Poker odds for texas holdem
Probabilities represent a mathematical model of events at the poker table "in a vacuum" while the odds and their computation is a very specific indicator that can be calculated in every individual hand.
In order to calculate your odds faster, you can use special poker calculators: Equilab or PokerStove. Also, with our Online poker odds calculator, you can quickly and easily calculate your chances of winning and the edge over other players at the table.
We will tell in detail about the mathematical principles of calculating poker odds. Understanding poker odds is important because it gives you a vision of how strong or how weak your hand is in each particular situation, which helps you to collect more value with strong combinations and lose less with weaker hands.
All poker players can be divided into two categories depending on their knowledge of poker math and odds. The first category is the players who rely only on luck and neglect the mathematical element of the game. The second category is the players who know basic poker math and earn money exploiting the players from the first category.
For clarity, let's consider an example. Suppose you have two hearts 8♥ 7♥ and the flop is 5♥ J♥ 2♣, your chances to collect a flush are 2 to 1. This means that one time out of three you will collect a flush with this hand and will be able to win the whole pot.
Outs in poker
To calculate your pot odds, you should first count how many outs your hand has.
Outs in poker are remaining cards in the deck that can improve your hand. Most often, it comes to outs when a player has a drawing hand, for example, a straight draw or a flush draw. In this case, you need to count the number of cards that can improve your draw to a made hand.
The ability to count outs helps to determine the probability of improving a hand or making a winning combination in a particular hand.
Purposes of counting outs are as follows:
- Determine the profitability of action from a mathematical standpoint.
- Understand the feasibility of investing in a pot. Your task is to refuse bets if the probability of making a winning combination is low and to invest in the pot if the possibility of hitting the right hand is high.
- Identify the nuts. By knowing that you are ahead, you will be able to act as aggressively as possible and make large value bets.
- Minimize unprofitable decision making. If profitable ones prevail, you will make profits over the long run.
How to count outs correctly
There are 52 cards in the deck, that is, 13 cards of each suit. Knowing the total number of cards, a player can calculate how many of them are suitable for making a particular combination.
Example. Suppose that your hand is A♣ K♣ and two clubs are already on the board. This means that 9 clubs are still left in the deck. Therefore, you have 9 outs that will give you a flush.
Here are some common outs to improve your hand postflop:
|Your holding||Hope to make||Outs|
|Pair||Three of a Kind||2|
|Two pair||Full House||4|
|Gutshot Straight Draw||Straight||4|
|Open-Ended Straight Draw||Straight||8|
|Four Flush (there are 4 cards of the same suit)||Flush||9|
|Straight & Flush Draw||Straight/ Flush +||15|
With the picture below, you can find more types of drawing hands as well as particular outs to complete your draw:
Double counting: how to avoid?
It often happens that a hand can improve to 2-3 combinations at once. Let’s consider a situation when a poker player was dealt two hole cards with which they can make a few combinations.
Example. Assuming Hero has A♠K♠, and there are two more spades on the board – J♠-9♠-Q♣. Hero needs any spade to come to make a flush, while any Ten will strengthen their hand to a straight.
There are 4 Tens and 9 spades in the deck, but the Ten of spades is counted twice here. It turns out that the hand has 12 variants of the turn that can improve it to a better combination: 9 (spades) + 4 (Tens) – 1 (T♠) = 12.
In the example above, T♠ is good for both a straight and a flush. Therefore, you should be very cautious when counting your outs, otherwise, the probability will be inaccurate.
The thing to remember: don’t count outs twice!
Additional information on outs
"But, what if someone has already folded the card of clubs or is still holding it in his hand, doesn't this reduce the number of outs?" – some beginners may ask.
If you are 100 % confident that someone has a card of the suit that you need, you can recount the number of your outs based on this information. But, in most situations, you don't know your opponents' cards, so you can only calculate your outs based on the available information: cards on the board and your pocket cards. It can be said that you conduct your calculations as if you are the only player at the table.
