Poker Combination Strength
Named after original poker legend Doyle Brunson, the 10 2 suited was used by Texas Dolly to secure his 1976 World Series of Poker Main Event championship. Brunson had built a big chip lead over his heads up opponent Jesse Alto, so when he found 10 2 of spades in the hole, he called Alto’s open and took a flop – hoping to finish his man off.
- There are 52 cards in a deck, 13 of each suit, and 4 of each rank with 1326 poker hands in total. To simplify things just focus on memorizing all of the potential combos to start: 16 possible hand combinations of every unpaired hand; 12 combinations of every unpaired offsuit hand; 4 combinations of each suited hand; 6 possible combinations of.
- The poker odds calculators on CardPlayer.com let you run any scenario that you see at the poker table, see your odds and outs, and cover the math of winning and losing poker hands. Texas Hold'em Omaha.
- Combinatorics is the practice of breaking down ranges and counting individual combinations of hands. Generally we won't have enough time during a hand to assign our opponent a specific number of combinations – it's standard practice to think more generally about our opponents range and make estimates.
Poker rules are easier than you may think, and there’s no better time to learn how to play poker than now, as this popular American game is played by many people today. The basic rules of poker are the same, and use the same 5-card poker hand ranking chart. There is one obscure poker game, named Badugi Poker, that uses a 4-card hand ranking chart, but the general rules of poker still apply.
Basic Poker Rules
Before you learn how to play poker games, you’ll want to familiarize yourself with basic poker rules, such as how one poker hand ranks against another. Learning the rules of poker hands and how to determine a winner in poker might seem difficult at first, but with a little bit of studying and experience, you’ll know how to play poker without having to think about it.
Poker Combinations Strength Games
Table of Contents
Poker Hand Strength
The first thing to understand about poker rules is that each hand has its own strength. This strength is determined by how well the cards in your hand interact with each other. You want hands that create a run, are of the same suit, match each other’s value, and are high in strength. Normal poker rules determine the strength of hands to be the higher value cards in the following order: Ace, King, Queen, Jack, Ten, Nine, Eight, Seven, Six, Five, Four, Three, and Two. The suit of each card does not determine any sort of strength in normal poker rules. There may be special poker rules for games where a suit is used to determine who gets to act first, but that is the only reason suit would be used.
Poker Hand Rank Chart
A normal poker hand must contain five cards. There are many games where more than five cards are used, but the winning poker hand is determined by the player who has the strongest five card poker hand. What is the best poker hand? Here is a list of basic poker hands. I’ve organized them from the strongest poker hands to the weakest poker hands: Royal Flush, Straight Flush, Four of a Kind, Full House, Flush, Straight, Three of a Kind, Two Pair, One Pair, and High Card.
Printable Poker Hand Chart
The printable poker hand chart on the right side of this page can be printed and brought with you to the casino and will help you learn how to play poker better. Next time you’re wondering about the basic hand strength poker rules during a game, simply pull this printable poker hand rank chart out of your pocket. If you’d like to print a copy of our poker hand chart, just click the image below and a new page will open. From there, click print in your browser.
Here are basic poker hand ranking images that I’ve just described. Again, these are organized from the strongest hands to the weakest hands.:
Royal Flush – 1 in 649,740.00
A Royal flush is the most powerful hand in poker. The hand involves having all cards being the same suit, as well as the highest possible run, which is Ace, King, Queen, Jack, Ten. This run is also known at the “Broadway” run. This hand is extremely rare to receive.
Straight Flush – 1 in 72193.33
A straight flush is similar to a royal flush, except a straight flush can be beat by a higher straight flush. A straight flush contains cards of the same suit, which also create a run. However, a straight flush changes its name to a royal flush when its highest card is an Ace.
Four of a Kind – 1 in 4165.00
Four of a kind is exactly what it sounds like, which is four of any card that is the same value. As you see in the example, we have four queens. The fifth card typically doesn’t come into play unless you’re playing a community game and the four queens are part of the community.
Full House – 1 in 694.16
A full house is a combination of three of a kind and a pair. The strength of a full house is determined by the value of the three of a kind that is part of the full house. If both players have the same three of a kind, then the pair determines the winner. For example, if Player A has QQQ88 and Player B has QQQ66, then Player A will win because his pair of 8’s are better than Player B’s pair of 6’s.
