The least common hands are the suited hands. Each suited hand have four possible combinations. For example A-Ks: A♥-K♥, A♦-K♦,A♣-K♣, A♠-K♠. Starting hands charts. All starting hands in Texas hold'em can be displayed shematically in a chart: All hands, both with suited and offsuited versions are included. Probabilities in Texas Hold'em Introduction An understanding of basic probabilities will give your poker game a stronger foundation, for all game types. This article discusses all the important, and interesting, probabilities that you should be aware of. Probabilities in poker Probability means the degree of certainty that a possible event will.
It depends on how you define 'starting hand.' There are permutations of any two cards. There are (52.51)/2 combinations of two cards, if you treat (Card A, Card B) as being equal to (Card B, Card A), e.g. Ace of spades, king of hearts as being equal to king of hearts, ace of spades). The total is 1326. This list of the top 10 best starting hands for Texas Hold 'em is a good place to start learning. Do keep in mind, however, that there is some disagreement over which hands are the best, and it does depend in part on your skill level and style of play. Also, a great starting hand can turn bad quickly with the wrong community cards.
I ran into a friend of mine yesterday who was jealous because a bunch of our mutual friends were playing Texas holdem Saturday night. She was bummed because she never learned to play poker.
I told her it was easy to learn, and the first thing she needed to do was learn about poker hands and poker hand rankings.
And that gave me the subject for my latest blog post.
Poker Hands Are Almost Always Made Up of Five Cards
In fact, I’m not sure of an exception to this rule. Poker isn’t one game, of course, it’s multiple games that have a couple of things in common:
- They have a betting structure where you can decide to continue to play or not
- They use five-card hands that usually win based on the standard poker hand rankings
The variations are nearly infinite. But one thing most variants have in common is that, no matter how many cards are used in the game, you win the pot if you have the best five-card hand at the end of the hand.
If you’re playing Seven-Card Stud, for example, you get seven cards, but you use the best five-card hand you can make to determine the winner.
If you’re playing Texas holdem, you have two cards in your hand and five face-up cards that you share with other players. You make the best five-card hand you can using any combination of those seven cards.
Possible Starting Hands In Texas Holdemas Hold Em
If you’re playing Omaha, you have four cards in your hand and five face-up cards that you share with the other players. But you still make the best five-card hand that you can, using two cards from your hand and three cards from the community cards.
Ranks and Suits
Poker is almost always played with a standard 52-card deck of playing cards. Each card has two attributes:
- A rank
- A suit
You have four suits—clubs, diamonds, hearts, and spades. In each of those suits, you have 13 ranks—2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, and ace. The ace is unusual because it can be the highest OR the lowest card. It can rank above the king, but it can also count as a “1.”
Flushes, Straights, and Straight Flushes
The ranks and suits become important when you have a flush, a straight, or a straight flush.
A flush is just five cards of the same suit. They can all be clubs, diamonds, hearts, or spades, it doesn’t matter. If you face an opponent who also has a flush, the player whose flush has the highest ranked card wins. An ace would be the highest card in any flush.
A straight is just five cards where the ranks are in succession. It doesn’t matter what suit the cards are, it only matters that the cards are made up of consecutive ranks.
For example, an A2345 is a straight, but so is a 10JQKA.
In the prior example, the ace counts as 1, but in the second, the ace counts as the highest card in the hand, above the king.
If multiple opponents have a straight, the one with the highest card in the straight wins. But if the ace is used as a 1 to make an ace to 5 straight, it counts as a low card for this purpose.
A straight flush is a hand where the cards are all consecutive, AND they’re all of the same suit.
Pairs, Trips, Quads, and Full Houses
All the other possible poker hands you can make have nothing to do with consecutive ranks or suited cards. They have to do with how many cards of a specific rank you have.
A pair, for example, is a hand where you have two cards of the same rank and three other cards. If you and your opponent both have a pair, the higher-ranked pair wins. A pair of aces beats a pair of kings, for example.
Two pair is a hand made up of two cards of one rank and two cards of another rank, plus a third card of still another rank. Three of a kind is a hand made up of three cards of the same rank and two other cards.
