Poker Math & Probabilities (Texas Hold'em) The following tables provide various probabilities and odds for many of the common events in a game of Texas hold 'em. Odds% Example Win% to-1% JJ v 77 80% v 20% A pair will flop four of a kind Two suited cards will flop a flush. Our Free Texas Holdem Poker game is targeted to players with a variety of skill levels. This Free Poker Application is designed to help players learn Texas Holdem without risking their own money as well as players who already know how to play Texas Holdem and want to test out various strategies. We have created a poker math and probability PDF chart (link opens in a new window) which lists a variety of probabilities and odds for many of the common events in Texas hold ‘em. This chart includes the two tables above in addition to various starting hand probabilities and common pre-flop match-ups. Using pot odds in Texas Hold’em will certainly help you beat the tables. While No Limit Hold’em may use more implied odds principles (as you can stand to win much more by being able to freely choose exactly how much you want to bet or raise at any given point), Limit Hold’em uses the concept of expressed pot odds incredibly well! Texas Holdem Math these days of coronavirus, we’re pretty sure all party plans are on hold. That’s OK – while we’re stuck inside, Texas Holdem Math we suggest you keep up the casino vibe and check out an online casino.

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Texas Holdem Guide Part 2

Welcome! This is part 2 of our 4 part guide where we take you from not knowing a thing about Texas Holdem to the point to where you can sit down, play your first game and possibly make some money.

Texas Holdem Guide » Part 1 » Part 3 » Part 4

In the last section I covered the basics to Texas Holdem including the rules, what hands beat what, and the different betting formats. I discussed betting in more detail, too. I basically covered all the details needed for you to be able to sit down and play your first poker game.

The plan for this next section is to dive into some basic poker strategy. Concepts that all beginner players should know, especially if they want to stop losing money and become winning players.

The specific topics I’m going to cover include table images and how they affect your strategy. Then I’ll get into some poker math. But don’t worry; it won’t be difficult to understand. But it will add some much needed structure to your game.

Texas Holdem Probabilities

Let’s get into it.

Understanding Table Image

Table image is an important concept to understand.

Table image is how you’re perceived by the other players at the table. Your image is determined by how often you play hands and how you choose to play them. So frequency and aggression, or lack thereof. Other factors come into consideration, too, such as history, mood and previous hands.

The reason why table image is so important to understand is because it will affect how you play against as opponent, as well as how your opponents play against you. If you can label an opponent with an image, you can get into their head and know how they’re going to play certain hands. With this knowledge you can think a level above and out play them.

Before I get into any strategy, though, lets go over the common table image “labels.”

Types of Table Images

• Tight – This player opens few hands. Also known as a nit.
• Loose – This type of players opens a lot of hands.
• Aggressive – Aggressive players open-raise and re-raise more often then calling and checking.
• Passive – Passive players prefer to call and check more often than raise and re-raise.

When labeling a player you’ll want to do so using a combination of my list above (using 2 of the 4 table nuances). In other words:

• Tight/Aggressive – This player opens few hands. The hands they do play are high value and raised or re-raised more often than not.
• Tight/Passive – This type of player opens few hands, and will limp, call or check when they do.
• Loose/Aggressive – This opponent will play a lot of hands, and raise or re-raise most of them. This player can come across as reckless.
• Loose/Passive – Plays a lot of hands, but calls, checks or folds often.

Table images aren’t static either. Table images are dynamic. They can change on a dime, either from good players switching gears and adapting to their opponents, or maybe due to multi-tabling, variance/tilt, mood, and so on.

The best way to determine a player’s image is to simply pay attention. How many hands does your opponent play? How do they play their hands? What do they showdown?

However, it’s not always possible to pay close enough attention to know what someone’s image is. In these cases you can use other clues to help you out:

• Check Sharkscope for your opponent’s stats.
• What is your opponent’s VIP status?
• Are your opponents multi-tabling?
• Do you know if your opponent participates (regularly) in forums?

As a rule of thumb, if your opponent has (good) stats, high VIP status, multi-tables and participates in forums, they are probably a good player (or trying to become one). The recommended strategy for good players (or to become a good player) is to be tight aggressive. Open high quality hands, and put a lot of money into the pot with them.

Texas Holdem Mathematics

This isn’t always the case, but it just gives you something to go off of if you’re not sure about an opponent or two at your table.

How Image Will Affect Your Strategy?

Ok, so now that we know what image is and how to determine the type of player someone might be, lets look at how this might affect our strategy.

The rule of thumb is to do the opposite of your opponent. In other words, if your opponent is a maniac (reckless, loose-aggressive player), they are opening a lot of hands. So your strategy should be to play fewer hands. To be clear, though, that means fewer hands than them, but possibly (ok, more likely) more hands than you usually play.

