply count the number of unknown cards that will improve your hand, right? Wait… there are one or two things you need to consider:

Don’t Count Outs Twice

There are 15 outs when you have both a straight and flush draw. You might be wondering why it’s 15 outs and not 17 outs, since there are 8 outs to make a straight and 9 outs for a flush (and 8 + 9 = 17). The reason is simple… in our example from table #2 the and the will make a flush and also complete a straight. These outs cannot be counted twice, so our total outs for this type of draw is 15 and not 17.

Anti-Outs and Blockers

There are outs that will improve your hand but won’t help you win. For example, suppose you hold on a flop of . You’re drawing to a straight and any two or any seven will help you make it. However, the flop also contains two hearts, so if you hit the or the you will have a straight, but could be losing to a flush. So from 8 possible outs you really only have 6 good outs.

It’s generally better to err on the side of caution when assessing your possible outs. Don’t fall into the trap of assuming that all your outs will help you. Some won’t, and they should be discounted from the equation. There are good outs, no-so good outs, and anti-outs. Keep this in mind.

Calculating Your Poker Odds

Once you know how many outs you’ve got (remember to only include “good outs”), it’s time to calculate your odds. There are many ways to figure the actual odds of hitting these outs, and we’ll explain three methods. This first one does not require math, just use the handy chart below:

Table #3 – Poker Odds Chart

As you can see in the above table, if you’re holding a flush draw after the flop (9 outs) you have a 19.1% chance of hitting it on the turn or expressed in odds, you’re 4.22-to-1 against. The odds are slightly better from the turn to the river, and much better when you have both cards still to come. Indeed, with both the turn and river you have a 35% chance of making your flush, or 1.86-to-1.

We have created a printable version of the poker drawing odds chart which will load as a PDF document (in a new window). You’ll need to have Adobe Acrobat on your computer to be able to view the PDF, but this is installed on most computers by default. We recommend you print the chart and use it as a source of reference. It should come in very handy.

Doing the Math – Crunching Numbers

There are a couple of ways to do the math. One is complete and totally accurate and the other, a short cut which is close enough.

Let’s again use a flush draw as an example. The odds against hitting your flush from the flop to the river is 1.86-to-1. How do we get to this number? Let’s take a look…

With 9 hearts remaining there would be 36 combinations of getting 2 hearts and making your flush with 5 hearts. This is calculated as follows:

(9 x 8 / 2 x 1) = (72 / 2) ≈ 36.

This is the probability of 2 running hearts when you only need 1 but this has to be figured. Of the 47 unknown remaining cards, 38 of them can combine with any of the 9 remaining hearts:

9 x 38 ≈ 342.

Now we know there are 342 combinations of any non heart/heart combination. So we then add the two combinations that can make you your flush:

36 + 342 ≈ 380.

The total number of turn and river combos is 1081 which is calculated as follows:

(47 x 46 / 2 x 1) = (2162 / 2) ≈ 1081.

Now you take the 380 possible ways to make it and divide by the 1081 total possible outcomes:

380 / 1081 = 35.18518%

This number can be rounded to .352 or just .35 in decimal terms. You divide .35 into its reciprocal of .65:

0.65 / 0.35 = 1.8571428

And voila, this is how we reach 1.86. If that made you dizzy, here is the short hand method because you do not need to know it to 7 decimal points.

The Rule of Four and Two

A much easier way of calculating poker odds is the 4 and 2 method, which states you multiply your outs by 4 when you have both the turn and river to come – and with one card to go (i.e. turn to river) you would multiply your outs by 2 instead of 4.

Imagine a player goes all-in and by calling you’re guaranteed to see both the turn and river cards. If you have nine outs then it’s just a case of 9 x 4 = 36. It doesn’t match the exact odds given in the chart, but it’s accurate enough.

What about with just one card to come? Well, it’s even easier. Using our flush example, nine outs would equal 18% (9 x 2). For a straight draw, simply count the outs and multiply by two, so that’s 16% (8 x 2) – which is almost 17%. Again, it’s close enough and easy to do – you really don’t have to be a math genius.

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Conclusion

In this lesson we’ve covered a lot of ground. We haven’t mentioned the topic of pot odds yet – which is when we calculate whether or not it’s correct to call a bet based on the odds. This lesson was step one of the process, and in our pot odds lesson we’ll give some examples of how the knowledge of poker odds is applied to making crucial decisions at the poker table.

As for calculating your odds…. have faith in the tables, they are accurate and the math is correct. Memorize some of the common draws, such as knowing that a flush draw is 4-to-1 against or 20%. The reason this is easier is that it requires less work when calculating the pot odds, which we’ll get to in the next lesson.

By Tom 'TIME' Leonard

Tom has been writing about poker since 1994 and has played across the USA for over 40 years, playing every game in almost every card room in Atlantic City, California and Las Vegas.

Many Texas holdem poker books do a good job of explaining how
to play profitably before the flop, but it’s hard to find a good
resource that teaches you how to play well after the flop.

We believe the reason for this is because playing strong
poker post flop is hard.

While many players never learn how to play well pre flop, it
can be learned by just about anyone. You have to focus on strong
starting hand selection, table selection, position, odds, and
your opponents.

