How Not to Suck at Poker: Learn Basic Odds

By: Sean Lind

Part 4 in a 10-part series for the beginner poker player, this article will look at some simple tricks and tips for understanding basic poker odds.

Like it or not, Texas Hold'em is an odds game. Every action you make, hand you play or bet you face has odds, probability and statistics attached to it.

For the math-phobes out there though, don't worry. You don't need to become a math expert to be a strong poker player.

In fact, there are tons of serious players who have no idea what a common denominator is. As complex as Hold'em strategy is, the game at its core is still very simple.

And this simplicity makes for simple equations and easy mathematics.

Many of the following things you don't need to fully understand - you just need to know enough to have a good feel for the game.

Figuring Out Your Pot Odds

Pot odds are the odds you're "being offered by the pot" to make your call. This is the amount of money in the pot compared to the amount of money you must pay to stay in the hand.

An example:

Say we go to the flop heads-up. There's $10 in the pot and your opponent bets $5. Since your opponent's bet is now part of the pot, you're being offered $15 for a cost of $5. In ratio form, that's 15:5

To simplify, you always make the right side of your ratio equal to 1 (you'll see why this is easier in a second). So to make the right side equal to 1, divide 5 by itself. 5/5 = 1.

Basic math rules say that whatever you do to one side of a ratio, you must do to the other. So since we divided the right side by 5, we divide the left side by 5. 15/5 = 3.

Your new ratio is 3-1 (If you want to skip a step, you can also just divide the left side by the right side (15/5) to find the left-hand side of the new ratio).

So in this situation, the pot odds are 3-1.

Figuring Out Your Equity

The next step after figuring out your pot odds is figuring out your equity (your chances of winning the pot compared to your opponent's).

Phil Ivey in the process of figuring out his equity is always 110%

To calculate your equity, take your total number of outs and multiply that number by 4 on the flop (or 2 on the turn).

This will give you your chance at winning the pot as a percentage.

So for example if you have a flush draw, you have 9 outs on the flop. 9x4 = 36% chance at making the best hand.

Since we have the pot odds as a ratio, we then need to make that percentage a ratio to compare the two. With 100 possible percentage points, your equity ratio is then 64-36 (64 times you don't make your hand; 36 times you do).

If we use the same ratio shortcut from the pot odds section to get the right side equal to 1, the equity ratio is (64/36)-1 or 1.7-1. Meaning for every one time you make your hand there will be 1.7 times that you don't.

If you don't want to be that precise in your pot-odds calculation (and poker math doesn't need to be exact at the table), the simple shortcut is to estimate that 36 will go into 64 a little less than twice.

It really doesn't matter if you think that means it's 1.6, 1.7, 1.8 or 1.9-1; even if you just round it to 2-1 that's probably close enough to decide on making the call or not.

Comparing Your Pot Odds to Your Equity

So how do you know if you should make the call? Simply compare the two numbers on the left-hand side of the ratios.

If your pot odds number is higher than your equity number, then it's a good call. If it's lower, then you're making a bad call.

In its most basic form, odds are no more complicated than this.

Some Random Odds and Ends to Keep handy

Probability of...	Odds	Example
Being dealt a pair	17-1 (5.9% )	7♠ 7♥
Being dealt Aces	221-1 (0.45%)	A♥ A♦
Being dealt Ace-King Suited	331.5-1 (0.3%)	A♠ K♠
Flopping a set with a pocket-pair	8.51-1 (11.76%)	8♣ 8♥ \| 2♠ 8♦ A♣
Flopping two pair (without a pocket-pair pre-flop)	48-1 (2.02%)	7♣ 10♦ \| 7♥ 10♣ 3♥
Making a Flush by the river (flopped 4 to a suit)	1.9-1 (35%)	A♦ Q♦ \| 9♦ 4♦ A♠ 10♦
Making an open-ended straight by the river	2.2-1 (32%)	6♦ 7♥ \| 8♥ 9♦ 2♣ 3♦ 10♣
A full house or better by the river (flopped three of a kind)	2-1 (33%)	4♦ 4♥ \| 4♣ K♦ Q♥ K♠

More on how not to suck at poker:

Related strategy articles:

Comments

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Arty Smokes
2011-05-30

One of the mistakes I see newbies making is calling bets that are the value of the pot when they are chasing a flush (or even a gutshot!). They end up contributing almost 50% of the total pot by the river, but only ever had a 35% chance of getting the flush.
If you go heads up to the flop and villain bets the pot, your pot odds are 2-1 or 33%. You only have about a 19% chance of hitting the flush on the next card, so unless you have overcards or a concurrent straight draw (which provides additional outs), folding is the right decision. It's never wise to put 33% of the money in when you have less than a 20% of chance of winning. Occasionally these newbies get lucky and hit their flush against the odds, but in the long term they are throwing their money away by not making wise laydowns.

Another thing to remember when calculating pot odds is that POSITION is once again very important. If you are on the button, you get to see all the action in front of you. If you are on a flush draw and only one player bet before you, folding is usually the right decision, but if there are 2 or 3 bettors, the pot odds move in your favour, as the size of the pot is much bigger, but you still only have to make a cheap call.
Port
2011-02-07

super article, Sean! took me three years to figure out i needed to know this and another to figure out what you have shared.

what helped me believe is that there are 52 cards in deck which is pretty close to 2% per card (100%/52 cards = 1.92% per card). the only thing you can do with this percentage is say if i deal one card i have a 1.92 (2%) chance of getting an Ad. so what. (all day long i will bet you $1 to your $1 that you will not be dealt an Ad. that is the point of this discussion. for you to bet even money (1:1) on a 2% chance (52:1) is BAD! an even bet is my $3 against your $1 that you will get a club. 3:1 = 39:13) if you don't believe this don't play poker!)