To give you an example, say your opponent opens more than 50% of their hands. You decide to play K9o and hit top pair on the flop (rainbow). Against your tighter or average player, you probably wouldn’t play K9o, let alone call too many bets with it postflop. However, against a maniac it’s the equivalent to playing KQ or AQ against an average or good player. So you should treat it as such. If your opponent bets, you call and plan on showing down your top pair.

Lets look at another example. Say you open-raise with KQ and an opponent that opens less than 10% of hands re-raises you. Think about it for a second. What type of hands does someone like this play, let alone re-raise? Aces, kings, queens and maybe AK. All better hands than KQ, so it makes sense to fold.

Do you see what I’m getting at here? Your opponent’s table image will give you an idea as to what hands they play. Then you take this information and determine how good your hand is, if it’s likely to beat theirs and then play accordingly.

Keep Your Table Image in Mind Too

It’s important to keep your own image in mind, too. Have you opened a lot of hands lately? Did you raise them all (like you probably should have)? Or have you gone the last 3 orbits without a hand worth playing? You need to be aware of these things so that you know what to expect from your opponents when you do decide to play your hand. You can use your table image to your advantage, too.

For example, say you haven’t played the last two orbits. You’re on the button, everyone folds to you and you look down to see 96s. Not a great hand, but it’s suited and connected. More importantly, though, is that you haven’t played a hand in so long that if you open-raise here, the blinds will think that you actually have a hand. They’ll be more likely to fold. The bonus (if you want to call it that) is that if they do call, your 96s can hit the flop hard (and be disguised), it’s easy to play postflop and you’ll be in position.

On the other hand, if you open-raised the last 7 hands, you might want to reconsider opening the next hand while holding JTo. At some point you have to expect that someone will get tired of you “bullying the table” and take a stand. In some cases you can use this to your advantage, but in others it’s just too close a call to bother with. So you’re better off folding and preserving or improving your table image.

That’s really all there is to table image and strategy. I hope you see the importance of table strategy and understand how to label your opponents and adjust your strategy for each type of player. It’s real simple, yet many players don’t pay attention or care enough to use it. Don’t be this player.

Poker Math for Beginners

What I’m going to cover in this next section is some poker math. Don’t worry, it won’t be as hard as you might think. So long as you can add, subtract, multiply and divide small numbers, you should be fine.

The following math concepts cover poker outs and pot odds. These are important to learn because they will teach you how to profitably draw to hands. You’ll see why drawing to gut shot straight draws are a bad idea, and how to choose your spots for when to draw to flushes and open-ended draws.

So with that in mind lets get right into it. The first thing I’m going to cover are poker outs.

Poker Outs

Lets start with defining poker outs. What is an out?

Poker outs are cards left in the deck that can improve your hand. For example, say you hold JTo and the flop is A-K-2 rainbow. A queen would improve your hand, so that would be an “out.” Since there are 4 queens in a deck of cards, you would have 4 outs.

Lets look at another example. Say you have AK of hearts. The flop is Q-8-3, two hearts and one club. You (should) know that there are 52 cards in a deck, 13 cards of each suit. Since you can see 4 hearts, basic subtraction will tell us that there are 9 cards left in the deck that will improve our hand to a flush, or 9 outs. In this case an ace or king would improve our hand, too, so if we assume there are 3 aces and 3 kings left in the deck, that means we actually have 15 outs to improve our hand.

Simple. Right?

Now before I move forward, there are 3 important points I want to make:

1. You should only discount the cards you can see. In my example above I don’t know if one of my opponents has an ace or king. Since I don’t know for a fact, I just assume they’re all available, as opposed to trying to discount them.
2. Don’t count outs to hands that won’t likely be the best at showdown. In other words, in my first example with JT, I didn’t count the jack or ten as an out because with an ace or king on the flop I don’t think jack or ten high will be good. However, in my AK example I think making a pair of aces or kings can be the best hand, so I count those as outs.
3. Don’t double count your outs. If the ace of spades will make you both a pair and a flush, don’t count that as two outs. That’s still only one out, even though it can make two hands.

Ok, so now we know what outs are, how to count them and what not to do. This is only half the battle. We now need to convert our outs into odds.

Converting Outs to (Card) Odds / Percentages

The next step is to take our outs and turn them into odds. There are two ways to calculate card odds in poker.

The Rule of 2 and 4

The rule of 2 and 4 is the easiest and fastest way to take your outs and turn them into odds. What you do is this —

If you want to know the odds of hitting your hand over one street (flop to turn, or turn to river) multiply your outs by 2. Then add 1. For example, if you have 8 outs, then the odds of hitting your hand on the next street is 17% ( (8*2) + 1). If you want to know your chances of hitting your hand by the river (from the flop), multiply your hand by 4 and add 1. With 8 outs this would be approximately 33%.

Note: Believe it or not, this method is very close, usually within 1-2%. That’s close enough, too, because if you’re worried about that margin of error you’re chasing hands you shouldn’t be.

