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.
Pot Equity – Simple Poker Math Pot Equity is defined as our percentage chance of winning the pot when in a hand. We can define our equity from preflop all the way until the river and once we know what our opponents has in his hand (oftentimes we have to estimate what he may have). Pot equity is your percentage chance of winning the pot at any given point in a hand. That percentage is the amount of equity you have in the pot or how much of the pot 'belongs to you'. Here's a Texas Hold'em example. You hold AsAh and you have a single opponent with what could be any hand.
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%).
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:
Pot Odds Poker
- 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
One of the first and most important examples of 'poker math' that new no-limit hold'em players need to learn is how to calculate 'pot odds.' In fact, when people talk about the 'math of poker,' a lot of the time they are mostly referring to pot odds and how an understanding of them can help you decide whether to bet, raise, call, or fold.
Poker Pot Odds Chart
Put most simply, pot odds represents the ratio between what you stand to gain in a hand of poker and what you have to spend in order to get it — that is, the ratio between your reward and your risk when making any given decision during a poker hand.
Calculating Pot Odds
For example, if there is $80 in the pot and your opponent bets $20, that makes a total of $100 in the middle. That $100 is the reward you can get if you're willing to risk $20 to call the bet. Pot odds are expressed as a ratio (reward-to-risk). In this case you're having to risk $20 to win $100, so your pot odds are 100-to-20, or 5-to-1.
That's the scenario poker players most often describe when talking about pot odds — that is, when facing a bet and deciding whether or not to call or fold. You add the amount of the bet to what is already in the pot to calculate the reward, the bet you need to call represents the risk, and the pot odds 'being given' to call is that reward-to-risk ratio.
Of course, you can also talk about pot odds after a player raises. Say you decide not just to call that $20 bet described above, but to raise to $80. That would mean your opponent has to call $60 to have a chance at winning what is now $180 in the middle — 180-to-60 or 3-to-1 pot odds.
That might seem simple enough — a little bit of addition and an easy division problem, and you can calculate pot odds.
But why bother? There are lots of reasons.
One big reason why you want to stay generally aware of what your pot odds are — which means keeping track of how big the pot is at all times and being able to compare the pot size to each bet — is that doing so helps you estimate whether or not the pot odds being offered to you are favorable or unfavorable given the situation.
Let's look at three common circumstances in no-limit hold'em in which pot odds can be helpful when making decisions.
Using Pot Odds When Playing a Drawing Hand
Say you are on a flush draw and have with the board showing . There is $120 in the pot, and your opponent has bet $60. You could call to see the river card, but are the pot odds favorable enough for you to make the call?
It's easy enough to see that the reward is $180 ($120 in the pot plus the $60 bet), and so with a $60 risk you are getting 180-to-60 or 3-to-1 pot odds. Is that good or bad?
You believe you probably have to make a flush in order to make a better hand than your opponent's, so that means you have nine outs — the nine remaining clubs — to make your hand. You can see six cards (the two in your hand plus the four on the board), leaving 46 unknown cards, so you can estimate your chance of seeing a club fall on the river to be 9 out of 46, or just over 4-to-1 against.
Compare your pot odds (3-to-1 to call) to the odds you'll make your flush (a little worse than 4-to-1 against). It's clear that calling isn't such a good choice — that the pot odds aren't favorable for calling — because over the long term calling is not a profitable play.
Let's say you were to make this call 100 times. About 20 times you'd make your flush on the river (actually a little less, but we'll round it up). You'd be risking $60 x 100 or $6,000. But your reward would only be $180 x 20 or $3,600. After making this call 100 times and winning only 20 hands, you'd have lost $2,400! (Note: we aren't considering what extra money might be won or lost after the river card, but just the profitability of this particular turn call.)
Pot odds are favorable when they are greater than the odds against making your hand. If the pot odds were 5-to-1 here, it would be a good call with it being just over 4-to-1 against making the flush. But 3-to-1 pot odds are unfavorable when drawing one card to make a flush.
Using Pot Odds to Decide Whether to Call a Preflop Raise
Pot odds can also be compared not just to a specific probability (like drawing to a flush), but also to a more general estimate of your chances in a hand.
Say for example you're playing $1/$2 no-limit hold'em and get dealt in the big blind. A player raises to $7 from the button and it folds to you.
First off... what are your pot odds here? There is $10 in the middle (the $1 small blind + the $2 big blind + the $7 raise), and you have to call $5 to stay in the hand. That's 2-to-1 pot odds.
Now, think about the prospect of playing out of position. It's a hand without a lot of potential that is almost certainly worse than whatever the player on the button who raised has. Unless you flop a couple of diamonds or perhaps trips or two pair, you're not likely to feel good about going very far with this hand. Are these 2-to-1 odds favorable?
No, they aren't. You could quantify this perhaps, noting how you with two suited cards you flop a flush draw about 11% of the time, you flop two pair about 2% of the time, and you flop trips about 1.3% of the time — that adds up to around 14% good flops, meaning it's worse than 6-to-1 against your seeing a good flop. That's just an estimate, really, but is obviously way worse than the 2-to-1 pot odds, so folding is in order.
What if a player raises to $7 from early position and five other players including the small blind call before the action reaches you in the big blind with your ? Now there's $44 in the middle and you have to pay $5 to see the flop. Those are almost 8-to-1 pot odds, which are in fact greater than the odds against your flopping something good — you might consider calling.
Using Pot Odds to Decide Whether to Call a Suspected Bluff
Pot odds can also be relevant when deciding whether or not to call what you think might be an opponent's bluff.
You've reached the river with your and the board shows . Your opponent raised before the flop and you called, and you called his bets on both the flop and turn. Now there's $100 in the middle and he's betting $50, giving you 3-to-1 pot odds to call.
You suspect strongly he could be bluffing, but you think it's possible he might have something like aces, kings, jacks, ace-queen, or king-queen and have you beat. While it's not feasible to calculate exactly the likelihood he's bluffing, you might be able to make a rough estimate — say, that he's probably bluffing at least a third of the time here.
That would make it 2-to-1 against your tens being best, making 3-to-1 pot odds favorable for you — a profitable call to make.
Conclusion
There are many other applications of pot odds in no-limit hold'em, but you can't take advantage of them until you start to become comfortable figuring out pot odds as a hand is playing out.
This is often easier to do when playing online poker, where the betting amounts and pot sizes are shown as numbers. But even when playing live, you can with practice become increasingly at ease keeping track of what's in the pot and calculating pot odds until it becomes second nature to you.
And once you do, you can then use pot odds to help direct your decision-making in a variety of contexts.
Also in this series...
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