Of the many concepts underpinning poker rules, hand rankings are perhaps the most fundamental. This is because they not only help players determine what beats what in community poker games like Texas Hold'em, but also help determine who's won a given pot in every other poker variant.

As a result, it would be impossible for a player to judge the strength of his hands without understanding poker hand rankings. Likewise it's impossible to imagine a player achieving this kind of understanding without ever looking at a standard poker hand rankings chart. After all, how could you possibly know when to hold ‘em or fold ‘em—how could you even know when and how much to bet—without knowing what your hand’s worth? It would kind of be like flying a plane blind-folded with a rabid monkey in your pants: Sure, maybe you’ve seen it on TV once or twice, but the likelihood is if you try it you’ll crash.

And yet you’d be surprised how many boneheads these days have a craving for self-destruction. Time was when most such morons were too embarrassed to show their mugs at a live poker table, but the advent of Internet poker sites has changed all that.

Now it’s all too common to read things like “Which is better, a flush or four of a kind?” or “What beats what in poker?” in the chat windows of online poker tournaments sporting pots in the tens of thousands of dollars. And, worse still, most of these “players” can’t understand what they’re doing wrong when they lose!

So to answer your first question: Yes, darling, you’ll have to learn poker hand rules in order to win at poker; you’ll probably even have to sit down some weekend, pull out a chart and study like you used to in high school. Of course, you could easily shirk this part of the game and lose your shirt on a regular basis. But here at AceHoyle.com we’d like to think our readers are a little smarter than your average amoeba.

The other thing, too, is you’d really be one dum bass if you didn’t put the time into learning poker hand rules because the following “Poker Hand Rankings” page does all the work for you. In it you’ll find a complete rundown on how poker hand rankings work, a chart showing what beats what in poker and an explanation of Texas Holdem poker hands. Plus, we’ve even included a brief history on the evolution of poker rules and hand rankings just in case you’re one of those armchair poker historians.

It’s all set to be another breezy, easy-to-understand AceHoyle.com guide, so why not take a few minutes and read it? We promise, it’ll be absolutely worth every second you spend, considering you won’t have to play the old monkey-blindfold game ever again.

Poker Hand Rules and Probabilities

In most card games played according to traditional poker rules, hand rankings follow a pretty simple principle: The more unlikely you are to draw a hand, the better it is.

Now, naturally, if you’ve already read our Razz and Omaha poker sections you’re probably leaping out of your seat right now, waving both hands like that kid in first grade with the continuous sugar buzz. And, yes, we realize some poker games do break the rules. But for the time being, let’s assume this isn’t the case, just until we’ve explained the basics.

Moving on, then, the first thing you need to understand is that all poker hands rank according to your odds of drawing them from a 52-card deck. As you probably know, there are four suits of 14 ranks in each deck, and each individual card has a 1-52 probability of winding up on top.

In terms of probability, 1-in-52 is highly unlikely. But there is hope. You see, with each card you draw your odds change. Once you take the first card off the deck it now contains 51 cards, and your likelihood of drawing something other than the card you already drew goes up.

This concept is called “dependent probability,” and it’s the basis for card counting in blackjack and for calculating outs in poker. Essentially, in both practices you are attempting to determine a deck’s composition mathematically with two known and several unknown variables. Think of this as a kind of basic algebra problem in which, instead of numbers, you have K, Q, J, 10…. all the way down.

At the start of an eight-handed Texas Hold em game, for instance, you know for certain what two cards (your own hole cards) are. You also know 17 other cards (including the first burn card) are out of the deck and that—because together these two totals equal 19—33 cards must still be in the deck. Essentially, then, you could express what you know about the game as follows:

a=K (Hearts)
b=8 (Clubs)
c through s = ?

K(ht)+8(cl)+c+d+e+f+g+h+i+j+k+l+m+n+o+p+q+r+s+33=52

What does this mean besides illustrating what a big bunch of nerds we are? Well, for one thing it helps us determine whether you’re likely to draw into a winning hand. But before we can go any further in that vein we’ll first have to bop into another set of math problems to explain the likelihood of drawing each type of hand.