Texas Hold'em Mathematics

Do you see how easy this is? It takes seconds to do. The rule of 2 and 4 is much better than the next method which is…

Doing the Math

The other way you can figure out your card odds is to do the math (the long way). I don’t recommend doing this while playing because it takes too long to do. I’m only sharing it because I think you might find it interesting or useful.

So what you do is this — take the number of cards you see and subtract that from the total number of cards in a deck. So, on the flop you would know 5 cards — your 2 hole cards and the 3 community cards. So we subtract 5 from 52, giving us 47.

Then using a calculator, what we do is take the number of outs we have and divide that by the cards left in the deck. Using my example above, take 8 and divide that by 47. You’ll see that gives us 17%, which is for one street, and matches what I said above. Then multiply that by 2 for two streets, which is 34%, just slightly more than my example above.

As you can see, this way is more time intensive to do.

But that’s all there is to poker outs; how to count them and turn them into odds and percentages. Keep this in mind as we move to the next section because we will need to compare these card odd percentages to our pot odds. That will determine whether or not we’re drawing profitably to a better hand.

Pot Odds

Like the last section, lets start with defining what pot odds are.

Pot odds is the number you come up with when you do the math between what is in the pot and how much you have to invest to win it.

Pot odds are important because you’ll compare them to your card odds to determine whether or not it makes sense to draw to a better hand. You may also use pot odds in tournament or sit and go situations where your opponent shoves all in, you determine their range (a more advanced topic) and you need to compare your pot odds to their hand range to determine if it’s profitable for you to call them.

The bottom line — pot odds are important. Pot odds are easy to calculate, too.

How to Calculate Pot Odds

Calculating pot odds is simple to do. I’ll explain it using an example so you can see how it’s applied to a real situation.

Say you are in a hand, in position, with one other player. There are 250 chips in the pot, the flop is A-K-4 rainbow and you have JTs. Your opponent bets 100 chips. To figure out your pot odds you just look at the ratio of money in the pot to how much you need to call to win it. In this case, the ratio would be written out as 250 to 100. To make your pot odds easier to use, however, you’ll want to find a common denominator and simplify the ratio as much as possible. So, 250 to 100 turns into 2.5 to 1.

However, pot odds are going to be easier to use if they’re in the form of a percentage. Remember that’s how our card odds from the last section are written. To do this, you’ll need to take what you need to invest, and divide that by the total you stand to win (the pot + your investment). Our equation would look like this — 1/3.5. This comes out to 28.5%.

Note: This will be hard to do in-game, so once I show you how to use this information, I’ll show you a few common pot odd percentages to memorize.

Alright, so lets use this information.

Using my example above, lets decide whether or not it makes sense to draw to our gut shot draw. The only card we can be sure will improve our hand is a Q, so we know we have 4 outs. From the flop to the turn (all we’ll worry about for now), we know that we’ll make our hand about 9% of the time.

We’ve already figured out our pot odds — 28.5%.

To (quickly) determine if the hand you’re drawing to is profitable or not, just compare the two percentages. If thepercentage that you’ll make your hand is higher than your pot odds, then it’s profitable. However, if it’s smaller than your pot odds, like in this case, then it’s not.

That’s all there is to it. There is further math you can do to see how this works, like calculating equity over the long run. But I’ll leave that for you to play around with.

Texas Holdem Math Book

Pot Odds worth Memorizing

I mentioned a second ago that it will be easier for you if you memorize common pot odd percentages. Memorize the following odds/percentages and you’ll find life a little easier — at least at the poker tables.

Pot odds of…

• 1:1 – 50%
• 1.5:1 – 40%
• 2:1 – 33%
• 2.5:1 – 28.5%
• 3:1 – 25%
• 4:1 – 20%

That’s all there is to it. So, to summarize the math section of this guide:

• Outs are the cards left in the deck to improve your hand.
• The rule of 2 and 4 is the fastest way to figure out your chances of improving.
• Turn your fractions / card odds into percentages.
• Compare your card odds to your pot odds. If your card odds are higher, you can profitably call, and if they’re smaller, then it’s better to fold.

There are exceptions of course, like implied odds, worrying about stack sizes, history, hand reading and so on. Those are advanced topics, though, which are for another day. This is what I’d stick to for now. It’ll keep you from making the most common errors that beginners tend to make (like chasing gut shot draws).

Conclusion — End of Part 2 of Our Texas Holdem Guide

Texas Hold'em Math Formulas

So that wraps up the second part of our guide. Our first section took you from knowing nothing to the basics of how to play Texas Holdem, and this part just took you from a losing player to (at least) a breakeven player.

You’re welcome ;)

In the next section I’m going to cover more important concepts. Things like table position, bluffing tips for beginners and the basics to playing from the blinds. Concepts that tend to trip beginners up and cost them a lot of money.