But when the flop comes you enter a new area of potential
profit and loss. Your goals are still the same after the flop as
before, but it can be more difficult to determine the best
course of action.

You want to make every decision based on how profitable it is
in the long run. Is it more profitable to bet or check? Is it
more profitable to play aggressively or slow down your play?

After the flop you have more information than beforehand. Not
only do you know the identity of three of the board cards you
also know how each of your opponents played before the flop and
the odds your hand will improve and / or make a best hand.

This information increases with the turn and the river. You
still end up working with incomplete information, but the more
you learn the better your chances are to make profitable
decisions.

With each extra bit of information you come closer to the
best play, so don’t miss anything during the hand.

Reading Your Opponent’s Hands

The way to do this is to see how they play each hand before
and after the flop and combine this with what you now about the
player from past experience.

This can be somewhat easier with better players, but it’s
always easier to make money off poor players. Poor players make
strange plays and play hands from positions that you never see a
good player play.

We see poor players enter the pot from early position with
middle suited connectors and suited aces with small kickers.
Good Texas holdem poker players understand that these hands
aren’t profitable in the long run from early position.

In the interest of full disclosure, a few of the top poker
players can play these hands from early position in some games
for a long term profit, but if you’re that good you’re not
reading this page. The main reason is because they know when to
get away from a second or third best hand and how to maximize
the few times they hit a big hand with these types of secondary
starting hands.

If you enter the pot with an ace and a small kicker are you
able to lay it down when you flop two pair and face an all in
raise?

We’re not saying the correct play is to always fold, but you
have to be able to consider folding based on your opponent and
her playing tendencies.

Poor players are harder to put on a specific hand, but they
usually play their hands so badly that you can still show a long
term profit against them by just playing solid straightforward
poker.

As soon as an opponent enters the pot you need to start
considering the range of possible starting hands they hold.

If they raise from early position they usually have a strong
hand. The same is usually true from a raise in middle position,
but they could also be trying to steal the button with a medium
strength hand.

A limp from middle or late position is often a trap hand that
needs to improve to win the hand. The same is often true from
late position. A raise from late position could show strength or
simply be trying to steal the blinds.

The hardest positions to read are the blinds in un-raised
pots. They could have almost anything in a hand that they see
for free or half a bet. Don’t make the mistake of thinking
they’re weak just because they started the hand in the blinds.

As you gather more information you need to narrow the
possible hands down as much as possible. The way your opponents
act before the flop is combined with how they act on the flop,
turn, and river to narrow their hand possibilities to the
smallest range you can.

Here’s an extended example of how you narrow a list of
possible hands as the hand plays out.

An early position player raises and you call from late
position. Everyone else at the table decides to fold. You know
the player is fairly good and plays a tight game from early
position.

This gives you a range of possible hands that include the
following:

• Pair of aces
• Ace king suited
• Ace king off-suit
• Pair of kings
• Pair of queens
• Pair of jacks
• Ace queen suited
• Pair of tens

This is a fairly wide range of hands for a good player
because the last three hands on the above list may or may not be
realistic.

The flop comes down as the following.

Your opponent fires a bet into the pot after seeing the flop.
At this time the bet doesn’t mean much because it’s probably a
continuation bet. Good players know that if they raise before
the flop it’s profitable to bet after the flop because most
players will miss the flop and a bet can win it without a
further fight.

You decide to call, and then the turn is dealt.

This is where you should be able to get a strong feel for
what your opponent holds. The ace on the flop was a scare card
for any of the hands not including an ace. The kings and queens
especially hate seeing an ace on the flop. But they’re strong
enough that they require more than a scare card to get them to
fold. Good payers may still bet on the turn with pocket kings or
queens, but the may check.

If they check at this point you can usually rule out any of
the hands that include an ace. The only players good enough to
check a hand with an ace in this situation are pro or semi pro
players and they have to be good enough to realize that you’re
likely to bet here. Unless you’re a pro and are playing at the
top levels, if your opponent checks in this situation they don’t
have an ace.

If you’re in this situation and hit a set of aces on the flop
and you’re playing against an aggressive opponent, check to them
and then check raise them or flat call and check to them again
on the river. An aggressive player will never check their hand
down in this situation unless they completely missed their hand.
Even when they miss they still might fire a bluff on the river.

At this point you need to decide what to do. Your opponent’s
reaction to your bet or check if they check will give you
additional clues. If they bet and you call or raise it will
force them to make another decision which will help you learn
more about their hand.

In this example they check and you make a small bet. They
call and the river card is a two.

Your opponent checks, you make a bet, and they call.

What hand or possible hands do you think they could turn
over?

The way this hand played out the most likely hand is a pair
of kings, but pocket queens are also possible.

If they had a hand with an ace they’d have played it more
aggressively, and they probably would have folded a pair of
jacks or tens.

Think through each hand as it’s happening this same
way and keep looking for ways to improve your hand reading
skills. Only practice and study of your opponents will make you
better at this important skill.

Immediately Following the Flop

At this point in the hand you need to plan how the rest of
the hand will play out. We always try to teach new players how
to plan out every hand and consider every possibility before the
hand starts.

