How Poker Odds Can Help You At The Poker Table
While a lot of people like to think of poker as a people game played with cards, the truth is that the game has become a lot more math-focused in the past few years. To succeed, grasping poker odds and other mathematical skills is necessary.
One of the most important aspects of poker math is poker odds. Knowing the odds of making certain hands or being dealt certain hands helps you make better decisions at the table. It gives you a mathematical basis for your game, so you’re not out there guessing what to do each time. We’re going to look at how poker odds work, how to use them, and the common poker odds you should remember.
How Poker Odds Work
When calculating poker odds, we use what we know about the deck to calculate the likelihood of certain events happening. For example, there are 52 cards in a deck, so the chance that the first card that you’re dealt is the ace of diamonds is 1/52, or 1.92%. The essence of using poker odds is to extrapolate information from the available data. We commonly split poker odds into two main categories, preflop and postflop.
When discussing preflop odds, we look at the likelihood of being dealt a certain hand. If we ignore the suits, there are 169 different hand combinations, but the odds of you being dealt any specific hand isn’t 1/169. We can split preflop hands into three categories, paired hands, suited unpaired hands, and unsuited unpaired hands.
There are six combinations of each paired hand in the deck. If we take pocket aces as an example, here are all the possible combinations you can be dealt:
There are four combinations of suited unpaired hands. One for each suit in the deck, and there are 12 different combinations of unsuited unpaired hands:
A♣K♦️, A♥K♣, A♣K♥, A♥K♠, A♣K♠, A♥K♦️, A♦️K♥, A♠K♣, A♦️K♠, A♠K♦️, A♦️K♣, A♠K♥.
This means it’s rarer to be dealt AKs than to be dealt aces!
Knowing these odds should impact how you view your opponent’s range. You’ll know that they’re 3x more likely to have an offsuit hand than a suited hand and 2.5x more likely to have an unpaired hand than a paired hand preflop.
When we look at postflop odds, we look at the odds of improving your hand or your opponent’s hand improving against you. When we get postflop, we have a little more information, as we know our two hole cards and the board cards. This reduces the number of unknown cards from 52 to 47 on the flop and 46 on the turn. This means that any card we haven’t seen has a 1/47 (2.12%) or 1/46 (2.17%) chance of appearing on the turn or river.
Knowing that each card has a roughly 2% chance of appearing next is all well and good, but we need to know how that relates to our hand. This is where counting our outs comes in.
How to Count Your Outs
In poker, an “out” is considered to be any card that improves the strength of your hand. People commonly talk about outs when they have draws, but they also apply to made hands. To count your outs, all you have to do is count the number of specific cards that improve your hand.
For example, if you have a heart flush draw on the flop, four of the thirteen hearts in the deck have been accounted for. This means that there are nine left in the deck that you can hit to improve to a flush. However, when counting your outs, it’s important that you consider all possibilities. If you have an ace-high flush draw, there’s a chance that hitting an ace will also give you the best hand. This gives you an additional three outs to make the best hand, meaning that there are 12 cards in the deck that can give you the best hand, rather than 9.
Counting Outs on One Street
While outs stay constant understand chances of completing your hand across single and multiple streets. When you face a flop bet, it’s better to calculate your odds to improve across one street rather than two. This is because you may face a bet on the turn that you can’t call. This means you don’t get to realize all of your equity. It’s also useful to know for when you face a turn bet, as there is only one more card to come.
We calculated earlier that each card has a roughly 2% chance of being dealt on the turn or river, so the easiest way to calculate your odds across one street is to count your odds and multiply them by two. For example, you have an open-ended straight draw on the flop. This means you have eight cards that can give you the best hand. If you want to calculate the chance of hitting one of those eight cards on the turn, multiply 8 by 2, giving you a 16% chance of making your hand on the next card.
Counting Outs from Flop to River
While calculating your odds for one street is important, it’s also worth knowing how to calculate your odds from the flop to the river. If your opponent is all in on the flop, you don’t have to worry about a turn bet. All you need to do is calculate your chance of improving by the river. It’s also useful when you think your opponent is unlikely to bet the turn. That means you’re more likely going to get to the river without facing another bet.
If you want to calculate your odds from the flop to the river, there’s an extra step to the equation. Let’s say you’ve got a 6-high flush draw on the flop, so you’ve calculated that you’ve got 9 outs to make your flush. The first thing you do is work out the odds of hitting your hand on the turn, so you multiply 9 by 2 to get 18. Now, because you’re calculating to the river, there’s another card you get to see, so you also multiply our first total by 2. In this example, you multiply 18 by 2 to get 36, which means you have a 36% chance of hitting your flush by the river.
