Poker List Of Winning Hands

This post works with 5-card Poker hands drawn from a standard deck of 52 cards. The discussion is mostly mathematical, using the Poker hands to illustrate counting techniques and calculation of probabilities

Poker Hand Combinations Explained. Poker hands fall into one of ten categories. The highest is a royal flush, followed by a straight flush, then four of a kind, a full house, a flush, a straight.

Working with poker hands is an excellent way to illustrate the counting techniques covered previously in this blog – multiplication principle, permutation and combination (also covered here). There are 2,598,960 many possible 5-card Poker hands. Thus the probability of obtaining any one specific hand is 1 in 2,598,960 (roughly 1 in 2.6 million). The probability of obtaining a given type of hands (e.g. three of a kind) is the number of possible hands for that type over 2,598,960. Thus this is primarily a counting exercise.

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1. Downlad Poker Hand Rankings PDF Subject: Learn which hands beat which using 888poker's concise poker hand rankings pdf from the worst to the very best, called a Royal Flush. Created Date: 11/4/2015 2:00:04 PM.
2. Use the list of poker hands below to know what beats what in poker. Commit this poker hands ranking list to memory today and print it if you need it (there's a button for it at the bottom).
3. Math and odds are important parts of Texas Hold’em poker. James Bond knows this (of course). In the final hand of Casino Royale, four players move all-in on the river and Bond scoops the $115 million pot, thanks to smart play. These were the cards on the board: Ah-8s-6s-4s-As And these were the players’ hands:.

Preliminary Calculation

Usually the order in which the cards are dealt is not important (except in the case of stud poker). Thus the following three examples point to the same poker hand. The only difference is the order in which the cards are dealt.

These are the same hand. Order is not important.

The number of possible 5-card poker hands would then be the same as the number of 5-element subsets of 52 objects. The following is the total number of 5-card poker hands drawn from a standard deck of 52 cards.

The notation is called the binomial coefficient and is pronounced “n choose r”, which is identical to the number of -element subsets of a set with objects. Other notations for are , and . Many calculators have a function for . Of course the calculation can also be done by definition by first calculating factorials.

Thus the probability of obtaining a specific hand (say, 2, 6, 10, K, A, all diamond) would be 1 in 2,598,960. If 5 cards are randomly drawn, what is the probability of getting a 5-card hand consisting of all diamond cards? It is

This is definitely a very rare event (less than 0.05% chance of happening). The numerator 1,287 is the number of hands consisting of all diamond cards, which is obtained by the following calculation.

The reasoning for the above calculation is that to draw a 5-card hand consisting of all diamond, we are drawing 5 cards from the 13 diamond cards and drawing zero cards from the other 39 cards. Since (there is only one way to draw nothing), is the number of hands with all diamonds.

If 5 cards are randomly drawn, what is the probability of getting a 5-card hand consisting of cards in one suit? The probability of getting all 5 cards in another suit (say heart) would also be 1287/2598960. So we have the following derivation.

Thus getting a hand with all cards in one suit is 4 times more likely than getting one with all diamond, but is still a rare event (with about a 0.2% chance of happening). Some of the higher ranked poker hands are in one suit but with additional strict requirements. They will be further discussed below.

Another example. What is the probability of obtaining a hand that has 3 diamonds and 2 hearts? The answer is 22308/2598960 = 0.008583433. The number of “3 diamond, 2 heart” hands is calculated as follows:

One theme that emerges is that the multiplication principle is behind the numerator of a poker hand probability. For example, we can think of the process to get a 5-card hand with 3 diamonds and 2 hearts in three steps. The first is to draw 3 cards from the 13 diamond cards, the second is to draw 2 cards from the 13 heart cards, and the third is to draw zero from the remaining 26 cards. The third step can be omitted since the number of ways of choosing zero is 1. In any case, the number of possible ways to carry out that 2-step (or 3-step) process is to multiply all the possibilities together.

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The Poker Hands

Here’s a ranking chart of the Poker hands.

The chart lists the rankings with an example for each ranking. The examples are a good reminder of the definitions. The highest ranking of them all is the royal flush, which consists of 5 consecutive cards in one suit with the highest card being Ace. There is only one such hand in each suit. Thus the chance for getting a royal flush is 4 in 2,598,960.

Royal flush is a specific example of a straight flush, which consists of 5 consecutive cards in one suit. There are 10 such hands in one suit. So there are 40 hands for straight flush in total. A flush is a hand with 5 cards in the same suit but not in consecutive order (or not in sequence). Thus the requirement for flush is considerably more relaxed than a straight flush. A straight is like a straight flush in that the 5 cards are in sequence but the 5 cards in a straight are not of the same suit. For a more in depth discussion on Poker hands, see the Wikipedia entry on Poker hands.

The counting for some of these hands is done in the next section. The definition of the hands can be inferred from the above chart. For the sake of completeness, the following table lists out the definition.