Going back to our 52-card deck, then, what we need to know is how many different possible permutations there are for a simple draw. To figure this out, we first need to establish that all poker games require you have the best five-card hand—which most do—and that the order individual cards appear in when they’re revealed never matters—which it doesn’t.

Also, we should assume for the sake of simplicity that we’re playing Five Card Draw without a discard round. This is pretty integral to understanding poker hand probabilities because considering choice as a mathematical variable—as you’d do when calculating probabilities for Omaha and Texas Hold em hands—opens a whole different, impossibly complicated can of worms.

At any rate, now that we’ve established our example scenario we can use the following to determine the number of different draw combinations possible at the start of a game:

Obviously, we aren’t expecting you to know what all the mathematical gobbledygook above means. Besides pointing out that a “!” indicates a “factorial,” all we’re going to tell you is to open a math book and leave it at that.

But what is important about this equation is that it tells us exactly how many different card combinations we can possibly draw from our example deck. What’s more, it gives us the basis for a way to calculate each hand type’s probability of occurring.

The way this works is that we can use equations similar to that above to determine how many different ways you can make each hand. Again, we aren’t going to bore you by piling on more numbers. But if you are feeling froggy enough to learn about factorials you’ll eventually come up with something like the following table:

Poker Hand	Number of Permutations
Straight Flush	40
Four of a Kind	624
Full House	3,744
Flush	5,108†
Straight	10,200†
Three of a Kind	54,912
Two Pair	123,552
One Pair	1,098,240
High Card/No Pair	1,302,540
†Note: The number of permutations for both flushes and straights is actually higher because straight flushes fall under both categories. As there are 40 possible permutations of straight flushes, to find the real number of either component hand, add 40 to the listed number of permutations.

With the numbers above we can now calculate the probability for each hand in our sample poker game. Because we want to determine probability, we’ll take the number of permutations for each hand combination over the total number of possible draws. For a straight flush, the equation looks like this:

Naturally, we could have made you repeat this process for each hand, but stand-up guys that we are, we figured we’d do the math for you and cram it all into another dandy little chart:

Poker Hand	Probability of Drawing
Straight Flush	0.0015%
Four of a Kind	0.024%
Full House	0.14%
Flush	0.20%
Straight	0.39%
Three of a Kind	2.1%
Two Pair	4.8%
One Pair	42%
High Card/No Pair	50%

As you can see, the worse the hand, the higher the probability of drawing it. Really, it’s as simple as that. Of course, we realize you’re probably totally bummed to find out we did all that hard work just to return to where we started, but there is a point to our lunacy: We can use the same principles to understand how outs work.

There are essentially two ways to calculate outs: “Simple outs” and “real outs.” Simple outs, as the name implies, are easy to understand. All you have to do to find them is assume all the cards you’d need to make the best possible Texas Hold em hands are still in the deck, then calculate the probability of drawing those hands.

In the case of our K-8 (off), we can make one of several straights on the flop (assuming there’s no “wrap around,” 4-5-6-7-8, 5-6-7-8-9, 6-7-8-9-10, 7-8-9-10-J, 8-9-10-J-Q, 9-10-J-Q-K and 10-J-Q-K-A), several flushes (too many to note here since there are about 1277 combinations for any one suit), and two possible four-of-a-kinds (8-8-8-8 and K-K-K-K). Then, we treat each type of hand as one and the same and find the dependant probability for each of them assuming the flop (and turn in the case of a straight) will make them:

AND

Finally, you take the largest percentage probability as your overall likelihood of winning the hand—in this instance, .026 percent—and, comparing it to your pot odds, determine whether or not to bet.

The problem with this, though, is that it isn’t really the proper way to find outs, but only a shorthand method for short-handed games. At long-handed tables these numbers are completely inaccurate because we can assume at least some of your outs (and, therefore, the hands you could make) no longer exist in the deck. Obviously, then, your only option in long-handed games is to calculate the hand’s real outs.

Calculating real outs, however, is a highly complicated procedure that few computers can perform even using a “brute-force search” (i.e. trying all the possible combinations and permutations and averaging the resulting probabilities). And explaining it is more a matter for an advanced calculus book. So for now we’ll simply give you an overview of how they’re found, then give you a chart of ready-made approximations as an example.

