Pot Odds & Probability - Texas Holdem Strategy Lesson - Poker. I cover pot odds and probability for poker. Specifically, No-Limit Texas Hold'em pot odds and basic poker math.
Learning how to calculate the odds of winning a poker hand is essential for every player. In this article we'll provide you with some techniques that you can use to calculate the odds of winning a poker hand on the fly, we'll equip you with a tool that can do that for you and provide you with some useful information that you can memorize.
Poker Odds and Outs Calculations
Let's start with the basics. With the exception of the very strong holdings like some flushes, quads etc. almost every poker hand can improve. Outs are the cards that will improve your hand if they show up at a later street. For example, if you're holding AQ on a Q34 board you can still improve to two pair or trips if you hit on of the three Aces remaining in the deck or one of the two remaining Queens.
- Gutshot Straight Draw (examples: JT on Q93, 57 on 69A etc.) - 4 outs
- Open Ended Straight Draw (examples: 98 on T72, KQ on JT5) - 8 outs
- Flush Draw (examples: AhQh on 2c7h9h, 4d6d on JdKd8s) - 9 outs
Pot Odds
Pot Odds - the size of the pot in relation to the bet that you have to call to continue playing the hand. Pot Odds are usually represented in the form of a ratio (2:1, 3.2:1, 4:1 etc.). Pot odds are essentially the risk you have to take (call) to gain the reward (size of the pot).
Let's say that the size of the pot on the flop equals 2$. Our opponent is betting 1$. To continue playing we have to call 1$ and if we do we can win 2$ + 1$ = 3$. We're getting 3 to 1 pot odds. Now let's make it a bit more complex, pot size is 3,55$, opponent bets 2,33$. We have to call 2,33$ to win 3,55$ + 2,33$ (5,88$). Our pot odds are 5,88$ / 2,33$ = roughly 2.5 : 1.
Let's say our opponent is betting 2$ into 6$ pot so our pot odds equal 4:1. To convert the ratio into % add both sides of the ratio (4 + 1) and use that number as a divisor for the right part of the ratio (1 / 5 = 20%).
Pot Odds Poker
In the example above you need to win 20% of the time to break even when your opponent is giving your 4:1 pot odds. How often do you need to win to make the call in other popular situations? Here are some examples for you to memorize:
- 1:1 = 50%
- 2:1 = 33%
- 3:1 = 25%
- 4:1 = 20%
Rule of 2 and 4
Now that you know what pot odds and odds are you can learn the quick way of calculating the percentage chance of your hand improving. It's called the rule of 2 and 4 and it's very simple:
With one more card to come (on the flop waiting for the turn or on the turn waiting for the river) multiply your outs by 2 to calculate the % chance of your hand improving. With two more cards to come (opponent all-in on the flop or any other situation when you have to call just one bet to see both turn and river) multiply your outs by 4 to calculate the % chance of your hand improving.
Example: You're holding T8 on a J24 board, you have 9 outs to hit your flush. Villain goes all in on the flop. Your % chance of improving to a flush equals 4 * 9 = 36%. Let's consider the same situation but this time flop went check/check, the turn is an Ace of clubs and your opponent is betting. Your % chance of improving in that situation would be 2 * 9 = 18%.
Hand vs. Hand All-in Pre-flop
Example | Odds | %Odds/Equity | |
Pocket Pair vs. Smaller Pocket Pair | AA vs. TT | 4 : 1 | 80% |
Pocket Pair vs. Two High Cards | 88 vs. AQ | 1.2 : 1 | 55% |
Pocket Pair vs. Two Low Cards | QQ vs. 67 | 4.9 : 1 | 83% |
Pocket Pair vs. High Card and Low Card | JJ vs. A9 | 2.3 : 1 | 70% |
Two High Cards vs. Two Low Cards | AJ vs. 78 | 1.9 : 1 | 65% |
High Card and Low Card vs. Unpaired Hand | AT vs. KQ | 1.2 : 1 | 55% |
Odds of Improving Post-flop
Example | Outs | Flop%/Odds | Turn%/Odds | |
Gutshot Straight Draw | JT on Q83 | 4 | 16.5%/5.1 : 1 | 8.7%/10.5 : 1 |
Two High Cards | AK on 962 | 6 | 24%/3.1 : 1 | 13%/6.7 : 1 |
Open-Ended Straight Draw | 89 on A76 | 8 | 31.5%/2.2 : 1 | 17.4%/4.7 : 1 |
Flush Draw | AhQh on Jh5h8c | 9 | 35%/1.9 : 1 | 19.6%/4.1 : 1 |
Flush Draw + High Card | As2s on 8sQs4d | 12 | 45%/1.2 : 1 | 26.1%/2.8 : 1 |
Open-Ended Straight Flush Draw | Td9d on Jd8dKh | 15 | 54.1%/0.85 : 1 | 32.6%/2.1 : 1 |
Poker Odds Calculator
So far you've learned about outs, odds, calculating the chance of improving your hand on the fly, and figuring out if it's profitable to make a call based on the pot size and bet size of your opponent. That's enough to get you started, but it probably doesn't answer every question you might have.