(back to the 2% point) BUT after dealing and flopping you see 5 cards -- leaving 47 unknown cards. Guess what, it is still about 2% per card (100%/47 cards = 2.13 % per card). And you will see two more cards -- the TURN and RIVER. 2% each is 4% for both. and for each 6 or 8 outs add an extra percent for the .13.
jay
2011-01-05

Hi ,
how do you work this out in you head mentioned above.

100*(8/47) = 17% can you simplfy this please thanks!
Tom
2010-07-08

great article. Really concise and easy to understand. think this is really going to help my game. been playing for 2 years nearly now and only recently started to work on odds and outs. Really helpful, thankyou
britton
2010-01-31

Yes, it is true that you calculate the probability of hitting your hand from the flop position by multiplying your outs by 4. However, you can't really use the percentage as a basis to make a monetary decision unless you would tolerate paying up to the same amount on the turn regardless of what the turn is. An example would be sitting on an open-ended straight draw at the flop and telling yourself you have a 32% chance of hitting a straight. That may sound pretty decent in order to call $xxx, but in actuality you should be basing your decision on a 16% chance (receiving only one card) if you would not be willing to put in $xxx with 16% odds after the turn. Only in a game where the turn and river card came out simultaneously would you ever tell yourself it's worth that call or raise with a 32% chance of hitting a straight. At least that's how I view it...
Sean Lind
2010-01-08

Alex,

The formula you're using is for the odds of being dealt specific cards.

For hitting your outs the actual formula is simpler.

You have 39 cards that don't help you and 8 that do (for an open ender)

39:8 is the ratio, or 4.8:1

If you want a percentage that's not to tricky either, you have 8 out of 47 cards so:

100*(8/47) = 17%

The outs*2 or outs*4 are just shortcuts to remove most of the work. 8*2 = 16. It's not dead on, but it's close enough to work with while in a hand.

If 17% is the odds for one street, the odds for two streets will be (100*(8/47)) + (100*(8/46))

17 + 17 = 34%

So when you multiply outs*4 for two streets, you're still going to be close enough.

In poker, you just have to get it close, being exact on your numbers isn't going to help you at the table.
Tony
2010-01-08

Sean,
Your Sept 1/09 clarification is important. The one item that confused me (fromt reading the article) is why you automatically assumed to multiply your outs by 4 (to get you pct to hit your drawing hand to the river). Once compared to your pot odds, you make the (math) decision to call or not if your pot odds are higher than your equity. Obviously there is another betting round on the turn so you conceivably will be investing more money to see the river card and therefore your original pot odd assessment has changed. The only time I would assume to see the river is if I'm "all-in" when I call his flop bet.
Alex
2010-01-08

Hey Sean, first I'd like to say Great article. I just started playing Poker, but I was curious as to why you multiply your outs by 2 and 4? I thought the chance of hitting your outs would be, after the flop, 1-((47-outs/47)*(46-outs/46)). If you could help me understand where the 4 and 2 come from I'd greatly appreciate it thanks!
Sean Lind
2009-10-22

Caluolin,

If you want your odds for one card to come, such as getting odds from the turn to hit the river, you multiply outs by 2.

That's just how the math works.
caluolin
2009-10-21

Why on the turn I multiply my outs by 2 to get the odds for 1 card to come?
Sean Lind
2009-09-01

Lar,

You multiply your outs by 2 to get the odds for 1 card to come. So on the turn, you use 2.

Also, on the flop, you use 2 if you expect to have to pay another bet to see the river. Multiplying by 4 is for hitting your draw on either the turn or river.
Lar
2009-09-01

I thought your outs were to be multiplied by 2. Thats what I'v eread in most places. Obviously these numbers (2&4) create dramatically different pictures of where you stand!
Morten Hard
2009-08-18

Well I can't help it..
They're all just so tasty! <:D
Sean Lind
2009-08-18

Thanks again Morten. You're really chewing through all the odds articles it seems.
Morten Hard
2009-08-18

Just wanted to pinpoint a small mistake in the article. Where it says.: (64 times you don't make your hand; 34 times you do). It should have been 36. Not 34. Got a little confused at first. No wonder. ;) lol
Sean Lind
2009-08-17

Hey Arne, you can try these articles:

<a href="http://www.pokerlistings.com/strategy/poker-math/how-to-calculate-pot-odds-and-equity-equity">How to calculate Equity</a>

<a href="http://www.pokerlistings.com/strategy/poker-math/how-to-calculate-pot-odds-and-equity-pot-odds">Pot Odds</a>
ArneMorten
2009-08-17

Um, sorry I am late about this but i just discovered this site.

Can anyone please post how you calcualte all the above odds? (some random odds and ends to keep handy)

it would help me a ton about calculating other types of odds in the furutre.
John Derek Miller
2009-05-30

Just to help a little 56% is misleading, its just the amount of times the hand will flush for every 100 it won't.

Out of 156 times this is played out 56 times you will be successful but does not mean you will necessarily win the hand!

It does not mean you will hit 56% of the time because it already states the chance is 36% and I personally think that's all the info you need.
Sean Lind
2009-05-29

I think some of the confusion here comes from people having a hard time understanding ratios.

let's look at 3-1

Most people would think that 3 is 3 times greater than 1, so it's 300%

that's a mistake.

3-1 means 3parts to 1 part. That means there are a total of 4 parts. the three is 3 out of 4, or 75%

Hope this helps a bit.
Sean Lind
2009-05-29

b,

For what we're doing, the number of players at the table is irrelevant.

The reason for this, is we're only calculating the chances of us hitting our hand. Since we don't know if our 9 outs are in the stub, another player's hand, or in the muck we have to assume they're all live, and make our calculations on that assumption.

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