- Basic Strategy For Texas Holdem
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Is poker a game of skill or chance? This question has been discussed and
argued in many places and is the center of the arguments for and against
legalizing Texas holdem and other forms of poker in many places, including
online.
The answer to this question boils down to the mathematics behind the game. If
the math shows one player can win more often than another based on the
mathematical and statistical truths about Texas holdem then the game is one of
skill.
Let’s look at a few facts before moving on.
- Fact 1
Texas holdem is played with a deck of 52 playing cards, consisting of
the same four suits, and 13 ranks in every deck. You know each deck has an
ace of spades, and ace of hearts, an ace of clubs, and an ace of diamonds.
The same is true for kings, queens, and all of the ranks down through twos. - Fact 2
Over a long period of time each player will play from each position at
the table an equal number of times. In other words, each player will play in
the small blind, the big blind, under the gun, on the button, etc. an equal
number of times as other players. If you take two individual players it
might not be 100% the same, but it’ll be close. When you take thousands of
players and average their times played in each position mathematically they
each play the different positions an equal number of times. - Fact 3
The rules in each game are the same for every player at the table.
- Fact 4
The player that starts the hand with a better two card starting hand
wins the hand more often than the player with a worse hand. This has been
proven by computer simulations that run millions of hands and consider every
possible outcome.
Poker is a lot like sex. Everyone thinks they are the best, but most don’t have a clue what they are doing. — Dutch Boyd (Titanpoker.com)It is very true, but hopefully by and reading our Texas Holdem Strategy section you will at least have a clue how to do well at one of them!
Why Is This Important?
The reason all of this is important to Texas holdem players is that you can
use all of this math to help you win.
Though there are thousands of possibilities on every hand of Texas holdem,
you can use the fact that everything is based on a set of 52 cards to predict
outcomes and possibilities at every stage for every hand.
If you start the hand with two aces as your hole cards, you know that the
remaining 50 cards in the deck only have two aces. The remaining 48 cards
consist of four of each rank below the aces. At the beginning of the hand you
don’t know where any of the other cards are located, but as the hand progresses
you learn where some of them are located.
Continuing with the example, if the flop has an ace and two fours, you hold a
full house. You also know the only hand at this time that can beat you is four
fours. Because two fours are on the flop, the number of times a single opponent
has the other two fours is 1 in 1,326 hands. This is such a small percentage of
the time that you always play the full house in this example as if it’s the best
hand.
How do we know the number of times the opponent has the other two fours?
Because two fours are on the flop, let’s say the four of hearts and the four
of diamonds, so you know that your opponent has to have the four of clubs and
the four of spades. The chances of the first card in their hand being one of
these two cards are two out of 52. If they get one of them as the first card
that leaves the single other card they need out of 51 unseen cards, or one out
of 51.
You multiply two over 52 times one over 51 and this gives us the 1 out of
1,326 hands.
Basic Texas Holdem Math
Some of the math we discuss on this page can be complicated and the truth is
some players won’t be able to use it all. But that doesn’t mean they can’t be
winning Texas holdem players. The math covered in this section forms the
building blocks for the advanced math covered lower on the page.
Every Texas holdem player can use the basic math included in this section,
and if you aren’t using it yet you need to start right away.
Starting Hands
At the most basic level of Texas holdem everything starts with your starting
hand. As we mentioned above, mathematically the player who stars the hand with
the better starting hand wins more than the player with the inferior hand.
This means the first math lesson you need to learn and start using is to play
better starting hand on average than your opponents. While this can get
complicated, especially in games with many multi way pots, you still need to
learn how to play better starting hands.
If you take nothing else from this page, if you simply tighten up your
starting hand selection it’ll immediately improve your results.
Position
It’s difficult to directly relate position to mathematics, but the main thin
to know is the later your position, the better your chances to play in a
positive expectation situation. We’ll discuss expectation in a later section,
but it’s important to understand that having position on an opponent is a strong
advantage that equates to a mathematical advantage over the long run.
