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
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
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
- Texas Hold’em Initiative. In an effort to improve border security, Texas has implemented the Texas Hold'em Initiative.The goal of this initiative is to reduce human and illegal contraband smuggling in commercial vehicles.
- A poker variation in which players receive 2 downcards that may be used individually and 5 face-up cards that are shared among all players. Players combine any number of their personal cards with the shared cards to make the highest 5-card hand according to standard hand rankings.
- If you play or watch Texas Hold'em at all, you'll start hearing people announce they've got 'Big Slick' or 'I've got snowmen!' They're not being literal - they're talking about the hole or pocket cards they've been dealt in the lingo of poker.
Texas Hold 'Em is a type of poker game that can be played with 2-10 players. The dealer can either be a designated dealer who does not play or the dealer can be a player. Texas Hold 'Em is called a community game which means that there are community cards that everyone who has bet or checked into the hand can use. Texas hold 'em (also known as Texas holdem, hold 'em, and holdem) is one of the most popular variants of the card game of poker. Two cards, known as hole cards, are dealt face down to each player, and then five community cards are dealt face up in three stages.
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,Here’s an Example
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
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
You multiply two over 52 times one over 51 and this gives us the 1 out of
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.
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.
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.
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
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.
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 theExample
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
Texas Hold'em Meaning Games
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 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
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
The best way to see how to determine expectation is by running through a
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
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
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
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,
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
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
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.
Commercial Driver License (CDL) Disqualifications
If you hold a commercial driver license (CDL) or commercial learner permit (CLP), you may have your CDL or CLP disqualified for a specified amount of time if you are convicted of certain offenses. A list of the most common types of convictions with the disqualification period is provided in the table below.
NOTE: You may also be disqualified from operating a commercial motor vehicle if you are a CDL or CLP holder and are convicted of certain types of moving violations in your personal vehicle. For more information on those types of violations and other CDL rules, please visit Texas Transportation Code 522.081.
Commercial Driver License (CDL) Disqualifications
|Alcohol, leaving the scene of an accident or commission of a felony||At least one year for first offense, lifetime for a second offense|
|Alcohol, leaving the scene of an accident or commission of a felony while operating a commercial motor vehicle placarded for hazardous materials||At least three years for first offense; lifetime for second offense|
|Two serious traffic offenses (i.e. excessive speeding, reckless driving, improper or erratic lane changes, following too closely, etc.) within three years||60 days|
|Three serious traffic offenses (i.e. excessive speeding, reckless driving, improper or erratic lane changes, following too closely, etc.) within three years||120 days|
|Railroad-highway grade crossing violations||60 days for first offense; 120 days for second offense within 3 years; at least 1 year for third offense within 3 years|
|Using a motor vehicle in the commission of a felony||Lifetime|
Texas Hold’em Initiative
In an effort to improve border security, Texas has implemented the Texas Hold'em Initiative. The goal of this initiative is to reduce human and illegal contraband smuggling in commercial vehicles.
Any individual who knowingly transports an alien is subject to federal penalties, including a fine, imprisonment, and lifetime disqualification of commercial driving privileges.
Texas Holdem Check Meaning
In certain circumstances, you may be eligible to request a hearing to contest the disqualification of your CDL. If the request is submitted within the required 20 days, the Texas Department of Public Safety (DPS) will send you a letter to the address on record. The letter will provide the date, time and location of the hearing. Please allow up to 120 days for a hearing to be scheduled. Requests made after the required 20 days will be denied and you will be notified by mail that the disqualification remains in effect.
Hearings are conducted in a municipal or justice court in the county where you live. During the hearing, you are responsible for providing facts to the hearing officer who will determine if the grounds for the disqualification are valid.
NOTE: If you have already been through the administrative hearing process and the decision resulted in the disqualification of your commercial driver license, you may be eligible to appeal that decision.
CDL Reinstatement Requirements
If your CDL or CLP is disqualified due to the conviction of two or more serious traffic offenses, you will not have any reinstatement requirements. The CDL/CLP is automatically reinstated after the required disqualification period if there are not any other enforcement actions against your driving record. CDL and CLP holders are not eligible to take the driver safety course.
The Department may reinstate any driver disqualified for life for offenses described below after 10 years, if that person has voluntarily entered and successfully completed an appropriate program approved by the Department*. Offenses not categorized as drug or alcohol-related do not have an established course requirement; therefore, course attendance is not required:
- Being under the influence of alcohol
- Being under the influence of a controlled substance
- Having an alcohol concentration of 0.04 or greater while operating a CMV
- Refusing to take an alcohol test as required under implied consent law or regulations
- Leaving the scene of an accident
- Using a vehicle to commit a felony other than a felony involving manufacturing, distributing, or dispensing a controlled substance
- Driving a CMV when, as a result of prior violations committed operating a CMV, the driver's CLP or CDL is revoked, suspended, or cancelled, or the driver is disqualified from operating a CMV
- Causing a fatality through the negligent operation of a CMV including, but not limited to, the crimes of motor vehicle manslaughter, homicide by motor vehicle or negligent homicide
You are not eligible to apply for reinstatement if you have been convicted of human trafficking or a felony involving the manufacturing, distributing, or dispensing of a controlled substance. To request reinstatement, you must be able to certify to the CDL Disqualification Reinstatement form (CDL-8) and submit it to the following address for consideration:
Texas Department of Public Safety
Issuance Services - CDL Help Desk
P.O. Box 4087
Austin, Texas 78773-0320
Upon receipt of your request for reinstatement, your driver record will be reviewed for eligibility and a notification of determination will be provided to you by mail. If you are approved for reinstatement, you will be required to apply as an original CDL applicant at your local driver license office. For additional information on obtaining a CDL, visit our webpage How do I apply for a Commercial Driver License.
*49 Code of Federal Regulations Part §383.51, Texas Transportation Code §522.082 and 37 Texas Administrative Code §16.68
Driver Eligibility Status
To check the status of your driver license or to determine if you are eligible for reinstatement, visit the License Eligibility webpage. This page will provide you with information on what you will need to reinstate your driver license or driving privilege, including any fees you may owe. Once all compliance items have been processed and your mandatory suspension period has ended, your driver eligibility status will be updated to reflect 'eligible'.