A full house is a three of a kind with a pair, three cards of one rank and two cards of another. And, of course, four of a kind is four cards of the same rank.
In all these examples, the highest-ranked card determines the winner.
The Standard List of Poker Hand Rankings
So far, I’ve discussed the various poker hands you can have in relation to the attributes of the cards. I haven’t given them a ranking. Almost all poker games use the same ranking system.
From best to worst, here are the poker hand rankings:
- Straight flush
- Four of a kind
- Full house
- Flush
- Straight
- Three of a kind
- Two pair
- A pair
A straight flush always beats four of a kind or anything lower. A four of a kind always beats a full house or anything lower. And so on, through the end of the poker hand rankings list.
The first element of poker strategy any new poker player should master is the poker hand rankings. If you don’t know what beats what in poker, you can’t possibly make the correct decisions.
How These Hand Rankings Are Determined
The poker hand rankings are sorted this way based on the probability you’ll be dealt such a hand. The less likely it is to get a hand, the more it’s worth.
For example, the probability of getting a four of a kind is 72,192 to 1. The probability of getting a full house, on the other hand, is 4,165 to 1. That’s a dramatic difference.
Also, most poker hand ranking lists include a separate listing for a royal flush, which is just the highest possible straight flush you can have. The only thing that makes it different from any other straight flush is how high your highest card ranks, but we don’t break four aces into a separate listing.
So, I don’t break a royal flush out into its own listing either.
Starting Hand Rankings in Texas Holdem
I could write about poker hand rankings all day, but for now, let me just address starting hands in Texas holdem.
Your starting hand in a game of Texas holdem consists of the two cards you get face down at the beginning of the game. These are the two cards you get to look at before deciding whether to play the hand at all.
The best possible starting hand in Texas holdem is a pair of aces. Often, a pair of aces can win a hand even if it doesn’t improve with the other cards. The rankings continue from there like this:
- Pocket aces
- Pocket kings
- Pocket queens
- Ace king suited
- Pocket jacks
- Pocket 10s
- Ace queen suited
- Ace king (not suited)
- Ace jack suited
- King queen suited
This might seem like a hard chart to memorize, but think about it like this… These are the best possible starting hands in the game. You should raise with any of them unless you have reason to believe that someone else has a better starting hand.
For example, if you have a pair of queens, you should raise with it, unless a couple of stingy players in front of you have already bet and raised. Even then, it often makes sense to raise with the queens.
Also, these hands all fall into categories. First are the pairs. Any pair of 10s or higher is a premium starting hand, even though there’s a huge difference between pocket 10s and pocket aces.
Then, you have the suited aces. An ace and a king, an ace and a queen, or an ace and a jack are great hands if they’re of the same suit. You have the potential to make the best possible flush, the best possible straight flush, and the best possible straight.
And if you miss those, you still might catch another ace or pair one of the other big cards, in which case, you’ll have a big pair with the best possible kicker.
Ace king offsuit is prized mostly for its high pair potential, but also for its high straight potential. And king queen suited has lots of potential to make big flushes and straights.
Conclusion
Poker hands aren’t that hard to understand, but if you’re a beginner, it’s probably the first thing you should learn.
Of course, the second thing you should learn is your betting options at various points in the game.
Did you already know everything about poker hand rankings? Did I leave something out? Let me know in the comments.
For a great training video on poker combinatorics, check out this poker combos video.
'Combinatorics' is a big word for something that isn’t all that difficult to understand. In this article, I will go through the basics of working out hand combinations or 'combos' in poker and give a few examples to help show you why it is useful.
Oh, and as you’ve probably noticed, 'combinatorics', 'hand combinations' and 'combos' refer to the same thing in poker. Don’t get confused if I use them interchangeably, which I probably will.
What is poker combinatorics?
Poker combinatorics involves working out how many different combinations of a hand exists in a certain situation.
For example:
- How many ways can you be dealt AK?
- How many ways can you be dealt 66?
- How combinations of T9 are there on a flop of T32?
- How many straight draw combinations are there on a flop of AT7?
