Poker Probability

Poker is a game of skill and also a game of probability. Understanding and calculating the odds of your hand and your opponent’s hands is essential to making informed decisions and maximising your winnings. This is where a poker odds calculator comes in.

To play poker successfully, you cannot rely on random chance. You must instead carefully consider the probability of poker hands. It is crucial to understand the mathematical aspect of the game and how it works while playing poker. In this blog, we will be going explore the significance of pot odds and hand equity in poker and how they can help you make informed decisions while playing.

What is a Poker Odds Calculator?

A poker odds calculator is a tool that helps players calculate the odds of winning a hand in real time. It uses algorithms to calculate the probability of various outcomes based on the cards on the table, the cards in the player’s hand, and the number of players in the game.

It can be helpful for the players to decide their next move in the hand while trying to improve their hand strength.

How to calculate poker odds?

Playing poker requires making difficult decisions at every step of the game. For instance, you may have to decide whether to call or fold, whether you are ahead of your opponent, or whether to chase your draws. To make these choices, you can use poker hands odds to help you identify the most profitable play in the long run.

When playing poker, it is important to understand the various poker hands odds involved in the game. Pot odds, equity, and implied odds are the key factors to consider while making decisions at each step of the game.
Pot odds refer to the ratio of the total size of the pot to the size of the bet faced by the player. These odds are the amount of money that needs to be invested in the pot against the total value of the pot to continue playing the hand.

The formula for calculation of poker hands odds is – the value of bet faced: total value of the pot
And when we talk in terms of percentage, then the formula is the value of the bet to call/ total value of the pot* 100%.

For instance, let us consider the player is playing on a table with blinds 25/50 and the opponent has made a bet of 100 rupees in a pot of 500 rupees so the pot odds in this would be 1:5 or (100/500*100%), which is 20%.

What are outs in poker?

In poker, an “out” refers to any card that can improve a player’s probability of winning a hand. Knowing the number of outs a player has is an important part of calculating poker hands chances of winning.

How to count the outs in poker?

Counting outs in poker is an important skill to have, as it can help you determine the strength of your hand and make better decisions.

Here’s a step-by-step guide on poker hands probability calculator:

Identify your hand: The first step is to look at your cards and determine your current hand. For example, you have a flush draw if you have two hearts in your hand and two more hearts on the board.

Identify the draws: Look at the community cards on the board and identify any potential draws that could improve your hand. Common draws include flush draws, straight draws, and open-ended straight draws.

Count the outs: Once you have identified the potential draws, you need to count the outs – the cards that can improve your hand.

For example, let’s say a player has a flush draw with four cards of the same suit in their hand. There are 13 cards of each suit in the deck, and four of them are already accounted for, leaving nine remaining cards of that suit. Therefore, the player has nine outs to make their flush on the next card.
Or if the player also has one overcard with him along with the flush draw then his outs increase to 12 and if he has two over cards along with a flush draw then his poker hands outs improve further to 15.

Another example would be if a player had a pair of 6s in their hand, and the board showed 7-8-2. If a 6 were to come on the turn or river, the player would make a three of a kind, so there are two remaining 6s in the deck that would give them an out to improve their hand.

In general, the more outs a player has, the better their poker hands chances of winning
. It’s important to remember, however, that outs are not guaranteed to improve a player’s hand, and other players may also have outs to improve their own hands. Nonetheless, Poker Odds Calculator is a fundamental skill in poker that can help players make more informed decisions when deciding whether to call or fold.

When the player has an open ended straight draw then there are eight cards that can help him to improve the hand to a straight
For example, let’s say the player has 9♥️10♣️ and the flop is 7♦️8♣️2♥️ so now either a 6 or a Jack can improve the hand to straight.

When the player has a gutshot straight draw then there are four cards that can help him to improve the hand to a straight
For example let’s say the player has 9♥️10♣️ and the flop is 6♦️8♣️2♥️ so now only a seven can improve the hand to a straight.

When the player has three of a kind hand strength and is looking to improve his hand to a full house then he has 15 outs in total to improve the hand to a full house.

Probability of Poker Hands

Probability of	odds	example
Being dealt a pair	~6%	9♥️9♣️
Being dealt a pair of Aces	.45%	A♦️A♣️
Making three of a kind on the flop	11.75%	3♣️3♥️ Board- A♥️3♦️7♥️
Two pair on flop	2.2%	A♥️Q♣️Board -A♣️Q♦️6♦️
Hitting a flush(till river)	35%	A♥️4♥️Board -7♥️8♥️2♣️10♣️J♥️
Completing open ended straight draw	32%	7♥️8♣️Board -5♥️6♣️10♦️Q♦️4♥️
Making full house from three of a kind on flop	33%	8♥️8♣️Board 3♥️8♣️9♦️K♥️3♣️

What is Poker Equity

The next thing that connects both pot odds and outs is poker equity(your chances of winning the pot against  your opponent’s). 

The commonly used formula for calculating equity is :

• On the flop, multiply the outs x4
• On the turn, multiply the outs x2

This will give the chances at winning the pot in terms of percentage %. 

For instance, if the player has a flush draw, he has 9 outs on the flop. 9×4 = 36% chance at improving the hand. And with an open-ended straight draw (eight outs) you have a 32% chance of making your straight on the flop – that is, with two cards left to come.

Meaning that when the same instance occurs 100 times then out of this 100 times 36 times the player can improve the hand and 64 times he won’t..

But when the number of outs on the flop is (>8),the previous method givea slightly incorrect equity which is why players use this formula for a more accurate number in these cases.

(number of outs * 4) – (number of outs – 8) = Equity

This means the equity of an open-ended straight flush draw (15 outs) would be:

• (15 * 4) – (15 – 8) = 53%

The idea here is that both pot odds and poker outs are interconnected with each other; whatever pot odds you are getting that has to be more than the poker equity in order to make a profitable call .

There are tools available on the internet as well which can give you a precise result for any case, however while playing the game at the tables it is not possible to use the tool every time which is why it becomes important to do these calculation in the head so that better informed decisions can be made by the players while playing the game.

FAQs

1. What are poker odds?

Poker odds are the cards that will help the player to improve their hand strength while playing a hand and there are some tricks discussed in this blog which can help the player to calculate their odds while playing the game

2. What are implied odds in poker?

Implied odds is the relationship between the size of the pot and the size of the pot you are expected to win when you hit your card.

3. Do poker odds depend on the number of players?

Yes, indeed the number of players involved in the hand changes the dynamics of poker odds, which is why it is important to keep the number of players involved in the hand to the minimum