As things happen throughout the hand you have fewer
possibilities to consider. Don’t let down at this point. Look at
everything you’ve learned so far and look for the best ways to
play every possibility moving forward.

Continuation Bets

Continuation bets are when the player who showed aggression
before the flop by raising fires another bet on the flop. The
important thing to remember about continuation bets is sometimes
the player has a strong hand but sometimes the player missed the
flop and is hoping to win it without having to play the rest of
the hand.

The basic rule of thumb is you have to ignore continuation
bets when you’re deciding how to play the rest of the hand. They
don’t provide enough detailed information to make decisions
based on them.

Of course you consider them for pot odds evaluations, but
they don’t help you read your opponent.

Should you make continuation bets when you raise pre flop?

Most of the time you should make a continuation bet, so the
answer is yes. If your opponents are good enough to pay
attention you need to alter your play from time to time so you
can check occasionally on the flop after being aggressive pre
flop, but most of the time the best play is to make a
continuation bet whether you hit the flop or not.

Poker Hands Odds Of Winning

Flops That Help You

Flops that help you fall into two categories. The first one
is the flops that make your hand so strong that the odds of you
losing are slim to none.

On these types of flops you need to consider the best way to
make the pot as large as possible. If a large bet will be called
you need to make a large bet. But against some opponents the
best way to build the pot is to let them be the aggressor. You
need to know as much about your opponents as possible to learn
how to build big pots in these situations.

The other kind of flop that helps you is the one that
improves your hand but leaves possibilities that an opponent can
draw to a better hand.

On these kinds of flops you need to bet aggressively to force
them to pay to draw to a better hand.

Dangerous Flops

Dangerous flops in Texas holdem are those that either don’t
improve your hand or those that have a high chance of improving
your opponents more than they improved your hand.

The way you choose to play dangerous flops depends somewhat
on your opponent, but for the most part you need to proceed
cautiously.

If you have a draw to a winning hand you need to check and
call if the pot odds are correct. You should rarely bet into a
dangerous flop. You should every once in a great while to vary
your play but for the most part proceed with caution.

Turn

On the turn you only have one more card, but at this point
you have seen 80% of the board and should know exactly where you
are in the hand. When you’re ahead you need to continue building
the pot and if you’re drawing you need to make sure the pot odds
are still favorable before committing any more money to the pot.

If you plan to make a bluff on the river you need to consider
how best to set it up on the turn. If you check the turn it
rarely is believable when you make a bluff on the river unless a
scare card lands. A scare card is one that looks like it could
complete a flush or straight.

River

The river usually plays itself. You either have the best hand
or you don’t. If you have the best hand you determine how much
your opponent will likely call and if you don’t have the best
hand you either check and fold or try a bluff.

The trouble hands are the ones when you have a decent hand
but aren’t sure what your opponent holds. These are the hands
that often separate the winners from the losers. Everyone makes
mistakes on these hands sometimes, but the best players get it
right more often than not.

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If you’ve done a good job of putting your opponent on a
narrow range of hands it helps, but here are a few general
guidelines to help you play the river in unknown situations.

• Just like in most aspects of Texas holdem, it’s usually
  beneficial to be aggressive.
• An over bet is usually a bluff, but sometimes it’s still
  too much to call.
• Bluffs are more about the players involved than the
  cards.
• You should bluff less than you do now. Almost every
  player bluffs too much.
• NEVER show your cards unless you have to.
• Practice is one of the few things that improve your play
  on the river.

Winning the Battle, but Losing the War

Poker Hand Odds Chart

A huge leak in most losing player’s Texas holdem game is
focusing too much on winning hands instead of winning money.

We realize at first glance it may seem like the two go hand
in hand, but the truth is that you can easily win more hands and
lose money while doing so. How much does it cost when you lose a
big pot in comparison to how much you win in two or three small
pots?

When this gets especially costly is when you refuse to stop
chasing pots where you’re losing. Many players seem to think
they can bet their way out of bad situations, even when they
should be folding.

Don’t latch onto hands and feel like you have to try to win
them no matter what. Focus on the hands you can win by
maximizing your value in them. At the same time look for ways to
save money in other pots so you have more to invest in the pot
when you’re winning.

The reason we include this information in the post flop page
is because by the time you see the flop you should have enough
information about your possible hands and your remaining
opponents to get a strong idea of where you stand in the hand.

Of course the pot may offer odds that make it profitable to
keep playing even if you aren’t winning yet, but if you don’t
have a good chance to win the hand or a profitable draw you need
to start looking for ways to get out of the hand.

If no one seems to want to claim the pot you can occasionally
fire a bet, but if anyone calls you need to check and fold.

Don’t win the battle but lose site of the war. Each hand is a
battle but your overall profitability is the war. Sometimes you
have to retreat, or fold a losing hand, in order to reserve your
resources for the war.

Summary

Post flop play in Texas holdem is a challenging thing to
master, but if you’re willing to practice you can improve over
time. Remember the keys discussed above including how to read
your opponent’s possible hands and how to visualize the rest of
the hand and you’ll be ahead of most players.