Maybe you want to figure out what's the equity of your set vs. two opponents holding a flush draw and straight draw? Maybe you want to know if your hand has any chance of winning in a 5-way family pot. Fortunately, we got you covered! You can answer those and many other questions using the Odds Calculator provided below:
Here's a quick guide on how to use the odds calculator:
- In the top right, you can choose your preferred game (you can even calculate the equity of winning a hand in games like Omaha Hi/Lo or Razz).
- Choose the number of players in the pot.
- Click on player's hole cards and assign them using the list provided at the bottom of the calculator.
- You can add cards to the board in the same way.
- Click 'Get Odds' et voila!
Now you can calculate the odds of winning any poker hand. With such a powerful tool at your disposal, you'll improve as a poker player in no-time!
Other Top Recommended Content
If you enjoyed reading this article, check out our other top recommended articles on poker mathematics!
- Poker Maths - Combinations
- Odds & Outs
- Odds & Outs
- Bitesize Poker Concept - Implied Odds
Pot odds, equity and expected value are important interrelated concepts in poker. As a beginner it is important that you understand the basics if you want to get ahead of your opponents.
The math side of poker is often ignored by a lot of new players but by simply spending a bit of time learning these simple concepts you will be able to improve your game drastically.
So we will first go through each of them individually and then a full example to tie it all together in the next few articles.
Table Of Contents
Pot Odds: The Definition
The odds which are being offered to you when your opponent bets are called pots odds. Essentially it is how much you will win vs how much you have to risk – your risk to reward ratio.
This is particularly useful when in a situation where you’re facing a bet with a drawing hand (such as a flush draw). Pot odds will tell you whether is it correct for you to call or fold based on what size our opponent bet and how many cards that will improve our hand.
We can also use pot odds to determine whether or not we can call a river bet based on how often we expect our opponent to be bluffing.
Pot Odds: Using Ratios
To take an example of when we are facing a bet on the river when we have A9 of diamonds:
On the river our opponent bets $26 into a $41.5. If we called would be risking $26 and our reward is $41.5 already in the pot plus our opponents bet of $26.
This means that we are getting odds of 67.5: 26 (67.5 = 41.5+26). This is approximately 2.6:1.
Pot Odds: The Percentage Method
We can also convert that into a percentage (percentages are typically more intuitive) the result is 28%.
So if we expect to win 28% of the time or more we can call profitably.
How did we get that number?
Take the amount we have to call ($26) and divide it by the amount we have to call plus how much is in the pot:
Pot odds percentage = 26/(26+67.5) = 27.8%
Here is a summary of the numbers of outs and the pot odds associated for number of outs:
Why Are Pot Odds Useful?
It first lets us determine our risk to reward ratio. We can then use this along with the strength of our and our opponents potential hands in order to make better decisions.
If we have a very weak hand we should not be willing to call very large bets, only smaller bet sizes; in other words we must have very good pot odds in order to call.
This makes sense – if someone was to bet $1 into a $100 pot on the river we will continue with almost all of our range.
The greater the pot odds (the smaller our opponent bets) the more likely we should be to continue with our hand. Conversely, the smaller the pot odds (the larger our opponent bets) the less likely we should be to continue with our hands. The larger our opponent bets the more the requirement for an extremely strong hand.
Implied Pot Odds
Implied odds is simply the additional chips we expect to win when we hit our hand.
For example if we were to hit a flush on the turn or river, the hand won’t just end – we still have an opportunity to win more money from our opponent.
This will reduce the pot odds we need to call profitably. The exception to this is when our opponent has pushed all in – we call we cannot win any more chips.
The reason we call preflop with small unpaired hands is not because we expect to have the best hand all that often; but because we expect to win a large pot when we hit a big hand such as three of a kind.
The reason we call is because with a hand like three of a kind, we have large implied odds and if we hit our hand we expect to win a big pot.
Here is an explainer video of implied odds from GreenBeanVideos:
A Real World Example of Implied odds:
The reason you go to College or University and get a degree is not because of the return you would expect immediately after graduation. It is because of the additional value a degree would bring you in the years after gradation through income, job opportunities etc. The same applied to poker.
Unfortunately implied odds cannot be directly calculated like pot odds – we have to guesstimate the amount our opponent will be willing to pay us off after we make our hand.
If we think our opponent has a very strong hand, and we stand to make a better one, we will have large implied odds.
If our opponent has a weak hand, we will have little implied odds.
Additionally, if we believe our opponent is a very bad player we will usually have large implied odds as he will be more likely to make mistakes and pay us with hands that he shouldn’t have.
Finally, if he is a good player we will have significantly less implied odds.
Pot Odds Poker Probability
Here is a quick recap on everything we covered on pot odds:
Poker Pot Odds Formula
Pot Odds Calculator
You do not need a fancy piece of software to work out your pot odds. As we have seen, it is simply the ratio of the bet you have to call to the size of the pot (including your opponents bet). You can also use a calculator to calculate the the percentage odds (or roughly do it in your head, you don’t need to be extremely accurate)
However, on of the best pieces of software you can use in conjunction with calculating pot odds from cardschat.com.
This piece of software can be used to work out your pot equity which we have discussed in detail in other lessons.
No Limit Poker Pot Odds
Conclusions
You should now be able to work out pot odds and when coupled with our other lessons, you should have a basic grasp on the math of poker.
Follow up this lesson first with Pot Equity and Expected Value (EV)