How To Calculate Poker Probabaility Odds: Learn The Mathematics Here

How To Calculate Poker Probabaility Odds: Learn The Mathematics Here

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Contrary to what most people believe, poker is far from just a game of luck. Instead, it is a game of skill wherein the ability to read opponents’ hands and predict situations helps you win the game. Moreover, poker is a game of mathematics as well. Yes, most professional poker players around the world commonly use poker math and probability regularly to make key decisions during a game of poker. Not only is poker math relatively simple, but it also helps the players make refined decisions they would otherwise have to make based on instinct. Probability also helps to understand the flip in poker.

To help you understand how math and probability work work in poker, we have detailed some common poker math and poker probability strategies. While some are used to calculate odds, some are for equity and hands. Read this comprehensive guide about different math strategies you can use online playing! Discover the thrill of real money poker games on our platform, where every move you make could lead to exciting victories and a rewarding gaming experience.

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Poker probability for calculating pot odds

Pot odds, in simple terms, is a poker math strategy normally used for calculating the odds or likelihood of winning when a player has a drawing hand. A drawing hand is a poker hand that is currently incomplete and thus needs other cards to be termed valuable and worthy of winning. This strategy is thus often used to determine whether or not a person should call (to call is to match the previous player’s bet), bet (to bet is to place a certain amount in the pot) or raise (to raise is to increase the size of the existing bet in the current hand of poker). Now, let us understand how to calculate pot odds using a simple example:

You hold - Ace of hearts and 8 of hearts

Flop (community cards) - 2 of hearts, 7 of spades and Jack of hearts

Only two people are left in the game - you and your opponent. There are $80 in the pot, and your opponent bets $20.

Since most of the players in the poker world commonly use ratios to calculate the pot odds in poker, let us concentrate on the ratio format for learning the calculation of pot odds:

Calculating the odds

First things first, we need to work out how likely it is that another heart will be dealt with on the turn. To do this, determine the ratio of the cards in the deck you do not want against the cards you want. To put it, there are 5 cards in the deck that you already know about; this leaves you with 47 cards you do no know about. Now, out of those 47, 9 will likely come in handy to make a flush (a flush is a poker hand consisting of 5 cards of the same suit), while 38 will not. So, to put this in ratio, the poker probability is 38:9 or roughly 4:1.

Compare with pot odds

As mentioned above, the opponent has bet $20 into an $80 pot, making it $100. To win $100 now, you have to call $20. So, your pot odds roughly come down to $100: $20 or 5:1. With the card odds 4:1 and pot odds 5:1, you must call as the pot odds are greater than the card odds.

Poker probability for calculating implied odds

Implied odds poker math strategy helps players determine how much money they will likely win after completing a draw or drawing hand. Even though although implied odds are just another extension of pot odd; there is no mathematical formula or rules in the poker world to calculate the implied odds in a game of poker. However, it is still possible to calculate the amount of money a player needs to win to make the calling profitable. To calculate the same, subtract the pot odds from the odds of hitting a draw and work out the required implied odds.

This will likely give you a new ratio to compare with the amount you must call. This will help you determine how much money you must take from your opponent to make the call profitable.

Poker probability for calculating expected value

An Expected value is a poker math strategy that details the amount of money a player expects to win or lose on average. In other words, in any poker game, a player usually has 5 options - to call, raise, check, bet or fold. Now, these options generally have some expected value attached to them. Therefore, while some of these plays might win you money, there might be some others that will lose you money. Now, out of the actions that will win you money, some might win you more than others on average. As a result, the basic aim behind using expected value poker math is to ensure that you make the play with the greatest expected value only.

Now, if you are aiming to learn the expected value poker probability strategy, then as a pro tip, first familiarise yourself with the two below-mentioned abbreviations:

+EV- This positive expectation play indicates you will likely win more money over the long run.

-EV- This is a negative expectation play that indicates you will likely lose money over the long run.

To use the expected value poker math strategy, all you have to do is multiply the results of the possible outcomes by their probability of happening and then add all the values together.

Let us understand the use of expected value poker math strategy with a short example:

The pot is worth $100, and you are facing a bet of $50. In such a situation, you must strive to have a 40% pot equity (more on this later) vs your opponent’s range. An opponent’s range is the set of hands a player might hold in a particular situation. So, what is the expected value of this call? Well, to begin with, we have 4 basic variables:

Probability of winning - 40%

Probability of losing- 60%

Win Amount - $150 (the pot amount + the bet)

Lose amount - $50 (your investment)

To simplify the calculation, we have expressed the percentage values as decimals. Now, by plugging the values in the formula, we get the following equation:

(0.4*150) -(0.6*50) =EV

(60)-(30) = $30

Therefore, you can expect to make $30 on average every time you make this call as per the expected value poker probability.

Poker probability for poker equity

Pot equity, or poker equity, is one of the most common poker math strategies used by most professional poker players worldwide. This poker probability strategy is generally used to determine whether a player should bet or check during certain situations in poker. Before we explain the basic concept behind poker equity, let us first understand what equity in poker implies.

