How To Calculate Poker Probabaility Odds: Learn The Mathematics Here
Table of content:
- Poker probability for calculating pot odds
- Poker probability for calculating implied odds
- Poker probability for calculating expected value
- Poker probability for poker equity
- Poker probability for reverse implied odds
- Poker probability for poker equity and drawing hands
Contrary to what most people believe, poker is far from being just a game of luck. Instead, it is a game of skill wherein the ability to read opponents’ hands and predict situations that helps you win the game. Moreover, poker is actually a game of mathematics as well. Yes, most of the professional poker players around the world commonly use poker math and poker probability on a regular basis 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 that they would otherwise have to make based on instinct.
To help you understand how math and probability works in poker, we have detailed some of the common poker math and poker probability strategies. While some are used to calculate odds, some are for equity and hands. Read on this comprehensive guide about different math strategies you can use while playing online!
Pot odds, in simple terms, is a poker math strategy that is normally used for calculating the odds or likelihood of winning when a player has a drawing hand. A drawing hand is basically a poker hand that is currently incomplete and thus needs further 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
There are only two people 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 is it that another heart will be dealt on the turn. To do this, just find out the ratio of the cards in the deck that you do not want against the cards that you do want. To put it simply, there are 5 cards in the deck that you already know about, this leaves you with 47 cards that you have no idea about. Now, out of those 47, 9 will likely come handy to make a flush (a flush is a poker hand consisting of 5 cards that are 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
The opponent as mentioned above 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 definitely call as the pot odds are greater than the card odds.
Implied odds poker math strategy basically helps a player determine the amount of money they will likely win after completing a draw or a drawing hand. Despite the fact that implied odds are just another extension of pot odd, there is actually 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 that a player necessarily needs to win to make the calling profitable. To calculate the same, just subtract the pot odds from the odds of hitting a draw and thereafter work out the required implied odds.
This will likely give you a new ratio which you can thereafter compare with the amount you must call. This in turn will help you figure out the amount of money you must take from your opponent to make the call profitable.
Expected value to begin with is a poker math strategy that details the amount of money that a player expects to win or lose on average. In other words, in any game of poker, a player usually has 5 options - to call, raise, check, bet or fold. Now, each of 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 money than others on an 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 is a positive expectation play that 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.
In order to use expected value poker math strategy, all you have to do is multiply the results of the possible outcomes by their probability of happening and thereafter 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 basically the set of hands that a player might be holding 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 make the calculation easier, we have expressed the percentage values in the form of 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.
Pot equity otherwise known as poker equity is one of the most common poker math strategies used by most professional poker players around the world. This poker probability strategy is generally used to determine whether a player should bet or check during certain situations in poker. Now, before we begin to explain the basic concept behind poker equity, let us first understand what does equity in poker actually imply?
“Equity” in simple terms is the amount of money currently in the pot that likely “belongs” to you. This equity in general is calculated based on the odds you have, of winning at a particular point in the hand. For instance - there is a 70% chance that you are going to win with a particular hand, 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 basically done to figure out an estimate of 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 be wondering how you can potentially incorporate this information into the game of poker. To begin with, while playing a game of poker, it is generally practically impossible to figure out what your opponent is exactly holding. In such a situation, as you might have guessed, it is actually not possible to work out the poker equity and use it to your advantage. However, if you are well aware of the concept of equity in poker, you should be able to find out the approximate equity a player usually holds during different stages of the game. Then, you can use this information to bet accordingly if you think you have the best hand at that moment.
As the name suggests, the reverse implied odds are the exact opposite of implied odds. In other words, implied odds poker math strategy is used for calculating the amount of money you would likely win after completing a draw. The poker probability strategy for reverse implied odds on the other hand helps to estimate how much a player stands to lose if he is able to complete a draw, but the opponent still ends up holding a better hand. Suppose, you have worked out your implied odds and you believe you must call a bet. Then, , make it a point to calculate your reverse implied odds to see if you should actually go ahead with the call to make your draw or not.
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 case of reverse implied odds as well 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 actually have the best hand at the table. Conversely, the reverse implied odds significantly decrease when there is a higher chance that a player will be having the best hand once he completes the draw. It is usually recommended that a player must make calls if he has a few reverse 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.
The concept of poker equity and drawing hands usually emphasizes that if a player holds the best hand (the best hand in poker 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 must keep betting for value even if his hand is not complete 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 jack of diamonds. Now in the flop round ( the first betting round in the game of poker 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 of spades and 4 of diamonds. Now, despite the fact that your opponent already holds 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%. In fact, the only hand that currently holds a better equity in the pot than you is 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 it is actually possible for already made hands to 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 possibly 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 thereafter aim to get as much money into the pot as possible, given the current situation.
The above examples might have made you feel like that there is a lot of math involved in poker. Yes, there is but it is all good because it just shows you how you do not always have to have a great hand to win the pot. You just need to identify the right strategy and play accordingly.
Learning to use poker math and poker 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.
To continue learning and be good at it, you can practice it regularly on the GetMega Poker app and play multiple poker games.