As for the overview, the process computer programs use to calculate real outs is similar to what we did above—just a little more complicated: First, they determine how many different possible draws there are for a given hand; then they use this number (usually upwards of a quadrillion) to determine the probability of one or several opponents’ hands beating yours given the cards you currently have and all the possible combinations of hole cards.

Because it would take a computer millions of years to calculate all the possible outcomes, usually such programs automatically treat all similar permutations as the same—for instance, an unsuited flop with a King of Diamonds is the same as an unsuited flop with a King of Spades. They then compare the probability of the most likely of your best possible Texas Hold em hands with the overall probability that an opponent will draw better than you.

When all is said and done, the programs’ rough estimates look something like the chart below:

Probability of Facing an Ace with a Larger Kicker When Holding:	Against 1 Player	Against 2 Players	Against 3 Players	Against 4 Players	Against 5 Players	Against 6 Players	Against 7 Players	Against 8 Players
A-K	0.24%‡	0.49%	0.73%	0.98%	1.22%	1.46%	1.70%	1.94%
A-Q	1.22%	2.43%	3.63%	4.81%	5.97%	7.13%	8.26%	9.39%
A-J	2.20%	4.36%	6.47%	8.53%	10.55%	12.52%	14.45%	16.33%
A-10	3.18%	6.27%	9.25%	12.14%	14.94%	17.65%	20.27%	22.81%
A-9	4.16%	8.15%	11.98%	15.64%	19.15%	22.52%	25.75%	28.84%
A-8	5.14%	10.02%	14.65%	19.04%	23.20%	27.15%	30.90%	34.45%
A-7	6.12%	11.87%	17.27%	22.33%	27.09%	31.55%	35.74%	39.68%
A-6	7.10%	13.70%	19.83%	25.52%	30.81%	35.73%	40.29%	44.53%
A-5	8.08%	15.51%	22.34%	28.62%	34.38%	39.69%	44.56%	49.04%
A-4	9.06%	17.30%	24.80%	31.61%	37.81%	43.44%	48.57%	53.23%
A-3	10.04%	19.07%	27.20%	34.51%	41.09%	47.00%	52.32%	57.11%
A-2	11.02%	20.83%	29.55%	37.32	44.22%	50.37%	55.84%	60.71%
‡Note: All values rounded to the nearest hundredth.

Neat, hunh? Just too bad even computers can only calculate one such problem at a time. They can’t, for instance, tell you the comparative probabilities of your catching a set, four of a kind and a full house are.

And, yes, it’s also too bad we here at AceHoyle.com aren’t willing to run the numbers for every possible poker situation you’ll come across. But what can we say? We’ve still got a lot of material to cover, and we’re already running out of space.

What we will do, however, is let you in on a little secret the pros use: As you can imagine, nobody—not even MIT brats—can make such complex calculations at an actual table; so instead, many use the “Rule of Four and Two.”

Basically, The Rule of Four and Two states that before the turn—when two cards remain—the percentage probability of hitting a given number of outs (x) is equal to that number times four (x * 4).

This won’t really help you before the flop, but it will help you after it, when you absolutely have to make a decision. So next time your opponents have got you bent over the proverbial rail try it. We’re sure you’ll be pleased with the results.

Poker Hand Rankings Chart

Yes, as promised we’re now going to post a snazzy pic of the different poker hands in order of their rank. Enjoy it. You earned it after wading through all that math talk:

Texas Holdem Poker Hands

We hate to state the obvious here, but there’s absolutely no difference between Texas Holdem poker hands and other poker hands. So if you’re new to poker, you can rest assured that the chart above applies to whatever terms you just plugged into Google’s search box.

