1. Holdem Poker Starting Hands Chart
2. Poker Starting Hand Chart By Position
3. Poker Starting Hands Chart Percentages

Starting Hand Charts. When you first start playing poker it can be helpful to use a starting hand chart as a point of reference. We’ve created a couple of starting hand charts that can be used by beginners. Please click on the following links to view these charts (they will open in a new window): No-Limit Hold’em Starting Hands Chart (PDF). Poker Hand Rankings & Charts: Evaluate Your Poker Cards. Before you take us up on our free poker money offer on your way to becoming a World Series of Poker champion, you must first master the basics. The most important in the game is to understand the poker hand strength and rankings. So, the game can be beaten, and be profitable for a winning player. But even a winning player will suffer extreme swings. It's easy to understand the amount of variance you should expect in Omaha by imagining a game of Hold'em in which you move all-in preflop every hand, each time holding the same hand of A-K, and your opponent calls every hand holding Q-T.

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

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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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

Holdem Poker Starting Hands Chart

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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.

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

I didn’t consider implementing poker ranges in my first few years of playing poker. One of the problems I used to experience at the tables was what to do with hands that weren’t so obviously strong (AA, AK – raise, raise, raise!) or so obviously weak (27o, J4o – ditch ‘em faster than green grass through a goose). Hands like K9o and 86s always gave me pause when it was folded to me. “Should I open… limp… or just fold?” I’d have to ask myself these questions all the time.

The answer to this problem was to create my own poker ranges. Bringing my off-the-felt analysis to on-the-felt play simplifies the game and ensures I’m making good opening hand decisions.

Finding ranges made by others online can help as a start, but they need to be tweaked and analyzed to fit your games and stakes. You can incorporate your own play style and the population tendencies at your stakes, with your own experiences and hand histories to help guide you in creating them.

The Poker Ranges You’ll Need

Here are the ranges that you’ll have to devise for the current stakes and games you play:

• Opening Ranges – Know what hands you’ll open in various positions (cash and MTT/SNG) as well as at different levels of the MTT/SNG (Early Stages, Mid-Stages, Late Stages).
• 3betting Ranges – You need to know which opponents you’ll 3bet and what you’ll 3bet with, both for value and as semi-bluffs.
• 4betting and 3bet Defending Ranges – Same considerations as your 3bet range.

The Importance of Building Ranges

There are three main reasons why we’d want to build ranges:

1. Simplification – by creating ranges that we drill into our heads, we’ve simplified our game. We’ve put these common spots into our unconscious competence, so we can act without thinking. We’re letting our subconscious mind direct our plays, so our conscious mind has more resources to devote to analyzing more difficult, less common situations. This has the added benefit of allowing for more multi-tabling, which in turn will increase your hourly.
2. Comfort – with your subconscious making decisions for you, you’ll be more comfortable and feel less stress at the tables. You’ll be more likely to avoid tilt and can continue playing longer sessions. Stress at the tables can lead to poor decisions, and making your subconscious work for you will be a great stress reliever.
3. Bringing off-the-felt analysis to on-the-felt play – by spending time off-the-felt, creating a thoughtful range that takes into account your position, blind structure and opponent type, you’ll be able to bring your stress-free analysis of the game onto the felt. How many times have you reviewed a hand history and thought, ‘Why did I fold TT? It’s obvious he’s opening 30%+, and TT dominates him!’ When you’re working on your game off-the-felt, you’re doing so without the stress of in-game play, which allows for more clear and level headed thought. You can spot patterns and weaknesses easier off the felt. Creating your ranges then using them in-game is a way to bring your level-headed, stress-free thoughts from off-the-felt analysis to on-the-felt play.

How to Create Your Poker Ranges

Start by building your own hand table in Excel (or just download this one that I built) like the following example (6-max Mid-level Open Ranges of a micro stakes SNG):

Different colors divide ranges into sub-ranges. For example with Opening Ranges:

• Use one color for your default opening range (dark blue in the example above)
• Utilize another color (green) for an expanded range when there are fish in the blinds
• Use another color (yellow) for an even more expanded range when there are nits in the blinds
• You can use as many colors as you want to differentiate ranges. You can even toss in some bluffs vs regs (red) if you feel it necessary.

Don’t try to memorize the ranges you build. Constant use will help to naturally ingrain them in your Unconscious Competence. Just print, laminate and have at the ready as you play online, and eventually you’ll end up memorizing them (or make flash cards to ensure they get in that noggin quicker).

Consider your opponent’s ranges

When creating your Opening Ranges, you’ll have to have a good idea of what your opponents will likely call or re-raise with. For 3betting Ranges, you’ll have to be aware of what your opponents are likely opening with and what they’ll continue with. And for your 4betting and 3bet Defending Ranges, you’ll have to have a good sense of what your opponents 3bet with and what they’re likely to continue in the hand with. This exercise takes plenty of experience at your stakes. You’ll want to devote a week to creating your ranges, putting them to the test in your sessions and assessing the effectiveness of your ranges through hand history reviews. Then go back and adjust your ranges based on what you’ve found.

Using well thought out, strategic ranges like this won’t turn you into a robot; it will enable you to have an effective game plan to use vs. your opponent’s ranges. You will be bringing your off-the-felt intellect, problem solving skills and controlled emotions to your on-the-felt play.

How do I know my ranges are good?

You can do a few different things to test the precision of your ranges at your stakes and game type:

1. Use Flopzilla

This program gauges the effectiveness of each hand in your range vs. an expected opponent’s range. For example, how well does ATs on the BTN fair vs. a BB cold call range of 30%? “Oh, it has 62% equity? Yep, it’s an open.”

2. Review the Profitability of Specific Hands

Don’t know if A9s should be in your Cut-off open range? Run a filter in your poker tracking software for this hand (I use PokerTracker 4), and specifically when you Raised First-In with it in the CO. Review at least 20 hands in your history and ask yourself if this is an overall profitable hand to open with. Did you lose or win an unexpected amount with it? Do you often wind up with a kicker issue when called, or terrible equity when you call an opponent’s 3bet? Do the players at your stakes call with hands much weaker, allowing you to extract value from them post-flop?

3. Get Help from a Study Group or Forum

Post your ranges in the appropriate threads and solicit feedback. This is a more subjective way to check your ranges, but it could give you insights into aspects of your range that you never considered.

4. Get Feedback on Your Poker Ranges

Your coach (or respected friends) will have plenty of thoughts on how your ranges would fare vs. your opponents, so use his feedback to adjust your ranges, test them on-the-felt, and make adjustments as necessary.

After going through these four modes of feedback, put them into play. Once you’re confident in your ranges, laminate them and use them all the time. *Remember: When you move up in stakes, move to a new site or game format you’ll need to adjust your ranges.

It’s a time consuming process if you do it correctly, but well worth it. Try to enjoy the process, because as your skills increase and you progress through the levels, you’ll be revising your ranges over and over to account for the population tendencies of your new stakes. I hope this first time creating ranges leads to two, three, four, even five or more times for you!

Please share with me your own poker ranges by emailing them to sky@smartpokerstudy.com. I’d love to review them for you and offer you some feedback.

Poker Starting Hand Chart By Position

Until next time, study smart, play hard and make your next session the best one yet!

Poker Starting Hands Chart Percentages

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