How To Calculate Pot Odds

[tiptheboss]

By: Rory Monahan

You DON'T need to be a "math genius" to understand
poker odds...

Not at all.

In fact, you can be TERRIBLE at math (like me) and

still be able to use "odds" to your advantage at

the no-limit Holdem tables.

There are TWO main things you need to learn right

away:

1. The concept of OUTS

2. The concept of POT SIZE

These are easy. Let's start with the first.

"Outs" refers to the number of cards in the deck

that will complete (or "make") your hand.

For instance... if you have Ace-King and the board

reads Q-J-4, you need a ten to make your straight.

Since there are four tens in the deck, you have

FOUR OUTS.

Or... let's say you're holding Q-J and the board

reads K-10-5. That means you have an open-ended

straight draw-- either the Ace or the nine will

complete your straight.

Since there are four nines and four Aces in the

deck, you have EIGHT OUTS.

Let's do one more. Let's say you've got 8-7 of

clubs and the board reads 2c-Ad-Kc-3s. That means

there are two clubs on the board and two in your

hand. If one more club hits on the river, you'll

have a flush.

There are a total of thirteen clubs in the deck

(thirteen of each suit times four suits equals

fifty-two cards).

But that DOESN'T mean you have thirteen outs,

because you're already using four of the clubs.

Instead, you have NINE OUTS (thirteen minus four).

If any of those nine cards hits on the river,

you'll have a flush.

OK... so that's how you calculate OUTS. We'll do

some more in-depth examples in a minute, but first

let's talk about POT SIZE.

Pot size is how much money is in the pot. Pretty

simple, right?

There are three main parts to pot size:

1. How much money is already in the middle

2. How much is bet in the current round of betting

3. How much WILL be bet in the current round

Let me explain.

Let's say four players call the big blind of $4 in

a game. That means there's $16 in the middle.

The flop comes out. You're on the button, which

means you're LAST to act. Player 1 bets $10 into

the pot. Player 2 calls, and Player 3 folds. Now

it's your turn. What's the current pot size?

The answer is $36. There's the $16 that was in the

middle first, then $20 more from Players 1 and 2.

The $16 is the first part, the $20 is the second

part, and there is no third part since you were

last to act.

Let's take another look. Let's say you were SECOND

TO ACT, instead of on the button.

Four players call the big blind of $4, which means

there's $16 in the pot. Player 1 bets $10, and now

you must make a decision. What's the pot size?

Well, it's $16 + $10 + UNKNOWN.

Why "unknown"?

The reason is you DON'T KNOW if the two players

BEHIND you are going to call, raise, or fold. So

you really don't KNOW the exact pot size.

This is a fundamental reason why math doesn't

solve all your problems in poker. You must use

your INSTINCTS to "guess" and "infer".

In this case, you would try to guess whether or

not the other two players would call or fold (or

raise) and make your decision then. This is also

another reason why POSITIONING in a hand is so

important.

One more thing about pot size before we move on...

A lot of players don't know whether to count THEIR

OWN MONEY in the actual pot size.

The answer is you count your own money that's

ALREADY THERE from before. In the example, your

big blind of $4 is already in the pot... so you DO

use it to calculate the pot size.

Once your money is in the middle, it isn't yours

any more. Period.

But you would NOT include your $10 in the pot

size, because you haven't put it in yet. You're

THINKING about putting it in.

Make sense?

Let's say you called the $10 bet from Player 1 and

the other players all folded. The turn card comes

and Player 1 bets $20. What's the pot size?

Well, it's $16 from pre-flop, $20 after the flop,

and now $20 after the turn.

You DO count your $10 after the flop because now

it IS already in the middle.

OK... so what does OUTS and POT SIZE have to do

with ODDS?

The answer is EVERYTHING.

Now that you know these two basics, you're ready

to start calculating "complicated" poker odds.

To calculate odds, you need four pieces of

information:

1. Number of outs

2. Number of "unknown" cards in the deck

3. Pot size

4. Current bet amount

We talked about the outs and pot size. The other

two are very straightforward.

The number of "unknown" cards in the deck simply

means how many cards you DON'T KNOW. Before the

flop, there are 50 cards you don't know. You only

know the two in your hand.

After the flop, there are 47 cards you don't know.

You know the two in your hand and the three on the

board and that's it.

After the turn there are 46 cards you don't know.

Like I said, this is simple stuff.

And the CURRENT BET AMOUNT is just... well, the

current bet amount. It's how much you must put in

the pot to "call".

OK, let's review.