The 2/4 Rule
When you’re playing poker, the easiest way to remember how to calculate your odds of winning is the 2/4 rule. If you’re calculating your chances on one street, multiply your outs by 2; if you’re calculating from the flop to the river, multiply by 4. While it won’t give you the exact percentages, it’s a close enough approximation to work with at the tables.
Pot odds – Working Out When to Call
So now that we can work out our chances of making the best hand by the river, we can introduce the second aspect of poker odds you should learn – pot odds. Your pot odds are the odds you’re getting on a call. Or to put it another way, how often you need to win the hand for your call to be breakeven. It might sound a little complicated, but the math is really easy. Here’s the equation:
Pot odds = (call / (call +pot size)) x 100
That might not mean a lot to any new players out there, so let’s break it down with a couple of examples.
Pot Odds Example #1
In our first example, you’re playing a $1/$2 cash game and facing a $100 bet into a $200 pot on the river. The first thing you need to do is calculate what the pot size would be if you were to call. In this case, it would be $300 + $100 (the pot size includes your opponent’s bet), making a total pot of $400.
Next, divide the amount of your call by the total pot size. In this case, it would be $100 / $400, which gives you 0.25. Finally, multiply this number by 100 to get your percentage, which in this case will be 25%. Let’s see how our equation looks when we’ve put some numbers in it:
- Pot odds = ($100 / ($100 + $300)) x 100
- Pot odds = (100 / 400) x 100
- Pot odds = 0.25 x 100 = 25%
In our scenario, you need to win more than 25% of the time to make a profit. Once you’ve worked that out, you need to figure out whether or not your hand has at least 25% equity against your opponent’s range. If it does, you should call; if it doesn’t, you should fold.
Pot Odds Example #2
In our second example, we’re on the flop with 4h3h and a board of 2c5s9d. Our opponent bets $20 into a $30 pot. Do we have the right odds to call? Let’s take a look.
First, we need to figure out our pot odds. We’re calling $20 into a $30 pot, so let’s see how that looks in our equation:
- Pot odds = ($20 / ($20 + $50)) x 100
- Pot odds = ($20 / 70) x 100
- Pot odds = 0.285 x 100 = 28.5%
So we know we need to win at least 28.5% of the time to break even with our call. Now we need to figure out the likelihood of making our hand by the turn. We have 8 outs with our open-ended straight draw, which means that we’ll make our hand on the turn 16% of the time to call. However, if we think our opponent won’t bet the turn very often, we could have a profitable call, as we’re 32% to make our hand by the river.
In spots like these, you need to make a judgment call about what your opponent is likely to do on future streets. Consider things like your opponent’s playing style, their likely hand strength, and their stack size.
What are Implied Odds?
Another thing you can consider is how likely you are to win a big pot if you do make your hand against your opponent. This is the basis of implied odds. Even though you may not have the right odds to call, the possibility of winning a big pot if you make your hand is enough to compensate for a mathematically incorrect call.
While most people think of implied odds as more of an art than a science, there is a formula you can use to figure out how much you would need to win on a later street to make your call profitable. Let’s take a look at it.
Hand equity = call / (pot size + call + $ needed)
We need to solve for “$ needed” (which we’ll call $X), so let’s look at the steps we take to do that.
- Hand equity = call / (total pot + $X)
- Hand equity * total pot + hand equity * $X = call
- and equity * $X = (call – hand equity * total pot)
- (call – hand equity * total pot) / hand equity = $X
That can be a little hard to visualize, so let’s take a look at an example and plug some numbers into that equation.
In a $1/$2 cash game, we’re on the turn with the nut flush draw, facing a $60 bet into an $80 pot. We’re not getting the right pot odds to call as our hand only has 18% equity, so how much would we have to win on the river to make this a good implied odds call?
- 0.18 = $60 / (($140 + $60) + $X)
- 0.18 = $60 / ($200 + $X)
- 0.18 * $200 + 0.18 * $X = $60
- 0.18 * $X = $60 – (0.18 * 200)
- 0.18 * $X = $60 – (36)
- 0.18 * $X = $24
- $24 / 0.18 = $X
- $133.33 = $X
This means we would have to win a further $133.33 on the river to make this a breakeven call. How likely this is will depend on your opponent, but as this is a roughly ⅔ pot bet, it’s not unlikely to happen if they also have a strong hand or will continue to bluff.
As you can see, it’s quite tricky to figure out exactly how much you need to make while you’re in the middle of a hand. Some players will round up their numbers to make the math easier, such as 0.18 to 0.2, or they’ll try and estimate how much they need to make using their experience of similar spots. The key to using implied odds is figuring out whether your opponent will pay you off on the river. Unfortunately, there’s no mathematical formula for this; you’re going to have to use your hand-reading skills to figure out how strong your opponent is.