“Equity” is the amount of money currently in the pot that likely “belongs” to you. This equity, in general, is calculated based on your odds of winning at a particular point in the hand. For instance - there is a 70% chance that you will win with a particular hand, and then you currently have 70% equity in the hand. Generally speaking, there is no mathematical formula for calculating equity in poker. Instead, the equity percentage figures are usually calculated using repeated poker math computer simulations in particular situations. This is done to estimate each hand’s chance of winning during a standard game of poker.

So, using an online equity calculator, you can calculate the equity and thus your chances of winning. However, you must wonder how to incorporate this information into the poker game. To begin with, while playing a poker game, it is generally practically impossible to figure out what your opponent is exactly holding. As you might have guessed, it is impossible to work out the poker equity and use it to your advantage in such a situation. However, suppose you know the concept of equity in poker. In that case, you should be able to find out the approximate equity a player usually holds during different game stages. Then, you can use this information to bet accordingly if you think you have the best hand.

Poker probability for reverse implied odds

As the name suggests, the reverse implied odds are the opposite of implied odds. In other words, the implied odds poker math strategy calculates the amount of money you would likely win after completing a draw. On the other hand, the poker probability strategy for reverse implied odds helps estimate how much a player stands to lose if he can complete a draw, but the opponent still ends up holding a better hand. Suppose you have worked out your implied odds and believe you must call a bet. Then, make it a point to calculate your reverse implied odds to see if you should go ahead with the call to make your draw.

Now, akin to implied odds, there is no standard mathematical formula or equation for calculating the reverse implied odds in poker. In other words, similar to implied odds, in the case of reverse implied odds, there is no standard way of calculating an exact figure that a player can expect to win or lose. As per poker math and poker probability, the reverse implied odds usually increase when there is a greater chance that a player does not have the best hand at the table. Conversely, the reverse implied odds significantly decrease when there is a higher chance that a player will have the best hand once he completes the draw. It is usually recommended that a player make calls if he has a few reverses implied odds, but the pot odds are relatively high. On the other hand, if both the pot odds and reverse implied odds are not in favour, then a player must fold his hand.

Poker probability for poker equity and drawing hands

The concept of poker equity and drawing hands usually emphasizes that if a player holds the best hand (the best poker hand is mostly determined based on the official poker hand rankings in poker) during any one stage of the game, then it is quite likely that his hand stands the highest chance of winning the pot after all the cards have been dealt. However, sometimes it so happens that a player initially does not hold the best cards to make a draw, but his chances of winning the pot are still high. In such a situation, it is usually advisable that a player keep betting for value even if his hand is incomplete, as he already has a high equity in the pot. Now, let us understand the poker equity and drawing hands poker math strategy with an example:

Suppose you currently hold a queen of diamonds and a jack of diamonds. Now in the flop round ( the first betting round in the poker game wherein three community cards are dealt face up), three community cards, namely - 9 of diamonds, 4 of spades and ace of spades are dealt face up. Your opponent, on the other hand, already holds a strong hand of 9 spades and 4 diamonds. Now, even though your opponent is already holding a near-made hand ( a type of poker hand wherein a player has already made a pair even before the community cards are dealt), your current equity in the pot still comes down to 52%. The only hand currently holds better equity in the pot than you are the one with a set. A set is another type of poker hand that is normally made using three of a kind.

A little confused? Well, allow us to explain. According to basic poker math and poker probability, already-made hands can have far less equity than strong drawing hands. Now, in the example described above, since you already hold a strong drawing hand, there is a high possibility that the cards left in the deck can help you make a better hand than your opponent. Therefore, as per poker equity and strong drawing hand poker math strategy, you must bet for value with the current drawing hand and aim to get as much money into the pot as possible, given the current situation.

The above examples might have made you feel like there is much math involved in poker. Yes, there is, but it is all good because it shows you how you do not always have to have a great hand to win the pot. You need to identify the right strategy and play accordingly.

Learning to use poker math and probability is generally considered a rather difficult process in the first go. However, if you keep trying, then you will likely master these strategies in no time.

You can practice it regularly on the GetMega Poker app and play multiple poker games to continue learning and be good at it.

Also Read:


Is poker mathematically solved?

  • Poker is not mathematically solved in the sense that the optimal strategy has been definitively determined for all situations. However, there are mathematical models and concepts that can be used to improve decision-making in the game.

How do you calculate poker?

  • In poker, players calculate their odds of winning based on their hand and the cards on the table. They consider factors like pot odds, outs, and equity to make informed decisions.

What is the formula for probability in poker?

  • The formula for probability in poker depends on the specific situation, but in general, it involves calculating the likelihood of achieving a certain hand based on the cards you have and the cards on the table.

What is the mathematical expectation in poker?

  • The mathematical expectation in poker refers to the average value of a hand or a betting situation over a large number of repetitions. It helps players make informed decisions based on the long-term profitability of their actions.

Is poker a 100% skill?

  • Poker is a game of skill, strategy, and psychology, but luck also plays a significant role in individual hands and outcomes.
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