Let's say you get dealt J-10 offsuit. You call the

big blind of $6 and so does one other player. The

small blind folds. The player in the big blind

checks. That means the POT SIZE is $21

($6 + $6 + $6 + $3).

The flop comes out Q-2-9. You've got an open-ended

straight draw. Either a King or an eight will make

your straight. Since there are four Kings and four

eights in the deck, you've got EIGHT OUTS.

There are 47 unknown CARDS in the deck (52 cards

minus the five that you see).

You're second to act. The first player bets $12.

That means $12 is the CURRENT BET AMOUNT.

The POT SIZE is $21 + $12 + UNKNOWN. The unknown

is what the player after you does...

So there you have it... those are the four pieces

of information you need. The only thing you don't

know for SURE is the pot size in this example.

Sometimes you'll know the pot size exactly (like

when you have good positioning). Other times

you'll just have to estimate.

OK, let's do some odds.

THE WAY TO CALCULATE ODDS IS TO COMPARE THE ODDS

OF MAKING YOUR HAND TO THE ODDS OF THE POT.

Here's the exact "formula":

(Unknown Cards - Outs) : Outs

VERSUS

Pot Size : Current Bet Amount

If the first comparison is smaller than the second

one, that's good. It means that "pot odds justify

a call" (or raise).

For instance, if you have 12 outs and there are 47

unknown cards, that means you have ABOUT a 25%

chance of "making" your hand.

The odds against you are 35:12, or about 3:1.

Remember... when you see two numbers like X:X, the

first number is the chance of one thing happening

against the chance of the second thing happening.

You'll miss your hand three times and make it

once. That's 1/4 or 25% or 3:1.

Now let's say the pot size is $50 and the current

bet amount is $10. That means the odds would be

$50:$10, or 5:1.

It's easiest to look at in the X:X format and not

use percentages.

OK, so here's what you've got for this example:

Outs = 12

Unknown Cards = 47

Current Bet Amount = 10

Pot Size = 50

There are 35 cards that WON'T HELP YOU (47 - 12).

So the odds are 35:12 for the cards.

And for the pot it's 50:10. You don't add your $10

to the first number. Just use the current pot

size.

35:12 is about 3:1.

50:10 equals 5:1.

The entire point of calculating odds is to make a

good decision. To make a decision of whether or

not to call a $10 bet here, you would compare the

3:1 versus 5:1.

The odds here are IN YOUR FAVOR.

If this scenario played out four times, here's how

it would look STATISTICALLY:

- You lose $10.

- You lose $10.

- You win $50.

_ You lose $10.

You lose three times and win once (3:1). When you

add your losses it equals $30 but your wins are

$50, giving you a $20 profit.

If the scenario happened eight times you'd win

twice and lose six times. That means you'd lose

$60 and win $100... for a $40 profit.

For real life poker situations, the key is to

calculate whether or not you can "justify" staying

in the hand.

Let's say you have A-8 and the flop comes out:

K-10-4

Someone bets $10 and the pot size is $20. What

should you do?

Well, you don't have anything but an Ace high. If

the Ace comes on the turn, you'd have top pair.

So let's ASSUME that your top pair would be the

winning hand.

That means there are three cards in the deck that

can help you (the other three Aces). And there are

exactly 47 unknown cards in the deck.

So we have our numbers:

Outs = 3

Unknown Cards = 47

Current Bet Amount = 10

Pot Size = 20

Using our formula...

(47 - 3) : 3

VERSUS...

20 : 10

So the numbers come out 44:3 (about 15:1) versus

2:1. Should you call?

Of course not.

You're only getting 2:1 for your money but your

chances of winning the hand are very slim.

If the hand played out 16 times you would win

ONCE. So you'd lose $150 (15 X $10) and win $20,

for a total loss of $130.

You're always striving for good odds on your money

and good odds on your hand.

Good odds on your hand means the X:X number is as

SMALL AS POSSIBLE... because you want lots of

outs. You don't want there to be only one or two

cards in the deck that can help you. You want

fractions like 47:12, 46:10, 46:8, and so on.

Good odds on your money means the X:X number is

BIG. You want 10:1, 5:1, 12:1, and so on.

OK, I'm going to give one more example. See if

you're smart enough to figure this out on your

own (you may need to use a scratch piece of

paper)...

You're second to act pre-flop and look down to see

Kc-Jc. You limp-in by calling the $4 big blind.

Three other players call. The small blind (who put

in $2) folds.

The player in the big blind decides to RAISE the

pot to $8. You call. Two of the other three

players call... but one folds.