Outs
One of the most important skills Texas holdem players need to develop is the
ability to determine the number of outs, or cards remaining in the deck that can
complete the hand they’re drawing to. You use this information to determine your
chances of winning the hand as well as to determine the pot odds. Pot odds are
discussed in the next section, but they show you whether or not a call is
profitable in the long run when an opponent makes a bet.
We can determine how many outs you have because we know what’s in the deck
and what we need to improve our hand. If you have a king, queen, jack, and 10
after the turn you know any of the four aces or four nines complete your
straight.
This means you have eight outs. You’ve seen six cards, so the deck has 46
cards remaining in it. Don’t make the mistake of thinking about the cards that
have been folded or your opponent holds. You haven’t seen these cards so any
unseen card is still considered a possible river card.
In other words, on average, if you play this situation 46 times you’re going
to complete your straight eight times and not complete it 38 times.
You should always consider how many outs you have in every situation while
playing. B knowing your outs you have another piece of information that can help
you make profitable decisions throughout the hand.
Pot Odds
The next question many players ask after they learn how to determine their
out sis how they can use this information to make more money at the table. This
is where pot odds come into play.
Pot odds are simply a ratio or comparison between the money in the pot and
the chances you have of completing your hand. You use this ratio to determine if
a call or fold is the best play based on the information you currently have.
If you consider the example in the last section concerning the straight draw,
you know that the deck holds eight cards that complete your straight and 38
cards that don’t. This creates a ratio of 38 to 8, which reduces to 4.75 to 1.
You reduce by dividing 38 by 8.
The way you use this ratio is by comparing it to the amount of money in the
pot and how much you have to put into the pot. If the pot odds are in your favor
it’s profitable to call and if not you should fold.
If the pot has $100 in it and you have to make a $10 call the pot is offering
10 to 1 odds. You determine this the same way as above, by dividing $100 by $10.
If you’re in the situation described above of drawing to a straight on the
river you can see that a call is correct because the pot is offering 10 to 1 and
you have a 4.75 to 1 chance of winning.
On the other hand of the pot has $100 in it and you have to put $40 in to see
the river the pot is only offering 2.5 to 1 odds and your chances of hitting
your straight are still 4.75 to 1 so you should fold.
Pot odds can get complicated, especially when you start considering how they
work when you’re determining the correct play with both the turn and river to
come.
Fortunately charts are available to quickly check the odds of hitting your
hand based on how many outs you have. We’ve included one next so all you have to
do is determine your outs and compute the odds the pot is offering. Then compare
the two to see if it’s profitable to call or fold.
| Number of Outs | Turn & River Combined | River Only |
|---|---|---|
| 1 | 22.26 to 1 | 45 to 1 |
| 2 | 10.9 to 1 | 22 to 1 |
| 3 | 7 to 1 | 14.33 to 1 |
| 4 | 5.06 to 1 | 10.5 to 1 |
| 5 | 3.93 to 1 | 8.2 to 1 |
| 6 | 3.15 to 1 | 6.67 to 1 |
| 7 | 2.6 to 1 | 5.57 to 1 |
| 8 | 2.17 to 1 | 4.75 to 1 |
| 9 | 1.86 to 1 | 4.11 to 1 |
| 10 | 1.6 to 1 | 3.6 to 1 |
| 11 | 1.4 to 1 | 3.18 to 1 |
| 12 | 1.22 to 1 | 2.83 to 1 |
| 13 | 1.08 to 1 | 2.54 to 1 |
| 14 | 0.95 to 1 | 2.29 to 1 |
| 15 | 0.85 to 1 | 2.07 to 1 |
| 16 | 0.75 to 1 | 1.88 to 1 |
| 17 | 0.67 to 1 | 1.71 to 1 |
| 18 | 0.6 to 1 | 1.56 to 1 |
| 19 | 0.54 to 1 | 1.42 to 1 |
| 20 | 0.48 to 1 | 1.3 to 1 |
Expand | Shrink
When you’re determining your pot odds for the turn and river you determine
them on the turn and then if you don’t hit your draw you determine them again on
the river. This often happens, especially in limit Texas holdem. But if an
opponent moves all in on the turn you simply use the turn and river combined
odds in your decision.