That said, Texas Hold em poker hands are particularly interesting because at the beginning of a game Texas Holdem hands consist of only two cards. This is known as your “hole,” “pocket” or “starting hand,” and it has its own Texas Hold em hand rankings chart to help players get the most out of each blind they pay:

Tier	Hands
1	A-A, A-Ks*, K-K, Q-Q, J-J
2	A-K, A-Qs, A-Js, K-Qs, 10-10
3	A-Q, A-Ts, K-Js, Q-Js, J-Ts, 9-9
4	A-J, K-Q, K-10s, Q-10s, J-9s, 10-9s, 9-8s, 8-8
5	A-9s...A-2s, K-J, Q-J, J-10, Q-9s, 10-8s, 9-7s, 8-7s, 7-7, 7-6s, 6-6
6	A-10, K-10, Q-10, J-8s, 8-6s, 7-5s, 6-5s, 5-5, 5-4s
7	K-9s...K-2s, J-9, 10-9, 9-8, 6-4s, 5-3s, 4-4, 4-3s, 3-3, 2-2
8	A-9, K-9, Q-9, J-8, J-7s, 10-8, 9-6s, 8-7, 8-5s, 7-6, 7-4s, 6-5, 5-4, 4-2s, 3-2s
*Note: “S” denotes Texas Hold em poker hands comprising suited cards.

Basically, the information above comes from compiling a bunch of computer-calculated probabilities like the ones we presented in this page’s first subsection. It originated with pro poker players David Sklansky and Mason Malmuth’s 1976 book “Hold’em Poker,” and it shows Texas Hold em hand rankings for starting hands from the best Texas Hold em starting hands (Tier 1) to the worst Texas Hold em starting hands (Tier 8).All you have to do to use it is memorize the depicted Texas Hold em hand rankings and fold whenever one of your Texas Hold em starting hands doesn’t fall within the first three tiers.

And yet, suppose you’re terrible at memorizing things. Does this mean you’re doomed to be terrible at judging hands in Texas Hold em? Actually, no because there’s a second way to determine where Texas Holdem hands would fall in a Texas Holdem hand rankings chart. And, as you’d expect, we here at AceHoyle.com are going to tell you all about it.

The “Chen Formula” is the work of poker pro Bill Chen and is probably the best shorthand way in Texas Hold em to figure out what beats what. All it involves is assigning point values to each card, then deciding how you should play based on your Texas Hold em poker hands’ total point scores.

But, to explain the process, the first thing you’ll do when you receive your Texas Hold em poker hands is assign points to the higher of each hand’s two cards according to the chart below:

High Card	Point Value
A	10
K	8
Q	7
J	6
10-2	1/2 the card’s numerical value

Next, you’ll double the number of points whenever your hands in Texas Hold em are pairs, assigning no fewer than five points if you’re holding pocket 2s and rounding up any half points.

When your Texas Hold em poker hands are unpaired, however, you’ll instead determine the gap between the higher and lower cards, where the “gap” is the number of outs for a straight—e.g. If you have a 10 and a 7, there is a gap of two because you would need an 8 and a 9 to connect for the straight.

Then, you’ll subtract the total gap value from the number of points you’ve assigned in each of your Texas Holdem starting hands so far. You’ll also score bonus points for hands in Texas Hold em that have the makings of a flush or a straight:

If both cards in one of your Texas Holdem starting hands are the same suit you’ll add two points to the total score; and if they’re connectors, i.e. their gap is zero, and the top card is a jack or lower, you’ll add one point.

Finally, tallying up your points you’ll be able to determine where your Texas Holdem starting hands fall on the standard Sklansky-Malmuth Texas Holdem hand rankings chart above.

If your hand scores 12 points or more, it is in Tier 1; if it scores 10 or 11 points, it’s in Tier 2; nine points, Tier 3; eight points, Tier 4; six or seven points, Tier 5; and five points, Tier 4. Any lower point total and you should assume your pocket cards would fall too low on a Texas Holdem hand rankings chart to be worth playing.

A Short History of Hand Rankings

As Nas

Just as in Texas Hold em what beats what hand ranking rules were integral to the game mechanics of poker’s possible forerunners. In fact, the links between these games and poker are so strong that part of one such game’s name is likely the origin of the word “ace.” That poker ancestor is the Persian game "As Nas.” And its name literally means “Aces and People” with “As,” or “ace,” referring to the game’s highest rank.

