1. Poker Hand Probability Calculator
2. Probabilities Of Poker Hands

Learning odds will expand your poker IQ in a way that makes learning advanced strategies and theory much easier. But there’s a problem. Up until now, poker odds was only taught by a handful of pros and books, and most of the time it’s been explained in a way that’s too complex to understand. Some common poker hand odds are open-ended straight draws at 4.8:1, four to a flush at 4.1:1, inside straight (belly buster) at 10.5:1, one pair drawing to two pairs or trips at 8.2:1, overcards on a ragged board on the turn at 6.7:1, drawing to a set at 22:1, and drawing to X outs at (46-X) / X:1. In the book Draw Poker Odds: The Mathematics of Classical Poker you will find sections for the probabilities of your opponents holding: one pair, two pair, three of a kind, straight, flush, full house, four of a kind, straight flush, higher one pair, higher two pair, higher three of a kind, higher straight, higher flush, higher full house, higher four of a kind, higher straight flush and the overall probability of one and at. In poker, the probability of each type of 5-card hand can be computed by calculating the proportion of hands of that type among all possible hands. Frequency of 5-card poker hands The following enumerates the (absolute) frequency of each hand, given all combinations of 5 cards randomly drawn from a full deck of 52 without replacement. Probability of poker hands explained since the urge to gamble is no respecter of classes, and Vingt-(et)-Un is a quick and easy and jolly way of doing it with cards, it was widely played wherever large quantities of men found themselves living in one another's company, such as schools, universities, pubs, working men's clubs, and (especially) the armed forces.One need only look at. Probability and Poker Royal Flush. The best hand (because of the low probability that it will occur) is the royal flush. Straight Flush. The next most valuable type of hand is a straight flush, which is 5 cards in order. Ranking, Frequency and Probability of Poker Hands. Ten, J, Q, K, A of. The number of such hands is (13-choose-1).(4-choose-2).(12-choose-3).(4-choose-1)^3. If all hands are equally likely, the probability of a single pair is obtained by dividing by (52-choose-5). This probability is.

Poker odds tell you how often an event fails to occur. In other words, how many times you’re going to lose versus how many times you’re going to win. A simple to way to use poker odds to your advantage is to compare them to pot odds and determine whether you’ll be able to play profitably or not.

What Are Pot Odds?

Pot odds are used to determine whether your decision is profitable or not. In fact, most of the poker theory revolves around the basic concept of pot odds. You always have to consider risk and reward and, no matter what, you always make decisions based on poker odds to some degree.

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Calculating Pot Odds

Calculating pot odds is about learning whether it’s beneficial to risk $X in order to win the pot when your probability of winning is Y%. The amount in the pot to the amount you have to call is your pot odds. In other words, the ratio of pot to involuntary bet.

Here’s the calculation: (Pot + Bet) / Bet = Pot Odds

Example:
With $2000 in the pot, your opponent bets $1500. What are your pot odds? Here’s the calculation: ($2000 + $1500) : $1500 = 2.3 : 1

So your poker pot odds are 2.3 to 1. The easiest way to understand what this actually means is to translate the ratio into a percentage. Here are two ways of doing it:

1. The pot odds ratio is 2.3 : 1, so you calculate the sum of those numbers (in this case, 2.3 + 1 = 3.3) and then calculate 100% : 3.3 = 30,3%.
2. Another way of translating the odds ratio into a percentage is to calculate the sum of the numbers in the ratio (2.3 + 1 = 3.3) and then calculate (1 : 3.3) * 100% = 30.3%.

The percentage tells us the minimum amount of time we need to win the pot in order to turn a profit. So in the example above, you need to win at least 30.3% of those situations in order to justify your call. If you win less than 30.3%, calling would be unprofitable.

And that is the basic idea of any poker hand: to figure out whether you win the hand often enough to call, bet or raise profitably.

Example #2: You’re on the button. There’s $500 in the pot. Your opponent bets $400. You suspect your hand beats the opponent in 40% of these situations, so how to figure out whether you can call profitably?

1. ($500+$400):$400 = 2.25:1
2. 100%:(2.25+1) = 30.8%
3. You would make a profitable call in this situation.

To become a winning player, the goal should be to learn how to calculate poker odds during actual play, not just afterward (although calculating them at any point is a good start). This is surprisingly easy, as most of the time you’re going to be in one of these situations, so memorize them and you’re well on your way:

Implied Pot Odds

Implied odds are used estimate the money that can be won (or lost) during the later stages of a hand. They consider what happens on future streets and give you a more realistic idea of your odds of winning. Calculating implied poker odds requires more skill and experience because you need a good idea of how the opponent is going to react in the future. Should you predict an opponent’s actions inaccurately, you’ve also made inaccurate calculations, which in turn affects your bottom-line negatively.