So now there are four players total in the hand...

the guy in the big blind, you, and the two other

callers. (Still with me here?)

The flop comes out:

Ac-4s-8c

What a great flop for you. You've got the nut

flush draw.

The player in the big blind is first to act. He

checks. You check also (which I would NOT

recommend doing here, by the way).

The next player bets $16. The next one calls. The

guy who made the original pre-flop raise folds.

So now the action is on to you.

What is the...

Number of outs?

Number of unknown cards?

Current bet amount?

Pot size?

AND MOST IMPORTANTLY...

Should you call?

See if you can figure it out before I give you the

answer.

...

...

...

...

OK, so the answer is this:

Yes, you should call.

The pot size is $70. The current bet amount is

$16. The number of outs is 9. And the number of

unknown cards is 47.

The pot size was the hardest thing to figure out.

Remember... the small blind folded his $2. Another

player folded their $4. So there was $6 in the

middle, plus $32 with the four callers. So $38

before the flop.

Then there were two players in for $16 after the

flop, which equals $32. $38 + $32 = $70. Luckily,

there weren't any other players left to act after

you in this exact round of betting.

The number of outs is simple. Thirteen clubs in

the deck minus the four you already see equals

nine. And the number of unknown cards is 52 minus

the five you see... which equals 47.

Plugging those numbers into our handy "formula"

gives us:

(47-9):9 Versus 70:16

That's equal to 38:9 versus 70:16

Now you might be wondering, "How the hell am I

supposed to know what 70 divided by 16 is or 38

divided by 9? It's not like I'll have a calculator

handy at the table!"

True.

But you don't have to know the EXACT numbers. All

you need to know is if the second one is bigger

than the first. And that's pretty easy.

When I do it, here's what goes on in my head:

"38 over 9 is about the same as 36 over 9, which

equals 4. That means 38 over 9 is 4 and 2/9ths.

70 over 16 is closest to 64 over 16, which also

equals 4. That means 70 over 16 is 4 and 6/16ths.

Now I just have to compare 2/9 to 6/16. 2/9 is

like 2/10, which equals .2. 6/16 is kind of like

6/18, which is .33. So the second one is bigger."

And that means the call IS justified.

Now let me clarify something...

In this example the two numbers are VERY close

(4.22 versus 4.375). Usually they WON'T be that

close. Usually they'll be something like 3.3

versus 8.2 or 2.5 versus 4.1.

That means in MOST cases you won't have to do all

that fraction stuff. OR, even if you DO have those

fractions, you won't need to calculate it. You'll

probably just consider it "about even" and make

your decision based on other factors.

All right... so that's basically how you calculate

pot odds. Of course, there's more.

You also want to know IMPLIED ODDS. Implied odds

aren't as math-related. Implied odds basically

pertain to hands where you can "bust" or

"surprise" your opponents.

In the last example, you were on the nut flush

draw, because you had the King of clubs and the

Ace of clubs was on the board.

If your opponent was ALSO on the flush draw and he

had the QUEEN of clubs, this would be very good

for you...

Because if another club hit on the turn, you and

your opponent would both have flushes. But yours

would be higher.

In this case, your opponent would likely go

"all-in" and you would win a TON of chips.

So even though the "odds" on your money are

4.375:1, they're actually higher because of the

"implied odds" of your NUT flush draw.

Besides implied odds, you'll also have to think

about the "unknown" pot size, as we discussed.

Many times you just won't KNOW the exact pot size,

and will be forced to guess.

Also... you must be careful to consider what your

OPPONENTS are holding...

Let's say you're holding As-5h and the board

reads: 8h-Qh-2h

You have the flush draw. And the odds of "making"

it are good. But that doesn't mean you want to

calculate the nine other hearts in the deck as

your "outs".

Why?

Because all your opponents need to BEAT you is a

heart higher than a FIVE. And someone most likely

has it.

The point is, when you calculate OUTS, you want to

calculate outs based on making the WINNING HAND.

And obviously there's no way to know for sure what

the winning hand will be... unless you've got the

nuts.

So as you can see... there are a LOT of different

factors to take into consideration.

Calculating pot odds is a useful technique for the

right situations. Over the long term, it can

become very handy and will help you make sound,

logical decisions at the poker table.

And fortunately, after practicing pot odds for a

few games, most of the numbers will become

"instinctual" very quickly.

But it's just a tool. One of MANY that you should

store in your Holdem "toolbox".

In the same way that you can't build a house with

just a HAMMER, you can't base your entire game on

ODDS or math.