Knowledge of basic mathematics gives an advantage over the weakest opponents who do not take into account the situation at the table but only play collecting aces, kings, queens, and jacks.
The odds of improving a hand in different situations
In all given examples we use the situations on the turn, excluding the flop. In our examples, you are on the turn before the river and you must calculate your odds of improving:
- Straight draw – 4.8 to 1
For example, you have 8 ♦ 7 ♣ and the board is A ♠ 9 ♣ 6 ♦ 3 ♥
In this situation, you have 8 outs: four outs for 5 and four outs for 10. It is necessary to take into account that in this situation the outs are counted without a possible flush draw on the board and if your draw is completed, you will have the best hand on the showdown.
Important! Beware of discounted outs.
In our previous article, we've already told you about the concept of discounted outs which strengthen not only yours but also your opponent's hand.
For example, you have 9 ♣ 8 ♥ and A ♦ 7 ♣ 6 ♠ K ♠ is on the board.
In this case, 10s may not be your outs, because someone might have a QJ and 10 will give that hand a higher straight. You should also be aware of the runner-runner flush of spades.
- Flush draw – 4.1 to 1
You have in your hand A ♥ 10 ♥ and K ♥ 3 ♥ 9 ♦ 5 ♣ is on the board.
In this hand, you have 9 outs for the nut flush. If you don't have an Ace in this hand, just another card of hearts, then you should play much more carefully because you may lose to the higher flush.
- Gutshot – 10.5 to 1
You have 9 ♣ 8 ♥ and the board is A ♦ 5 ♣ 6 ♠ K ♠
Any of the four 7s in the deck will give you the nut straight. If the board looked like Ax 9x 6x 5x and you had 7x 4x as your pocket cards, then 8 could also give you a straight but not the nut one because one of your opponents may have 10x 7x.
- Improving to two pairs or trips – 8.2 to 1
You have QJ, and K ♣ Q ♠ 6 ♦ 2 ♥ is on the board
In this situation, you have 5 outs: two Queens and three Jacks. These are your odds if you know that your opponents don't have KQ or KJ as their pocket cards. This is a dangerous situation and you must have the pot odds much better than 8.2 to 1 in order to play profitably in such spots.
- Two overcards – 6.7 to 1
This is a really dangerous situation. If you have KQ, the board is 8 4 3 J, and you know that the opponent has nothing better than the medium pair, then you have 6 outs (any Q or K will give you a top pair). Your odds are 6.7 to 1 but if you are not confident about your opponents' ranges, you should play as carefully as possible.
- Set – 22 to 1
If you have a medium or weak pocket pair and you did not hit the set on the flop or turn, your odds of getting into the set on the river equal 22 to 1. You should try to reach the showdown as cheaply as possible.
Pot odds are the ratio between the size of the existing pot and the amount of money you need to add in order to continue the game.
Pot odds are very important mathematical basis for spots that involve calling. Without them, players wouldn’t be able to understand which calls can bring them profit and which are not profitable.
Important! Be advised, the size of the total pot covers bets (or just one bet) placed in the current round of betting.
How to calculate pot odds
There are two methods that can be employed to help you calculate the pot odds in Texas Hold'em:
- Ratio method;
- Percentage method.
It’s worth noting that both of them give the same results, so it’s just up to you which method to choose in order to calculate your pot odds.
Ratio method. For example, the pot is $5 and your opponent bets $1. The action moves to you and now you have to call just $1 in order to potentially win $6 (that is, $5 in the pot and your opponent’s $1). This translates into pot odds of 6 to 1 ($6:$1).
So to put it another way, you need to pay 1/6th of the pot in order to have a chance to win it.
Percentage method. A player will probably want to convert their pot odds into a percentage to know exactly how much equity their hand needs to profitably call the bet (or raise). For this, the player should complete a few steps:
- Calculate the final size of the pot as if the player was to make a call. In the example above, the total pot is $6 and it's $1 to call, so the final pot would be $7 ($6 total pot + your $1 call) if you decide to call.
