Poker Hands Ranking Probability
A “poker hand” consists of 5 unordered cards from a standard deck of 52. There are 52 5 = 2,598,9604 possible poker hands. Below, we calculate the probability of each of the standard kinds of poker hands. This hand consists of values 10,J,Q,K,A, all of the same suit. Since the values are fixed, we only need to choose the suit. The Probability of drawing a given hand is calculated by dividing the number of ways of drawing the hand (Frequency) by the total number of 5-card hands (the sample space; =,). For example, there are 4 different ways to draw a royal flush (one for each suit), so the probability is 4 / 2,598,960, or one in 649,740. This is the idea behind ranking the individual hands. A hand that is less likely to occur is given a higher rank than one that is more likely to occur. Some players will claim hands like 3 5 are worse, because when you input 2 7 and 3 5 into a poker hand calculator, the 2 7 actually rates higher. But that’s a heads up battle involving only two hands, so naturally the seven high has a better chance to win based on the many occasions when both hands.
What are the Probabilities of the Best Poker Hands?
If you’ve ever watched a movie in which people play texas holdem poker, it seems like the best hands — full houses, royal flushes, and four of a kind — just seem to pop up all over the place. The truth is that they are extremely rare — so let’s take a look at some of the real odds for some of the best poker hands.
A Loot at the Best Poker Hands and their Probabilities
Before we look at some of the really rare poker hands, let’s start out with a basic pair. The probability involves a poker hand that has this pattern: AABCD, where you have two cards of the same rank, and three other cards that don’t match the first two or each other. You’ve actually got a fairly good probability of getting a pair: 42.3%.
After that, though, things go downhill quickly. Getting a second pair (AABBC) in your hand. The odds of that drop to 4.8%.
How about three of a kind? This pattern (AAABC) might seem like you would get more of them at first, because you just have to get one more “A” card instead of finding a match for “B” or “C.” However, the probability of that third card showing up is actually lower: 2.11%.
Then there’s the full house: combining AAA with BB. If you played 100 hands, you might not even get one full house, because the probability is 0.14%.
You’re more likely to land a straight (five cards in order, either from the same or different suits) or a flush (all from the same suit) than you are to land a full house, in fact. But the odds aren’t that much greater. Your probability of a straight is 0.39%, and the probability of a flush is 0.19%.
How about a straight flush? All in a row, all from the same suit. The odds of that are 0.0014%.
You’ve got better odds of drawing four of a kind than you do of landing a straight flush, in fact. But the odds aren’t much better, sitting at 0.024%. Then there’s the rarest hand of all, the royal flush. That’s the cards 10, J, Q, K and A, all from the same suit. Your odds of landing that humdinger are 0.000154%.
So what Does this Mean for Poker players?
Poker Ranking Of Hands
Since you’re not even going to get a pair half the time, the key involves waiting around, doing some folding now and then, while holding firm for one of those hands to show up. The best poker players know that luck is a factor, but for those who really succeed at it, skills and strategy are much more important. This involves knowing when you can bluff the rest of the table into walking away even though you don’t even have a pair of 5’s in your hand, and knowing when you can push hard with what you have. It also involves learning your opponents so that you have an idea when they are trying to pull a bluff even more audacious than yours, or when they are simply too scared to do anything, so even if they do have a fairly good hand, you can scare them away from the pot.
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This article will look at the entire hierarchy of poker hands, from the highest to lowest. Each hand will be accompanied by a probability outlook, advice on betting strategy if you are holding this hand, and how it compares to the rest of the possible hands you may be betting against.
These rules apply to a number of different types of games that can be found at online poker sites. However, some of them also apply to various casino poker games like Caribbean Stud Poker and Five Card Poker. This is also true of many video poker titles.
List of Poker Hands
The following hands apply to Texas Hold’em. There are nine differentiating categories that are the first consideration when it comes to ranking poker hands against one another. The superiority of hands is then further determined within the category that it sits by the individual card ranking – this is from highest to lowest: Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3 and 2. Overall dealing poker cards from a 52-card deck has 2,598,960 distinct hands, but since cards are not ranked by a difference in the suit, there are just 7,462 discrete hand ranks.
Royal Flush: Once in a Lifetime Hand
The Royal Flush is an ace-high straight flush, for example, Ace-King-Queen-Jack-10 all of the hearts (or any of the other three suits), it is the highest possible hand a player can hold in poker. There are clearly four possible combinations of this hand, one for each of the four suits; Hearts, Diamonds, Clubs, Spades. Landing this hand requires a lot of composure as it is easy to let the excitement of the moment flicker across your face, alerting opponents that you’re holding something strong. Assuming that you don’t hold the Royal Flush out the Flop, it’s advisable to make your first bet small to keep as many parties interested as possible – and then gradually increasing to a maximum amount on the Turn and River.