Simply put, you calculate whether it’s a good decision to commit money into the pot based on how often you’re going to fold in the future (and lose no additional bets) and how often you’re going to hit your draw and make more money in the future (and win additional bets).

So the idea is the same as with pot odds except you also consider future bets. It’s easier to calculate implied poker odds in fixed limit Hold’em since you know how much your opponents can bet. In no-limit, need to correctly predict an opponent’s bet sizes. In pot-limit, you know the maximum your opponent can bet.

Example: You’re on the turn. You check and your opponent bets. There’s $30 in the pot (including your opponent’s bet) and you have $10 to call.

You get 3:1 pot odds.

If you call now, you expect the opponent to call your bet on the river each time you hit your draw, but only when the bet is max. 75% of the pot. You, on the other hand, are going to check/fold each time you fail to hit your draw.

You’re on a flush draw, and therefore you have 9 outs out of 46 remaining cards, meaning 5.1:1 odds of hitting your draw.

By simply looking at pot odds, you would either fold or raise (hoping to bluff your opponent out of the pot). But what about implied odds? As mentioned, the opponent calls your bet 100% of the time, so how much is the minimum you have to be able to bet (and get called) in order to make the play profitable?

Obviously you haven’t got very good pot odds at all. What about implied pot odds? The actual challenge when determining implied pot odds is to calculate the amount of money that you think you can likely win, and the amount of money that you absolutely have to win in order to make profit.

You have 3:1 odds and you need better than 5.1:1 odds, so you need to improve your odds by at least 2.1:1. In this case, 2.1 multiplied by the amount to call ($10) is $21. By getting your opponent to call your bet when it’s more than $21 every time you hit your draw, you would play profitably.

And how do you make sure of that the math above works? Here’s how:

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0.836*10 = 0.164(30+x)
8.36 = 4.92+0.164x
-0.164x = 4.92-8.36
-0.164x = -3.44
0.164x = 3.44
x = 3.44/0.164 = 21

You multiply the amount you have to call by the times you fail to hit your draw and also multiply the amount in the pot and the money you need to win to justify a call (“x”) by the times you do hit your draw. Then you simply figure out what “x” is.

75% of the pot, which the opponent calls every time, is $30. You would make a profitable play here, since the opponent had to be willing to call $21 or more.

If the example above was hard to understand, please re-read it until you get it. The conditions were simplified for the sake of the example (the opponent always calls when bet is max. 75% of the pot, for instance–this is rarely the case).

Value of nut draws:
Nut draws are more valuable mainly because of two reasons:

1. A player might end up in situations where he and his opponent both hit their draws, and if you’re the one with the nut draw, you’ll be able to make a lot of money out of that hand.
2. It can go the other way around, and you’ll be in huge trouble if both of you hit your draws, but your opponent’s got the nut draw.

Overestimating implied odds:
Many players often learn about implied poker odds and start justifying every other situation with “plus, I’ve got implied odds” without doing the math. You need to go through the calculations 100s of times before you can make educated estimates on your implied odds, and even still, you should keep doing them until the day you stop playing poker for real money.

Determining correct implied odds relies on how well you can analyze opponents. Unless you have a good idea of what the opponent is going to do, use basic pot odds. Implied odds work only if you can make an educated prediction on how your opponent is going to react.

Can you sell it?
The success of your implied odds decisions also depends on your skills to extract money from your opponents. Players have different success rates in different situations (because of their image, for example). While one player might be able to get his opponent to commit the needed $21+, another player might not. You truly need to understand your capabilities.

Poker Hand Probability Calculator

Odds, Math, and Poker

Poker isn’t just about math but it’s all about odds. What are the odds of your opponent folding, calling or raising? What are the odds of you hitting your outs? What are the odds of your opponent hitting his outs? On some level, you’re always thinking about odds.

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In poker, the probability of each type of 5-card hand can be computed by calculating the proportion of hands of that type among all possible hands.

Frequency of 5-card poker hands

The following enumerates the (absolute) frequency of each hand, given all combinations of 5 cards randomly drawn from a full deck of 52 without replacement. Wild cards are not considered. The probability of drawing a given hand is calculated by dividing the number of ways of drawing the hand by the total number of 5-card hands (the sample space, five-card hands). The odds are defined as the ratio (1/p) - 1 : 1, where p is the probability. Note that the cumulative column contains the probability of being dealt that hand or any of the hands ranked higher than it. (The frequencies given are exact; the probabilities and odds are approximate.)