Advanced Texas Holdem Math
Many beginning Texas holdem players look at a discussion about expectation
and instantly decide it’s too hard and ignore it. When they do this they
severely hurt their long term chances at being a profitable player.
We’ve broken down how to look at situations while playing poker in a simple
manner that almost any player can use below. Do yourself a favor and go into
this with an open mind. Once you understand it at a simple level you can learn
more as you gain experience. You may be surprised at just how easy it gets to
determine positive and negative expectation with a little practice.
Expectation
Expectation is what the average outcome will be if you play the same
situation hundreds or thousands of times. Once you determine the expectation you
know if a situation offers positive or negative results on average.
Your goal as a Texas holdem player is to play in as many positive expectation
situations as possible and avoid as many negative expectation situations as
possible.
You need to understand that expectation is something that can be applied to
almost any situation in poker, but it’s also subjective in many areas.
- If you play at a table where every opponent is better than you in the long
run you’re going to lose money. This is a negative expectation situation. - If you play at a table where every opponent is a worse
player than you it’s a positive expectation situation because you’re going to
win in the long run.
The problem is determining whether a situation is positive or negative
expectation when you sit down at a table with some players who are better than
you and some who are worse.
You can find many situations where it’s easier to determine expectation
mathematically, and we’ll teach you how to do this now. While this may seem
overly complicated at first, especially to do at the table while playing, you
don’t need to know exactly how negative or positive a situation is, you only
need to know if it’s positive or negative.
Once you determine if a situation is positive expectation or negative
expectation you simply remember the next time you’re in a similar situation.
Once you start determining expectation you’ll find that you learn mist
situations quickly and only have to think through an occasional situation at the
table.
The best way to see how to determine expectation is by running through a
couple examples.
Example 1
You’re facing a bet after the turn and you have four to a flush.
The pot had $400 in it and your opponent bet $100. You’re certain that if you
miss your flush draw you’ll lose and when you hit your flush draw you’ll win.
In order to see the river you have to call the $100 bet. When you lose you
lose $100, and when you win you get back $600. You get your $100 back plus the
$400 that was in the pot plus the $100 bet your opponent made.
Many players claim that part of the money already in the pot is theirs, but
once you put money into the pot it isn’t yours. The only way to get it back is
to win the pot. So you can’t consider it in any other way when determining
expectation.
The way to see if it’s positive or negative to call is to determine what will
happen on average if you play the same situation many times. Most players find
it easiest to determine by pretending to play the hand 100 times.
In this example you’re going to hit your flush 9 out of 46 times. This means
19.56% of the time you’re going to win and 80.44% of the time you’re going to
lose. To make this simple we’ll round these numbers off to 20% and 80%.
If you have to put $100 in the pot 100 times your total investment is
$10,000. The 80 times you lose you get nothing back. The 20 times you win you
get $600. 20 times $600 is $12,000. When you take the $12,000 you win and
subtract the $10,000 you lose when you play the situation 100 times, you see
that you win $2,000 overall.
To determine how much you win on average per hand simply divide the $2,000 by
100 to get a positive expectation of $20 per hand. This means that every time
you’re in this situation you’ll win on average $20.
The truth is you may win a little more because we’re ignoring the river.
Because you know you can’t win if you miss your flush, you always need to fold on
the river when you miss your draw. Every once in a while you may be able to
extract a small bet from your opponent on the river when you hit your flush,
increasing your average expectation. Sometimes it’s even correct for your
opponent to call on the river in this situation. See the next example to see
why.