Using combinatorics, you will be able to quickly work these numbers out and use them to help you make better decisions based on the probability of certain hands showing up.
Poker starting hand combinations basics.
- Any two (e.g. AK or T5) = 16 combinations
- Pairs (e.g. AA or TT) = 6 combinations
If you were take a hand like AK and write down all the possible ways you could be dealt this hand from a deck of cards (e.g. A K, A K, A K etc.), you would find that there are 16 possible combinations.
- See all 16 AK hand combinations:
Similarly, if you wrote down all the possible combinations of a pocket pair like JJ (e.g. JJ, JJ, JJ etc.), you would find that there are just 6 possible combinations.
- See all 6 JJ pocket pair hand combinations:
So as you can see from these basic starting hand combinations in poker, you’re almost 3 times as likely to be dealt a non-paired hand like AK than a paired hand. That’s pretty interesting in itself, but you can do a lot more than this…
Note: two extra starting hand combinations.
As mentioned above, there are 16 combinations of any two non-paired cards. Therefore, this includes the suited and non-suited combinations.
Here are 2 extra stats that give you the total combinations of any two suited and any two unsuited cards specifically.
- Any two (e.g. AK or 67 suited or unsuited) = 16 combinations
- Any two suited (AKs) = 4 combinations
- Any two unsuited (AKo) = 12 combinations
- Pairs (e.g. AA or TT) = 6 combinations
You won’t use these extra starting hand combinations nearly as much as the first two, but I thought I would include them here for your interest anyway.
It’s easy to work out how there are only 4 suited combinations of any two cards, as there are only 4 suits in the deck. If you then take these 4 suited hands away from the total of 16 'any two' hand combinations (which include both the suited and unsuited hands), you are left with the 12 unsuited hand combinations. Easy.
Fact: There are 1,326 combinations of starting hands in Texas Hold’em in total.
Working out hand combinations using 'known' cards.
Let’s say we hold KQ on a flop of KT4 (suits do not matter). How many possible combinations of AK and TT are out there that our opponent could hold?
Unpaired hands (e.g. AK).
How to work out the total number of hand combinations for an unpaired hand like AK, JT, or Q3.
Method: Multiply the numbers of available cards for each of the two cards.
Word equation: (1st card available cards) x (2nd card available cards) = total combinations
Word equation: (1st card available cards) x (2nd card available cards) = total combinations
Example.
If we hold KQ on a KT4 flop, how many possible combinations of AK are there?
There are 4 Aces and 2 Kings (4 minus the 1 on the flop and minus the 1 in our hand) available in the deck.
C = 8, so there are 8 possible combinations of AK if we hold KQ on a flop of KT4.
Paired hands (e.g. TT).
How to work out the total number of hand combinations for an paired hand like AA, JJ, or 44.
Method: Multiply the number of available cards by the number of available cards minus 1, then divide by two.
Word equation: [(available cards) x (available cards - 1)] / 2 = total combinations
Word equation: [(available cards) x (available cards - 1)] / 2 = total combinations
Example.
How many combinations of TT are there on a KT4 flop?
Well, on a flop of KT4 here are 3 Tens left in the deck, so…
C = 3, which means there are 3 possible combinations of TT.
Thoughts on working out hand combinations.
Working out the number of possible combinations of unpaired hands is easy enough; just multiply the two numbers of available cards.
Working out the combinations for paired hands looks awkward at first, but it’s not that tricky when you actually try it out. Just find the number of available cards, take 1 away from that number, multiply those two numbers together then half it.
Note: You’ll also notice that this method works for working out the preflop starting hand combinations mentioned earlier on. For example, if you’re working out the number of AK combinations as a starting hand, there are 4 Aces and 4 Kings available, so 4 x 4 = 16 AK combinations.
Why is combinatorics useful?
Because by working out hand combinations, you can find out more useful information about a player’s range.
For example, let’s say that an opponents 3betting range is roughly 2%. This means that they are only ever 3betting AA, KK and AK. That’s a very tight range indeed.
