# Poker odds for texas holdem

In this article we will talk about the poker chances (odds). Beginners should understand that poker possibilities and odds are not the same. 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.

We will tell in detail about the mathematical principles of calculating the poker odds. Knowledge of 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 using 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 odds 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 pot.

To calculate the odds of your hand, first you should know how many outs your hand has. 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.

"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 once more. 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.

## The odds of improving 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 on imroving:

**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 calculated without a possible flush-draw on the board and if your draw is completed, you will have the best hand on the showdown.

**Beware of discounted outs**

In our previous material we've already told you about the concept of discounted outs which strengthen not only yours, but also the 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.

**Improvement 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.

## Implied odds

**The pot odds** are the ratio between the size of the existing pot and the amount of money you need to put in order to continue the game.

How to calculate pot odds? For example, the bank is 5$ and your opponent makes a bet of 1$. You need to post 1$ more in order to potentially win 6$. Your odds are 6 to 1.

**Potential odds of the pot (Implied odds)** - is an estimate of how much money you can win with a draw-hand if your draw is completed on one of the streets.

Let's consider the implied odds on the example of the hand:

You are in the hand with K ♣ 9 ♠

The board is: Q ♣ 7 ♦ 8 ♣ A ♣

Let's say that the hand occurs in situation small blind versus big blind. Before the flop your opponent on the small blind limped in and you checked. On the flop both you and your opponent have checked and on the turn the opponent made a bet of 1 BB. Your odds on improvement 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 odds of the pot it's not profitable to call in this situation.

If your opponent has an Ace and on the river you will manage to hit your flush, would he 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 catch the flush. Unless your opponent has J ♣.

In this hand it's more profitable for you to raise your opponent on the turn: in this situation he will call with all his Ax and Qx hands but can muck a lot of 7x and 8x hands. In the case of call, you 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 the odds

We offer you a few hands where you need to calculate the outs and the odds of the pot. Write your answers in the theme on the forum.

**Task №1**

Hero: K ♣ 6 ♣

Board: 8 ♣ 7 ♣ 4 ♦

Bank: 3$

Opponent's bet: 1$

**Task №2**

Hero: 10 ♦ 9 ♠

Board: J ♦ 8 ♦ 5 ♦

Bank: 10$

Opponent's bet: 8$

**Task №3**

Hero: A ♠ K ♣

Board: Q ♣ 10 ♦ 6 ♠

Bank: 5$

Opponent's bet: 3$

**Task №4**

Hero: K ♠ Q ♠

Board: 10 ♦ 8 ♣ 7 ♠

Bank: 7$

Opponent's bet: 2$

**Task №5**

Hero: J ♦ 9 ♦

Board: 5 ♦ 6 ♦ 7 ♠

Bank: 10$

Opponent's bet: 9$

Knowledge of the poker math and odds is a necessary factor of a profitable game, both in tournaments and in a cash game. Understanding mathematical concepts will quickly turn you from the beginner into an advanced regular player.