Probability of a Royal Flush = 1 in 649,739
Straight Flush
The Straight Flush hand is similar in essence to the Royal Flush but the high card doesn’t matter. You’ll need 5 consecutive cards all of the same suits to land this hand. There are 36 combinations of straight flush to be made, and that’s 9 from each suit. Betting on this hand is again a question of concealing the poker face – you’re almost certainly holding the strongest hand at the table, so extracting the most amount of bets from the opposition before going big on the River is the game plan here.
Probability of a Straight Flush = 1 in 3,217
Four of a Kind
When it comes to Four of a Kind it holds a certain unique place in all the poker hand ranked list. Consisting of four of the same card in each of the four suits it can present itself in many different ways. This powerful combination of cards clearly becomes more valuable if the player is holding a pocket pair and able to match it with two on the table, in this scenario it would be impossible for another player to trump your hand unless they have managed to build a Royal or Straight Flush. Again, bet big if you’re lucky enough to land this combination.
Probability of a Four of a Kind = 1 in 594
Full House
The Full House is a very strong hand that has won its holders a considerable amount of cash in the past. It consists of a pair and a three of a kind in the same hand. Clearly the minimum requirement here is that a pair is dealt on the table by the dealer. From this, a player could possibly construct a full house if they can build out a three of a kind and match one other card. A Full House is first ranked by the three matching cards and then the pair, in a case where two players have matching three of a kind the pair is then used to determine the winner.
Probability of a Full House = 1 in 39
Flush
A Flush is a mid-strength hand that can be used to win the holder a considerable pot if they play their wagering strategy correctly. The cards needed to form a Flush are simply 5 of the same suit. The higher the face value of the highest card in the Flush is used to determine who wins if two players are holding this hand. If two or more players are both holding the highest card in the Flush, the second card is then consulted, and so on.
Probability of a Flush = 1 in 33
Straight
To land the Straight, a player must form a sequence of 5 consecutive cards by face value, for example, 7-8-9-10-Jack. A powerful hand that will most likely give the holder a lot of confidence to bet big depending on what else has been laid down. The top-ranking Straight also known as “The Broadway” consists of the top ranking cards in the deck in a row, the same as a Royal Flush but without matching suit. The lowest ranking Straight is known in the business as “the Wheel”, holding this should invoke a cautious betting strategy as there is a chance an opponent is holding a higher Straight.
Probability of a Straight = 1 in 22
Three of a Kind
The Three of a Kind is a hand in the bottom half of the poker hand rankings, but it is not without merit. It can be an incredibly powerful hand in the right circumstances. If the Three of a Kind is assembled from a pocket pair and one community card, it is known as a “set”. However, if the Three of a Kind is assembled from a pair of community cards and one hole card, it is known as “trips”. Betting on a set and trips are very different things, and players are advised caution if betting on trips as their position can be easily be trumped by a player with strong hole cards, possibly holding a Full-House.
Probability of a Three of a Kind = 1 in 21
Two Pair
The Two Pair is statistically the most frequent winning hand on average across all poker hands. It is strong enough to win in many cases and comes around often enough to make it occur more than any other winning hands presented on this list. If you’re holding a Two Pair that doesn’t mean you should bet the house though, there are plenty of other stronger combinations out there as we have shown. Tread with caution and always adopt a smart approach to betting strategy when engaging in live poker sessions.
Probability of a Two Pair = 1 in 4.25
One Pair
One Pair accounts for almost half of all poker hands and is by that number the most common of all poker hands to be dealt. To achieve One Pair is fairly easy, simply match two cards together either with the community cards or by holding one hole card matching a community card. This hand is not very strong at all, and therefore should not be bet on too heavily. Approximately 40% of players are able to achieve at least One Pair on any given hand.
Probability of a One Pair = 1 in 2.28
High Card
Poker Hand Rankings Chart
The High Card is the weakest of all the possible combinations of poker hands. It is determined by the highest card out of the 5. The odds of getting a High Card as your best hand are actually lower than the One Pair and Two Pair, this is because it is more likely you will match something rather than missing with everything with the seven cards available. The only bets you should be making with these are desperate bluffs, and even then it is better to fold early if this one is looking likely. Make sure to educate yourself properly before playing for real money, read our guide to best poker training courses to improve your knowledge.
Poker Hands Ranking And Probability
Probability of a High Card = 1 in 5.74