Poker Chances Of Hands

Based on the tabulated data and chart generated, there are a few interesting observations to be made. The are listed below:

• Online Poker Odds
• Odds On Poker Hands
• Poker Chances Of Hands Against

1. Pair A is best hand

There should be no surprise that Pair A is the best hand. Having a pair A, helps you to easily get the best possible double pair combo or three-of-kind combo. While it might be harder to strike straight or flush with it, those scenarios are typically less likely to happen. Thus, making pair A better in general.

2. Offsuit 72 is the worst hand

More on Calculating Poker Hand Odds. Good poker, at its heart, is a mathematical game now. Calculating hand odds are your chances of making a hand in Texas Hold'em poker. For example: To calculate your hand odds in a Texas Hold'em game when you hold two hearts and there are two hearts on the flop, your hand odds for making a flush are about 2 to 1.

This might be less known to people and it could be counter intuitive. Some might have thought that perhaps Offsuit J2 would be worse than Offsuit 72. But, that is not the case.

To understand why this is the case, we can start thinking about what are combinations that are most likely to lead to a winning combo assuming no one folds. Given any hands, we are more likely to win with double pair, followed by 3-of-a-kind, straight flush and so forth.

With offsuit 72, we are more likely to win double pair of pair 7 and pair 2, followed by three-of-a-kind and so on. However, it is also worthwhile to note that it is highly like other players has a better double pair or three-of-a-kind. This bring us to the next important lesson to learn.

3. Having a suited, closely connected hand with A, K or Q is better than having pairs that is less than 9

If you were to investigate the table or chart, the hand ranked 5th is Suited AK. What is even more interesting is pairs hand only took 6 spots from rank 1 to rank 20. Most of the remaining spots were taken up by suited, closely connected hands with a high card like A, K or Q.

The reason for this is similar to previous point that we made. It is more frequent that players will win using double pairs or 3-of-a-kind. Therefore, having a higher card helps to push you to a better standing to win.

One final note on this topic - Pair 9 is the last pair hand ranked in the top 20 hands. Playing any other pairs hand may not be as good as conventional wisdom might suggest.

4. Winning chance drops fast within the top 7 ranked hands

This is the lesson that really took us by surprised. While developing our poker odds calculator, we did had a sense that odds of winning was somewhat asymmetric. But, the chart above really solidify how much the asymmetry was.

Within the top 7 ranked hands, the probability of winning drops really fast from paired A to paired K and so forth. If you get the top 7 hands, you really should work hard to get through the preflop.

5. You are more likely to win a 6 players match than a 9 players one

A player with hands that are in the top 7 ranks in a 6 players game have a much better chance of winning in a 9 players game. For example, Paired A has roughly 49.5% preflop winning probability in a 6-player game compared to only 35% in a 9-players game. While 14.5% difference is not as big as it sounds, it has a significant impact on the pot odds that you will need to make a value play. In short, it might be easier to make money off a 6 players game rather than a 9 players game.

6. In a no-folding six players match, your hand range to play is very large

This point is not as crucial as other points we have made. But, we find this observation quite interesting although it is unlikely to happen in real life.

Suppose that we are in a no-folding 6 players Texas Hold'Em match. During every betting session, our pot odds is 5-to-1. This means that for every $1 we bet, we stand to win $5.

Based on this pot odds, our break-even pot equity or winning odds is around 16.67%. Using the chart above, we can see that we can play any hands better than rank 106. This means that players can play 105 types of hands out of 169 types (59.2% of all types) and still perform better than break even! Basically, you have a very large hand range to play in this type of situation.

Nonetheless, this is a just-for-fun analysis, which does not happen that often in real life. Based on some of our experience playing, it could happen sometimes during preflop though.

7. Our hand rankings are similar to Sklansky hand groups

Sklansky hand groups was formulated by David Sklansky and Mason Malmuth. Both of these old school poker players understand the math very well. It is no surprise that our hand rankings aligns very well with their proposed hand groups.

Sklansky hand group proposes that Tier 1 group consists of pair A, pair K, pair Q, pair J and suited AK. These cards are essentially ranked 1 to 5 via our Monte Carlo simulation. The same observation can be made for Sklansky Tier 2 and Tier 3 hand group.

POKER PROBABILITIES

• Texas Hold'em Poker
  Texas Hold'em Poker probabilities
• Omaha Poker
  Omaha Poker probabilities
• 5 Card Poker
  5 Card Poker probabilities

Online Poker Odds

POKER CALCULATOR

• Poker calculator
  Poker odds calculator

POKER INFORMATION

• Poker hand rankings
  Ranking of poker hands

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. There are 7,462 distinct 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:

Odds On Poker Hands

• 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.

Poker Chances Of Hands Against

Home > 5 Card Poker probabilities