Flush – 1 in 508.80
A flush is a hand where all of the cards are of the same suit. Strength of a flush is determined by the highest card in the flush. If two players have flushes that have the same high card, then the next card us used to determine the winner. This goes on until one player has a higher card than the other. For example, If Player A had Q8652 and Player B had Q8653, then player B would win because his 3 is higher than Player A’s 2.
Straight – 1 in 254.80
A straight is also known as a run. A player has a straight when all cards in his cards are in sequential order and at least two suits exist. If only one suit exists, then the hand would be considered a straight flush. The strength of a straight is determined by the highest card. If Player A has 87654 and Player B has QJT98, then Player B has the stronger hand.
Three of a Kind – 1 in 47.32
Three of a kind is exactly how it sounds, three cards of the same value. The strength of this hand is determined by the value of the three of a kind. If both players have the same three of a kind, which is common in community games such as Texas Holdem, then the next highest value card is used to determine the winner.
Two Pair – 1 in 21.03
Two pair is when a player has two sets of two cards that have the same value. The strength of two pair is determined by the top pair first, then the second pair. For example, if Player A has JJTT4, and Player B has KK223, then Player B wins the hand because his top pair is higher than Player A’s. In another example, if Player A has JJTT4 and Player B has JJ994, then Player A wins the hand because their top pairs match, but Player A’s second pair is higher.
One Pair – 1 in 2.36
Having one pair is to have two cards of the same value. Determining the strength of a pair is simple; whoever has the higher value pair wins. If the pair is the same strength, then the next highest card determines the winner.
High Card – 1 in 1.99
Having high card is a weak holding. It’s strength is determined by the single highest value card in the hand. If players have the same top card, then the next card is used to determine the winner, and so forth. Some people think that the odds of getting this are 100%. However, that figure is only correct when considering what your odds of getting high card or better are. In reality, you’ll only get high card once in about every two hands you’re dealt.
Popular Poker Games
Poker players tend to play games in herds, meaning that they all tend to play the same poker games as each other. Players will typically start by learning Texas Holdem Poker rules, then move on to another poker game. Once a poker player is comfortable with the poker rules of their favorite game, then tend to play that game the most often and won’t change games until a new and exciting poker game is released with different rules.
At this time, the most popular poker game is Texas Holdem. This poker game has been around since before 1970 and was used as the poker game of choice in determining the World Champion of the World Series of Poker. The next most popular games are Seven Card Stud and Omaha Poker. There are many other poker games though, and all have different poker rules. Some poker games are played using a community, which are cards laid in the middle of the table for all players to share, and some poker games only allow players to use their own cards, which may be either hidden or exposed to other players. Here are the names of some other popular poker games. This list certainly does not cover all of the games, but it does give you a general idea of what other poker games people are playing: Razz, Lowball, Badugi, Chinese Poker, Big-O, Deuce to Seven Triple Draw, Five Card Draw, Five Card Stud, Pineapple, and Crazy Pineapple.
Last updated: January 1, 2018
I recently took a Hackerrank challenge for a job application that involved poker. I'm not a poker player, so I had a brief moment of panic as I read over the problem the description. In this article I want to do some reflection on how I approached the problem.
The hackerrank question asked me to write a program that would determine the best poker hand possible in five-card draw poker. We are given 10 cards, the first 5 are the current hand, and the second 5 are the next five cards in the deck. We assume that we can see the next five cards (they are not hidden). We want to exchange any n number of cards (where n <= 5) in our hand for the next n cards in the deck. For example, we can take out any combination of 2 cards from the hand we are given, but we must replace these two cards with the next two cards from the deck (we can't pick any two cards from the deck).
Suit and value make up the value of playing cards. For example, you can have a 3 of clubs. 3 is the value, clubs is the suit. We can represent this as 3C.
Suits
Clubs CSpades SHeart HDiamonds D
Value (Rank)
2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, Ace
Hands
Here are the hands of poker
Royal flush (the problem didn't ask me to consider Royal Flush)
A, K, Q, J, 10, all the same suit.
Straight flush
Five cards in a sequence, all in the same suit. Ace can either come before 2 or come after King.
Four of a kind
All four cards of the same rank.