Definitions of Poker Hands

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Counting Poker Hands

Straight Flush
Counting from A-K-Q-J-10, K-Q-J-10-9, Q-J-10-9-8, …, 6-5-4-3-2 to 5-4-3-2-A, there are 10 hands that are in sequence in a given suit. So there are 40 straight flush hands all together.

Four of a Kind
There is only one way to have a four of a kind for a given rank. The fifth card can be any one of the remaining 48 cards. Thus there are 48 possibilities of a four of a kind in one rank. Thus there are 13 x 48 = 624 many four of a kind in total.

Full House
Let’s fix two ranks, say 2 and 8. How many ways can we have three of 2 and two of 8? We are choosing 3 cards out of the four 2’s and choosing 2 cards out of the four 8’s. That would be = 4 x 6 = 24. But the two ranks can be other ranks too. How many ways can we pick two ranks out of 13? That would be 13 x 12 = 156. So the total number of possibilities for Full House is

Note that the multiplication principle is at work here. When we pick two ranks, the number of ways is 13 x 12 = 156. Why did we not use = 78?

Flush
There are = 1,287 possible hands with all cards in the same suit. Recall that there are only 10 straight flush on a given suit. Thus of all the 5-card hands with all cards in a given suit, there are 1,287-10 = 1,277 hands that are not straight flush. Thus the total number of flush hands is 4 x 1277 = 5,108.

Straight
There are 10 five-consecutive sequences in 13 cards (as shown in the explanation for straight flush in this section). In each such sequence, there are 4 choices for each card (one for each suit). Thus the number of 5-card hands with 5 cards in sequence is . Then we need to subtract the number of straight flushes (40) from this number. Thus the number of straight is 10240 – 10 = 10,200.

Three of a Kind
There are 13 ranks (from A, K, …, to 2). We choose one of them to have 3 cards in that rank and two other ranks to have one card in each of those ranks. The following derivation reflects all the choosing in this process.

Two Pair and One Pair
These two are left as exercises.

List Of Poker Winning Hands

High Card
The count is the complement that makes up 2,598,960.

The following table gives the counts of all the poker hands. The probability is the fraction of the 2,598,960 hands that meet the requirement of the type of hands in question. Note that royal flush is not listed. This is because it is included in the count for straight flush. Royal flush is omitted so that he counts add up to 2,598,960.

Probabilities of Poker Hands

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2017 – Dan Ma

by Updated : Jul 04, 2020 in Holdem strategy

Winning hands in poker: games rules, list of hands and winning tricks

This article is an excellent introductory guide for beginners who want to start playing poker or have just started and have not yet had time to get experience. In this article we will analyze all the basic details: the rules, winning hands in poker, poker hand rankings and mini-tips and strategies for victory, which you still do not know about.

What is so remarkable about poker? Why is it played by millions of gamblers around the world? Absolutely all players are united by one common desire – to win big jackpots. At high limit tables, a pot can reach up to $ 100,000, and prize tournaments have long exceeded millions of dollars. Become good at poker and maybe you will win this bag of money.

Poker basic rules

The main foundation of any game is the rules. In poker, they are quite complicated:

1. Players join the game table for 2-10 players.
2. At the beginning of the round, one player becomes the big blind, and the next one clockwise becomes the small blind.
3. These two players make bets according to table limits.
4. After that, all players receive 2 cards face down.
5. The first round of betting begins.
6. The player can call the big blind, raise x2 from the big blind or fold the hand.
7. After bets, the dealer draws 3 open cards on the table – flop.
8. Players bet clockwise from the big blind.
9. You can fold, call, raise or check.
10. After the bets on the table appears 4th card – turn.
11. All bets are repeated.
12. The dealer draws the final fifth card – river.
13. Players make their last bets and open their cards.
14. The player who landed the strongest combo of 5 cards takes the pot.

The rules of the game are complex, but you will quickly learn from a few games. In addition, you still need to learn poker hands, poker combinations and winning hands in poker.

Top poker hands

List Of Winning Poker Hands In Order

As you learned from the rules, at the beginning of the game each player receives 2 cards – poker hands. At this moment, the game begins and you need to decide whether you play with these cards or fold. Here are the poker rankings of the 5 most powerful pocket cards that you always need to play:

• Pocket Aces.
• Pocket Kings.
• Pocket Queens.
• Ace King suited.
• Pocket Jacks.

These are the most powerful starting combos that will give you a huge advantage in the game.

Winning tips and strategy

There is no strategy in poker that guarantees you a 100% victory. But there are tricks and tips that will significantly increase the chances. The first rule for beginners is to never bluff. More experienced players will quickly figure it out and you will lose money.

The second rule is to play only strong winning hands in poker. So, you will win less often, but with a great chance.

The third rule – try to understand your opponent. If he bluffed 3 times, then next time he will also bluff. And if a player makes a bet only with a strong hand, it is better not to compete with him and immediately fold.

And the last rule – do not be fooled by emotions. Do only the best and logical actions.

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List Of Winning Poker Hands Printable

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