Now, just looking at this range of hands you might think that whenever this player 3bets, they are more likely to have a big pocket pair. After all, both AA and KK are in his range, compared to the single unpaired hand of AK. So without considering combinatorics for this 2% range, you might think that the probability break-up of each hand looks like this:
- AA = 33%
- KK = 33%
- AK = 33%
…with the two big pairs making up the majority of this 2% 3betting range (roughly 66% in total).
However, let’s look at these hands by comparing the total combinations for each hand:
- AA = 6 combinations (21.5%)
- KK = 6 combinations (21.5%)
- AK = 16 combinations (57%)
So out of 28 possible combinations made up from AA, KK and AK, 16 of them come from AK. This means that when our opponent 3bets, the majority of the time he is holding AK and not a big pocket pair.
Now obviously if you’re holding a hand like 75o this is hardly comforting. However, the point is that it’s useful to realise that the probabilities of certain types of hands in a range will vary. Just because a player either has AA or AK, it doesn’t mean that they’re both equally probable holdings - they will actually be holding AK more often than not.
Analogy: If a fruit bowl contains 100 oranges, 1 apple, 1 pear and 1 grape, there is a decent range of fruit (the 'hands'). However, the the fruits are heavily weighted toward oranges, so there is a greater chance of randomly selecting an orange from the bowl than any of the 3 other possible fruits ('AK' in the example above).
This same method applies when you’re trying to work out the probabilities of a range of possible made hands on the flop by looking at the number of hand combinations. For example, if your opponent could have either a straight draw or a set, which of the two is more likely?
Poker combinatorics example hand.
You have 66 on a board of A J 6 8 2. The pot is $12 and you bet $10. Your opponent moves all in for $60, which means you have to call $50 to win a pot of $82.
You are confident that your opponent either has a set or two pair with an Ace (i.e. AJ, A8, A6 or A2). Don’t worry about how you know this or why you’re in this situation, you just are.
According to pot odds, you need to have at least a 38% chance of having the best hand to call. You can now use combinatorics / hand combinations here to help you decide whether or not to call.
Poker combinatorics example hand solution.
First of all, let’s split our opponent’s hands in to hands you beat and hands you don’t beat, working out the number of hand combinations for each.
Worst Starting Hands In Texas Holdem
Adding them all up…
Seeing as you have the best hand 79% of the time (or 79% 'equity') and the pot odds indicate that you only need to have the best hand 38% of the time, it makes it +EV to call.
So whereas you might have initially thought that the number of hands we beat compared to the number of hands we didn’t beat was close to 50/50 (making it likely -EV to call), after looking at the hand combinations we can see that it is actually much closer to 80/20, making calling a profitable play.
Being able to assign a range to your opponent is good, but understanding the different likelihoods of the hands within that range is better.
Poker combinatorics conclusion.
Working out hand combinations in poker is simple:
- Unpaired hands: Multiply the number of available cards. (e.g. AK on an AT2 flop = [3 x 4] = 12 AK combinations).
- Paired hands: Find the number of available cards. Take 1 away from that number, multiply those two numbers together and divide by 2. (e.g. TT on a AT2 flop = [3 x 2] / 2 = 3 TT combinations).
By working out hand combinations you can gain a much better understanding about opponent’s hand ranges. If you only ever deal in ranges and ignore hand combinations, you are missing out on useful information.
It’s unrealistic to think that you’re going to work out all these hand combinations on the fly whilst you’re sat at the table. However, a lot of value comes from simply familiarising yourself with the varying probabilities of different types of hands for future reference.
For example, after a while you’ll start to realise that straight draws are a lot more common than you think, and that flush draws are far less common than you think. Insights like these will help you when you’re faced with similar decisions in the future.
The next time you’re doing some post session analysis, spend some time thinking about combinatorics and noting down what you find.
Poker combinatorics further reading.
Hand combinations in poker all stem from statistics. So if you’re interested in finding out more about the math side of things, here are a few links that I found helpful:
- Combinations video - Youtube (all the stuff on this channel is awesome)
If you’re more interested in finding out more about combinations in poker only, here are a few interesting reads:
Go back to the awesome Texas Hold'em Strategy.
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