The nCr function on most scientific calculators can be used to calculate hand frequencies; entering ​nCr​ with ​52​ and ​5​, for example, yields as above.

The royal flush is a case of the straight flush. It can be formed 4 ways (one for each suit), giving it a probability of 0.000154% and odds of 649,739 : 1.

When ace-low straights and ace-low straight flushes are not counted, the probabilities of each are reduced: straights and straight flushes each become 9/10 as common as they otherwise would be. The 4 missed straight flushes become flushes and the 1,020 missed straights become no pair.

Note that since suits have no relative value in poker, two hands can be considered identical if one hand can be transformed into the other by swapping suits. For example, the hand 3♣ 7♣ 8♣ Q♠ A♠ is identical to 3♦ 7♦ 8♦ Q♥ A♥ because replacing all of the clubs in the first hand with diamonds and all of the spades with hearts produces the second hand. So eliminating identical hands that ignore relative suit values, there are only 134,459 distinct hands.

The number of distinct poker hands is even smaller. For example, 3♣ 7♣ 8♣ Q♠ A♠ and 3♦ 7♣ 8♦ Q♥ A♥ are not identical hands when just ignoring suit assignments because one hand has three suits, while the other hand has only two—that difference could affect the relative value of each hand when there are more cards to come. However, even though the hands are not identical from that perspective, they still form equivalent poker hands because each hand is an A-Q-8-7-3 high card hand. Online casino new user bonus. There are 7,462 distinct poker hands.

Probabilities Of Poker Hands

Derivation of frequencies of 5-card poker hands

of the binomial coefficients and their interpretation as the number of ways of choosing elements from a given set. See also: sample space and event (probability theory).

• Straight flush — Each straight flush is uniquely determined by its highest ranking card; and these ranks go from 5 (A-2-3-4-5) up to A (10-J-Q-K-A) in each of the 4 suits. Thus, the total number of straight flushes is:
  • Royal straight flush — A royal straight flush is a subset of all straight flushes in which the ace is the highest card (ie 10-J-Q-K-A in any of the four suits). Thus, the total number of royal straight flushes is

    or simply . Note: this means that the total number of non-Royal straight flushes is 36.

• Four of a kind — Any one of the thirteen ranks can form the four of a kind by selecting all four of the suits in that rank. The final card can have any one of the twelve remaining ranks, and any suit. Thus, the total number of four-of-a-kinds is:

• Full house — The full house comprises a triple (three of a kind) and a pair. The triple can be any one of the thirteen ranks, and consists of three of the four suits. The pair can be any one of the remaining twelve ranks, and consists of two of the four suits. Thus, the total number of full houses is:

• Flush — The flush contains any five of the thirteen ranks, all of which belong to one of the four suits, minus the 40 straight flushes. Thus, the total number of flushes is:

• Straight — The straight consists of any one of the ten possible sequences of five consecutive cards, from 5-4-3-2-A to A-K-Q-J-10. Each of these five cards can have any one of the four suits. Finally, as with the flush, the 40 straight flushes must be excluded, giving:

• Three of a kind — Any of the thirteen ranks can form the three of a kind, which can contain any three of the four suits. The remaining two cards can have any two of the remaining twelve ranks, and each can have any of the four suits. Thus, the total number of three-of-a-kinds is:

• Two pair — The pairs can have any two of the thirteen ranks, and each pair can have two of the four suits. The final card can have any one of the eleven remaining ranks, and any suit. Thus, the total number of two-pairs is:

• Pair — The pair can have any one of the thirteen ranks, and any two of the four suits. The remaining three cards can have any three of the remaining twelve ranks, and each can have any of the four suits. Thus, the total number of pair hands is:

• No pair — A no-pair hand contains five of the thirteen ranks, discounting the ten possible straights, and each card can have any of the four suits, discounting the four possible flushes. Alternatively, a no-pair hand is any hand that does not fall into one of the above categories; that is, any way to choose five out of 52 cards, discounting all of the above hands. Thus, the total number of no-pair hands is:

• Any five card poker hand — The total number of five card hands that can be drawn from a deck of cards is found using a combination selecting five cards, in any order where n refers to the number of items that can be selected and r to the sample size; the '!' is the factorial operator:

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.

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