Common Poker Odds you Should Know
While it’s all well and good working your odds out at the table, it’s much quicker to commit them to memory so you can spend your time analyzing other aspects of the hand. Here are some common poker odds that you should know if you want to become a serious player.
Odds of Preflop Hands
Knowing the odds of preflop hands is useful when constructing your opponent’s range.
- Odds of getting a pocket pair (AA) – 6/1326 – 0.45%
- Odds of getting a suited unpaired hand (AKs) – 4/1326 – 0.3%
- Odds of getting an unsuited unpaired hand (AKo) – 12/1326 – 0.9%
- Odds of getting an unpaired hand (suited or unsuited AK) – 16/1326 – 1.2%
Odds of Draws
You need to know the odds of making a draw to figure out whether you can profitably call to try and make your hand.
Flop-Turn / Turn-River
- Odds of making a set with a pocket pair – 2 outs – 4%
- Odds of making a gutshot straight draw – 4 outs – 8%
- Odds of making two pair – 5 outs – 10%
- Odds of making an open-ended straight draw – 8 outs – 16%
- Odds of making a flush draw – 9 outs – 18%
- Odds of making an open-ended straight flush draw – 15 outs – 30%
- Odds of making a set with a pocket pair – 2 outs – 8%
- Odds of making a gutshot straight draw – 4 outs – 16%
- Odds of making two pair – 5 outs – 20%
- Odds of making an open-ended straight draw – 8 outs – 32%
- Odds of making a flush draw – 9 outs – 36%
- Odds of making an open-ended straight flush draw – 15 outs – 60%
Odds of Flopping Hands
Knowing the likelihood of flopping hands isn’t vital to know, but it’s good to have in your back pocket as an extra bit of knowledge.
- Odds of flopping a pair – 1/2.45 – 29%
- Odds of flopping two pair – 1/50 – 2%
- Odds of flopping three of a kind (unpaired hand) – 1/74 – 1.35%
- Odds of flopping three of a kind (paired hand) – 5/1 – 11.8%
- Odds of flopping a straight (connectors e.g. 87) – 76/1 – 1.3%
- Odds of flopping a flush – 118/1 – 0.8%
- Odds of flopping a full house (paired hand) – 1/1110 – 0.09%
- Odds of flopping a full house (unpaired hand) – 1/101 – 0.98%
- Odds of flopping quads (paired hand) – 1/407 – 0.245%
- Odds of flopping quads (unpaired hand) – 1/9800 – 0.01%
- Odds of flopping a straight flush (suited connectors e.g., 7s6s) – 1/5000 – 0.02%
- Odds of flopping a royal flush – 1/19,600 – 0.005%
Odds of Making Strong Hands
Knowing how likely you are to make a royal flush isn’t really necessary in-game; this is one for the stats geeks. Bear in mind that these percentages are cumulative and don’t take into account your starting hand as the above percentages do. They also presume that each hand gets to the river.
- Odds of making a royal flush – 1/30,939 – 0.0032%
- Odds of making a straight flush – 1/3589 – 0.0279%
- Odds of making quads – 594/1 – 0.199%
- Odds of making a full house – 5/1 2.6%
Poker Odds Summary
If you’re looking to become a better poker player, it’s essential that you have a solid understanding of how poker odds work. Knowing poker odds helps you in a number of ways at the table. It can help you get a graph on exactly how your opponent’s range is constructed. It also can help you figure out your chances of improving to the best hand. Additionally, it gives you a foundational basis to decide whether to call when facing a bet. Once you’ve mastered poker odds, why not check out one of our other strategy articles to help improve your game even further?
The odds of flopping a set (three of a kind whilst holding a pocket pair) are 1/7.5, or roughly 12% of the time.
Over one street, the chances of hitting a flush draw are 18%, and from the flop to the river, the chances of hitting a flush draw are 36%
Over one street, the chances of hitting a straight draw are 16%, and from the flop to the river, the chances of hitting a straight draw are 32%
You will be dealt aces 6/1326 times preflop, which equates to 0.45% of the time.
The easiest way to calculate odds at the table is to use the 2/4 rule. This multiplies the number of outs you have by 2 if you’re calculating odds over one street and by 4 if you’re calculating odds from the flop to the river.
No, you have the same chance of hitting a flush draw whether you’re playing against one person or ten people. We don’t know what other players are holding, which means there’s an equal chance of every unknown card being the next card dealt.
The best way to figure out when to call is to use poker odds with pot odds. Once you’ve figured out your chance of winning, compare that to the pot odds you’re being given. If your likelihood of winning exceeds your pot odds, you have a profitable call.