Example 2
Let’s say you’re playing the same hand as above but you have a
straight and your opponent appears to be drawing to a flush. You’re on the
river, the pot has $600 in it, and the board has the third suited card hit on the
river.
If your opponent was drawing to the flush, they completed it and you’re going
to lose the hand. In this situation your opponent bets $20.
In this situation you clearly have to call.
The reason you have to call is because you can’t know for certain your
opponent was drawing to the flush. They may be bluffing or have two pair or any
other number of hands that aren’t as good as your straight.
Let’s look at the math behind this decision.
If you play the situation 100 times your total investment is $20 times 100,
or $2,000.
When you win you get $640, consisting of the original $600 pot, your
opponent’s $20 bet, and your $20 call. If you win three hands you get back
$1,920 for a loss of $80, or 80 cents per hand.
If you win at least four times you’re in a positive expectation situation.
Four wins nets $2,560 for an overall win of $560, or $5.60 per hand.
What this means is if your opponent is bluffing or has a weaker hand just
four times out of 100 or more, calling is a positive expectation situation. Four
times out of 100 is only 4%. You’ll win at least 4% of the time in this
situation.
The numbers get closer the more your opponent bets on the river, and the
closer the numbers get the more you’re going to need to use what you know about
your opponent to determine if a situation is positive or not.
Start looking at every decision you make at the Texas holdem tables in terms
of positive and negative expectation.It’s hard at first, but the more you
practice the better you’ll get at predicting if a situation offers positive
expectation.
Summary
Texas holdem math is often the only thing that separates winning and losing
players. Take the time to learn the basics now so you can improve your game in
every way possible as you gain experience. This guide is the perfect place to
start for players of every experience level.
Starting Hand Selection:Chen Formula : Sklansky Starting Hand Groups
In Texas Holdem, it is important to have good starting hand selection. This is important as it prevents you from entering pots with sub-standard hands, which could eventually lead to you losing a lot of money in the process.
'Starting hand selection' is simply choosing the good hands over the bad, and thus folding the bad hands when you get them.
It is true that any hand can win in Texas Holdem (or poker in general for that matter), but the fact of the matter is that some hands will win more than others. So if we stick with the good hands, then we should see better results in the long run.
Basic starting hand selection.
Top tier starting hands - top 2% of starting hands.
Good Texas Holdem starting hands are typically hands like big pocket pairs and big connecting cards. So some of the top starting hands would be:
- AA
- KK
- AKs
The little ’s’ indicates that the cards are suited, which will increase the value of the cards because it makes it more likely that they will be able to make a flush compared to if the cards were not suited.
This is obviously the top tier when it comes to starting hands, and if we were to only ever be dealt these starting hands we would be making a lot of money. In fact, if we folded every other hand that we were dealt and only played these hands, there is a fair chance that we would be winning money in the long run. But this would only work at the lower limits where other players probably wouldn’t be aware that we only play premium hands.
Second tier starting hands.
If we only ever played with this elite group of cards, we would be folding numerous hands along the way and missing out on other opportunities to win money. Even though these are the cream of the crop when it comes to starting hands, there are still other great hands out there that can win us a lot of money in the long run if we play them.
Such hands are:
- AK
- AQs
- AJs
- JJ
- TT
Basic Strategy For Texas Holdem
This gives us another 6 starting hands that we can play with, increasing the number of pots that we will be entering. Although these are not as good as the first set of premium hands mentioned, they are still great starting hands that should help us to win money.
Top 10 Texas Hold’em starting hands.
Now if we stick with this set of 10 starting hands we should definitely by on the right track to winning some money from poker. So for any player new to the game you should try your best to stick to the following top 10 hands (also throwing in some of top 20 hands if you have good position):
- A A
- K K
- Q Q
- A K (suited)
- A Q (suited)
- J J
- K Q (suited)
- A J (suited)
- A K
- T T
- A T (suited)
- K J (suited)
- A Q
- 9 9
- Q J (suited)
- K T (suited)
- 8 8
- Q T (suited)
- A 9 (suited)
- A J
These hands can be played profitable from most positions by experienced players, but you should only play these hands from late position if there has been no action before you (no betting or raising) if you are still learning the basics.