As Nas is particularly interesting because it incorporates betting, bluffing and, like Texas Hold em, a what beats what hand ranking system. Some sources say the game’s invention resulted from the Seljuq and Mongol invasions in the 11th and 13th centuries, respectively.

And yet there is no proof either invading people introduced more than the game’s most basic component, playing cards, and the oldest record of people playing As Nas dates back to 17th century.

Nor is there much by way of a surviving description of the game. And any rules that currently exist are modern conjectures based on incomplete descriptions and the number of cards in recovered As Nas decks.

One such reconstruction comes from Modar Neznanich of ModarUniversity.org and has two to five players drawing two cards from a 20- to 25-card deck—if four or fewer players participate, the deck should have 20 cards; if five players do so, it should have 25.

According to Neznanich, after the deal players would decide whether to bet. If they did not they would fold their hands and sit out the rest of the game; while if they did they would receive two more cards for a total of four.

Yet another betting round would ensue, again giving players a chance to fold and bluff. Then, Neznanich surmises, players would receive a fifth card, would bet a final time, then reveal their hands in a showdown.

As in modern poker, Neznanich says, if there were only one player remaining he would win the pot. If, on the other hand, two or more players made it to the showdown round, they would reveal their cards and the one with the highest-ranking hand would win. The hand ranking system of this version of As Nas can be summarized as follows:

As Nas Hand	Modern Equivalent
One card of each rank	Straight flush
Five identical cardsŧ	Five of a kind
Four identical cards	Four of a kind
Three identical cards coupled with two identical cards	Full House
Three identical cards	Three of a kind
Two identical cards	Two of a kind
ŧ Note: Only found in poker dice

Today, no complete As Nas deck exists as after the Islamic Revolution in 1979 Iranian authorities banned all forms of wagering and, subsequently, wagering paraphernalia. If, however, you’d like to try the game, you can make a simple As Nas deck with two packs of French tarot cards.

Basically, to create your As Nas deck you will have to emulate As Nas’s five ranks: The “As” (usually represented by a lion), the “Padishah,” or king, the “Bibi,” or queen, the “Sarbaz,” or soldier, and the “Kouli,” or huntsman.

To do so, then, you will remove the all four suits of ace, king, queen, jack and knight from one French tarot deck, then remove one suit of court cards from the second deck. Combining them, you will shuffle up, deal two cards to each of your fellow players and follow the rest of Neznanich’s rules from there.

Historical Controversy

As strong as As Nas’s claim to being the first poker ancestor is, it probably isn’t strong enough. And, according to most game historians, the biggest flaw in the As Nas hypothesis is when it appears in the historical record.

Modern card games that incorporated both betting and some semblance of a ranking structure appeared as early as 1601 in Europe in the form of blackjack. But even more compelling is how closely the French game “poque,” or “glic,” resembles modern poker, and the first mention of it dates to the 15th century.

To be sure, poque, or “pochspiel” as it survives today in Germany, isn’t poker’s immediate ancestor as the game is played with a board and the variety of winning hands is far more limited.

But the theory that it evolved into poker holds quite a bit of weight because it best explains how the modern game could have first appeared in the Louisiana Territory—a French imperial holding until the U.S. purchased it in 1803. At that point the game already displayed many of the standard mechanics that all poker variants share, including most of today’s hand rankings.

The most likely story, then, is that poker’s earliest ancestor originated in Europe. It then likely made its way to Persia, where players transformed it into As Nas, after Shah Abbas I reopened the Silk Road in the late 16th century.

As Nas, in turn, made its way back to Europe where people in the newly minted French Republic used aces as high cards, symbolically stressing how France's lowliest citizens defeated King Louis XVI. From there it traveled with France’s colonial settlers to North America, where it stewed until the region became part of the United States.

It was here that the game as we know it came into its own. Despite the former British colonies’ Puritanical culture, early 19th century America hardly had the resources to enforce morality in its western territories. As a result, the Mississippi River became a hotbed for gambling dens, casinos and riverboats.

Free from religious persecutors and state prosecutors the game flourished there, and its popularity spread from Pittsburgh to New Orleans. Eventually, due to America’s prominence in the 19th and 20th centuries, poker again spread abroad, returning to Europe and the Middle East as a totally new game..

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