Full house
Three of a kind with a pair.
Flush
Any five cards of the same suit, but not in a sequence.
Straight
Five cards in a sequence, but not of the same suit.
Three of a kind
Three cards of the same rank.
Two pair
Two different pairs.
Pair
Two cards of the same rank.
High Card
When you haven't made any of the hands above, the highest card plays.In the example below, the jack plays as the highest card.
Evaluating a hand of cards
A hand is five cards. The first thing I did was write out functions to evaluate if a group of 5 cards satisfies the conditions of one of the ten hands.
Here's a sample hand:
To write functions, I reached for using 2 important python features: set and defaultdict.
Here's an example of a simple function to detect a flush, a hand with cards of all the same suit:
Checking a flush
This function creates a list of the suits in our hand, and then counts the unique elements in that list by making it a set. If the length of the set is 1, then all the cards in the hand must be of the same suit.
But wait, what if we have a straight flush? Also, a hand that satisfies a flush could also be described as a two pair hand. The problem asked me to find the highest possible hand for a given set of cards, so I tried to keep things simple by writing a check_hand() function that checks each hand starting from straight flush down to high card. As soon as a condition for a hand was satisfied, I returned a number that corresponded to the strength of the hand (1 for high card up to 10 for straight flush). The problem didn't include Royal flush, so I will not include that here.
Here's the check_hand function:
This function starts checking the most valuable hands. After it checks the second to lowest hand (pair), it returns a value of 1. This value of 1 corresponds to the 'highest card' hand. Since I'm not comparing the relative value of hands, it doesn't matter what the highest card is, so the number just represents the type of hand that is the strongest.
Other hands
Here are the all of the functions I used to detect hands:
defaultdict is a great built-in that is good to use when you don't know what elements will be in your dictionary, but you know what the initial values of any key that could be added should be. We don't need it here, but the alternative would be to write a very long dictionary where keys are the possible card values and the values of each key is 0.
It would certainly be cleaner and more efficient to write out the above functions into one large function, but I wanted to keep things simple as I was under time constraints.
The next step in the problem is to determine the best possible hand we can get given the hand we are dealt and the 5 cards on top of the deck. I decided to first solve this problem with brute force. Here was my logic for this part: use itertools to get all combinations of groups of 0, 1, 2, 3, 4 and 5 cards from my hand and add the first 5 - n cards from the deck so we get a five card deck. For each combination of cards we can run check_hand() and keep track of the highest rank hand, and then return that hand as the best hand. Here's the code I wrote for this part of the problem:
Poker Combination List
Lastly, I need to check each hand and print out the best hand possible. Here's the loop I wrote to do this:
This will accept one round of cards per line:
and it will output the following:
This was an interesting problem to deal with as the solution contained several parts that worked together. While solving the problem I aimed worked through to the end leaving some parts to come back to that I felt confident in solving. Instead of writing each function to check differnt hands at the beginning, I filled most of these functions with pass and moved on to write the next part that involves checking each different combination of cards. Recently having worked through python's itertools exercises on Hackerrank, the combinations functions was fresh in my mind.
While I was able to arrive at a solution that satisfied the test cases, I did not have time to think about the efficiency or Big O analysis of the problem.
There is obviously some refactoring that I could do to make things cleaner. With more time I would take an object oriented approach by making classes for cards and hands, and adding class methods to evaluate the hands.
For each round, we have to run check_hand() on each hand combination. Let's think about how many hands we have to evaluate:
We have to consider combinations of cards formed by taking out groups of 0, 1, 2, 3, 4 and 5 cards and adding the next number of cards in the deck that bring the total card count to 5, which means we have to do 5C0 + 5C1 + 5C2 + 5C3 + 5C4 + 5C5 calls to check_hand(). So the sum of total calls is 1 + 5 + 10 + 10 + 5 + 1 = 32.
For each of these 32 calls that happen when we run play(), check_hands() runs through each of the check_ functions starting with the highest value hand. As soon as it finds a 'match', check_hands() returns a number value (hand_value) corresponding to straight flush, four of a kind, etc. This value is then compared with the highest value that has been previously found (best_hand) and replaces that value if the current hand's hand rank has a higher value.
I'm not sure if there is faster way to find the best hand than the brute force method I implemented.