- Divide the size of their call by the size of the final pot. In this example, the player should divide $1 (size of the call) by $7 (size of the final pot), which comes out to 0.14.
- Multiply the result by 100 to get a percentage. Now, the player has to multiply 0.14 by 100 to know a percentage. In this case, that’s 0.14 * 100 = 14%.
This means that, when the player calls, they need to win more than 14% of the time in order to profit.
Please note that the ratio method is used to calculate pot odds more often. Besides, most poker books and forums provide pot odds as a ratio. However, a lot of players, especially beginners, find the percentage method much easier.
How to make use of pot odds to make a decision about a specific hand? It’s very simple:
- First, you should calculate your pot odds as shown in the examples above.
- Next, you should estimate your odds of winning the hand at the showdown (using the x4 and x2 rule).
- Then, you have to compare the ratios.
If the pot odd ratio is higher than our odds of winning the pot, then we should call. If it’s lower than our odds of winning the pot, we should fold.
Pot odds for different bet sizes
|Bet sizing (% of the pot)||Required equity to call|
We suggest that you familiarize yourself with the given table so that you can estimate pot odds for different bet sizes later in real play. This will allow you to make more accurate decisions.
What are Implied Odds?
Implied odds – is an estimate of how much money you can win with a drawing hand if your draw is completed on one of the streets.
Implied odds will also factor in your decision as they suggest that even if you are not getting the right odds, you can bet on the river and your opponent will call probably.
Let's consider the implied odds through an example of the following hand:
- Your hole cards: K ♣ 9 ♠
- Board: Q ♣ 7 ♦ 8 ♣ A ♣
Let's say there is the small blind versus big blind spot. Before the flop, your opponent on the small blind limped in and you checked. On the flop, both you and your opponent checked and on the turn, the opponent made a bet of 1 BB. Your odds of improving are 9 outs for a flush or 4 to 1. There are 3 big blinds in the pot, and you need to post one more blind to see the river, your pot odds equal 3 to 1. Should you call? According to the pot odds, it's not profitable to call in this situation.
If your opponent has an Ace and you hit your flush on the river, would they bet or call your bet on the river? It is unlikely to happen. You can hardly win more money than is already in the pot even if you manage to complete the flush. Except your opponent has J♣.
Considering this hand, it's more profitable for you to raise your opponent on the turn: in this situation, they will call with all their Ax and Qx hands but can muck a lot of 7x and 8x hands. In case of calling, you will have to bet on any river (even if your flush draw is not completed), except for the paired board: Q, 7, 8, A won't suit you for bluffing.
Tasks for calculating pot odds and outs
We offer you a few hands so that you can practice calculating outs and pot odds.
Hero: K ♣ 6 ♣
Board: 8 ♣ 7 ♣ 4 ♦
Opponent's bet: $1
Hero: 10 ♦ 9 ♠
Board: J ♦ 8 ♦ 5 ♦
Opponent's bet: $8
Hero: A ♠ K ♣
Board: Q ♣ 10 ♦ 6 ♠
Opponent's bet: $3
Hero: K ♠ Q ♠
Board: 10 ♦ 8 ♣ 7 ♠
Opponent's bet: $2
Hero: J ♦ 9 ♦
Board: 5 ♦ 6 ♦ 7 ♠
Opponent's bet: $9
Knowledge of the poker math and odds is a necessary factor of a profitable game, both in tournaments and cash games. Understanding mathematical concepts will quickly turn you from a beginner into an advanced regular player.
Pot odds may seem like a daunting topic at first glance, but, it is actually one of the most important parts of poker mathematics. If you make decisions with your drawing hands based on pot odds, then you will profit over the long run.
If you think your rival is drawing to a straight and your hand is the best, then you should bet such an amount that will give them poor pot odds to call. Keep in mind, even if your rival completes their draw and you lose that specific hand, you will still make money in the long run, and your opponent will lose it.