As your game improves, you can look to open up your starting hand requirements and require more marginal hands like suited connectors. However, if you’re new to the game you are better off sticking with the big cards that hit bigger flops and make post-flop play a hell of a lot easier for you.
Starting hand selection and table position.
Your table position should always play a big role in determining the range of hands that you choose to play with.
You should stick to playing much stronger hands from early position than you would from late position.
This means that if you are in one of the early position seats, you should stick to playing the top two tiers of hands and avoid lesser hands like; AQo, AJs, AT, KQs and so on. Conversely, if you are in late position and there has been little action before you, you can afford to play these sort of hands far more comfortably.
Why is table position important in starting hand selection?
If you are one of the first to act in a hand, you are going to be at a serious disadvantage to the rest of the players who are acting after you. Therefore, to avoid making things worse, you do not want to be entering a pot with anything less than a premium hand.
Acting first means that you are going to have little information on your opponents. If you are playing with a mediocre hand, it is likely that you are going to be in a spot where you have no idea whether you have the best hand or not. These situations are the ones that lose you the most money in poker, so avoid falling into them by playing stronger hands from early position that will make it easier to determine whether or not you have the best hand.
The importance of starting hand selection.
Starting hand selection is key because it helps to save us from sticky situations post flop, especially if we are new to the game.
Starting hand selection example.
Say for example we are not exercising very good starting hand selection and we decide to call a raise with K T. The flop then comes K 8 2 giving us top pair, which looks like a very strong hand. Our opponent bets into us and we decide to call, because after all we do have top pair.
The turn comes a 4, and our opponent bets once again. We have top pair and we call seeing as we are still happy with the strength of our hand.
The river comes a 7, and our opponent bets into us one final time. We make the call with our top pair thinking we might still have the best hand, but our opponent turns over K Q.
He also has a pair of Kings but he has the higher kicker, so he takes down the pot.
Starting hand selection example evaluation.
This is an all too common problem for poker beginners, and it could have been so easily avoided by being a little stricter with our starting hand selection. Having top pair is great, but all so often an opponent can easily beat it with a better kicker. This is why it is important to have two big cards instead of one, because the size of our kicker can play a vital role in determining who the winner of the pot will be.
You are dealt two cards in Texas Hold’em; make sure that they are both good cards before you enter a pot. An ace with a low kicker is going to lose you more money than it wins.
Don’t be tempted to call raises or enter pots with hands like A4 (rag aces) or K7, because they will just get you into more trouble than they are worth. Make sure that you are the one with the better kicker every time and take the money from the players who are entering the pots with weaker hands than you.
It is actually reasonable to bring down our starting hand requirements if we have good position. Position will give us an advantage over our opponents if we are last to act, so we do not necessarily have to have such a strong hand to play with because will be obtaining information from the way our opponent plays because they will be acting first.
This information and knowledge of our opponent’s hand from the way they play will compensate for the fact that our starting hand is a little weaker than normal. However, we still have to be prepared to fold as having position does not guarantee that we will win the hand, it simply gives an advantage. It is advised that you only enter pots with weaker hands in position once you have become a little more experienced.
Conclusion.
As you continue to play poker and gain experience from the game, it is a good idea to start expanding your starting hand requirements and experimenting here and there. However, if you are new to the game it is strongly advised that you stick to the big cards so that you give yourself the best opportunity to win money from poker.
Texas Holdem Payout Chart
If you are entering pots with a poor hand, you should be expecting to see poor results.
Basic Strategy Chart For Texas Holdem
Go back to the awesome Texas Hold'em Strategy.
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