The main underpinning of poker is math – it is essential. For every decision you make, while factors such as psychology have a part to play, math is the key element.
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- Is Ace High Or Low In Texas Holdem Poker
In this lesson we’re going to give an overview of probability and how it relates to poker. This will include the probability of being dealt certain hands and how often they’re likely to win. We’ll also cover how to calculating your odds and outs, in addition to introducing you to the concept of pot odds. And finally we’ll take a look at how an understanding of the math will help you to remain emotional stable at the poker table and why you should focus on decisions, not results.
What is Probability?
The game of poker - Texas Hold'em in particular - is exciting and vibrant. An Ace can count as either a '1' or the high face card. Three of a Kind. The Nut Low: The lowest possible hand in. In Texas Hold'em an Ace can be high or low. So a low example is the straight you talked about also known as a wheel. It can also be high TJQKA. And as others have said it cannot wrap like QKA23. In the case of a flush that has an ace in it, that is always the highest possible flush. The most usual kind of poker is “high poker” where aces are always high, except the ace can optionally be low for the purpose of making a straight (that is, A-2-3-4-5 is a straight, and so is 10-J-Q-K-A). That is the only exception. An ace-high flush is higher (and beats) a king-high flush, regardless of the other cards in each hand. When two or more players hold a flush, the hands are compared card-to-card until one hand wins (the highest next card wins, such as when A-7-6-3-2 beats A-7-5-4-3).
Probability is the branch of mathematics that deals with the likelihood that one outcome or another will occur. For instance, a coin flip has two possible outcomes: heads or tails. The probability that a flipped coin will land heads is 50% (one outcome out of the two); the same goes for tails.
Probability and Cards
When dealing with a deck of cards the number of possible outcomes is clearly much greater than the coin example. Each poker deck has fifty-two cards, each designated by one of four suits (clubs, diamonds, hearts and spades) and one of thirteen ranks (the numbers two through ten, Jack, Queen, King, and Ace). Therefore, the odds of getting any Ace as your first card are 1 in 13 (7.7%), while the odds of getting any spade as your first card are 1 in 4 (25%).
Unlike coins, cards are said to have “memory”: every card dealt changes the makeup of the deck. For example, if you receive an Ace as your first card, only three other Aces are left among the remaining fifty-one cards. Therefore, the odds of receiving another Ace are 3 in 51 (5.9%), much less than the odds were before you received the first Ace.
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Is Ace High Or Low In Texas Holdem
Pre-flop Probabilities: Pocket Pairs
In order to find the odds of getting dealt a pair of Aces, we multiply the probabilities of receiving each card:
(4/52) x (3/51) = (12/2652) = (1/221) ≈ 0.45%.
To put this in perspective, if you’re playing poker at your local casino and are dealt 30 hands per hour, you can expect to receive pocket Aces an average of once every 7.5 hours.
The odds of receiving any of the thirteen possible pocket pairs (twos up to Aces) is:
(13/221) = (1/17) ≈ 5.9%.
In contrast, you can expect to receive any pocket pair once every 35 minutes on average.
Pre-Flop Probabilities: Hand vs. Hand
Players don’t play poker in a vacuum; each player’s hand must measure up against his opponent’s, especially if a player goes all-in before the flop.
Here are some sample probabilities for most pre-flop situations:
Post-Flop Probabilities: Improving Your Hand
Now let’s look at the chances of certain events occurring when playing certain starting hands. The following table lists some interesting and valuable hold’em math:
Many beginners to poker overvalue certain starting hands, such as suited cards. As you can see, suited cards don’t make flushes very often. Likewise, pairs only make a set on the flop 12% of the time, which is why small pairs are not always profitable.
PDF Chart
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. You’ll need to have Adobe Acrobat installed to be able to view the chart, but this is freely installed on most computers by default. We recommend you print the chart and use it as a source of reference.
Odds and Outs
If you do see a flop, you will also need to know what the odds are of either you or your opponent improving a hand. In poker terminology, an “out” is any card that will improve a player’s hand after the flop.
One common occurrence is when a player holds two suited cards and two cards of the same suit appear on the flop. The player has four cards to a flush and needs one of the remaining nine cards of that suit to complete the hand. In the case of a “four-flush”, the player has nine “outs” to make his flush.
A useful shortcut to calculating the odds of completing a hand from a number of outs is the “rule of four and two”. The player counts the number of cards that will improve his hand, and then multiplies that number by four to calculate his probability of catching that card on either the turn or the river. If the player misses his draw on the turn, he multiplies his outs by two to find his probability of filling his hand on the river.
In the example of the four-flush, the player’s probability of filling the flush is approximately 36% after the flop (9 outs x 4) and 18% after the turn (9 outs x 2).
Pot Odds
Another important concept in calculating odds and probabilities is pot odds. Pot odds are the proportion of the next bet in relation to the size of the pot.
For instance, if the pot is $90 and the player must call a $10 bet to continue playing the hand, he is getting 9 to 1 (90 to 10) pot odds. If he calls, the new pot is now $100 and his $10 call makes up 10% of the new pot.
Experienced players compare the pot odds to the odds of improving their hand. If the pot odds are higher than the odds of improving the hand, the expert player will call the bet; if not, the player will fold. This calculation ties into the concept of expected value, which we will explore in a later lesson.
Bad Beats
A “bad beat” happens when a player completes a hand that started out with a very low probability of success. Experts in probability understand the idea that, just because an event is highly unlikely, the low likelihood does not make it completely impossible.
A measure of a player’s experience and maturity is how he handles bad beats. In fact, many experienced poker players subscribe to the idea that bad beats are the reason that many inferior players stay in the game. Bad poker players often mistake their good fortune for skill and continue to make the same mistakes, which the more capable players use against them.
Decisions, Not Results
One of the most important reasons that novice players should understand how probability functions at the poker table is so that they can make the best decisions during a hand. While fluctuations in probability (luck) will happen from hand to hand, the best poker players understand that skill, discipline and patience are the keys to success at the tables.
Ace High Low Texas Holdem Tournaments
A big part of strong decision making is understanding how often you should be betting, raising, and applying pressure.
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Conclusion
A strong knowledge of poker math and probabilities will help you adjust your strategies and tactics during the game, as well as giving you reasonable expectations of potential outcomes and the emotional stability to keep playing intelligent, aggressive poker.
Remember that the foundation upon which to build an imposing knowledge of hold’em starts and ends with the math. I’ll end this lesson by simply saying…. the math is essential.
Related Lessons
By Gerald Hanks
Gerald Hanks is from Houston Texas, and has been playing poker since 2002. He has played cash games and no-limit hold’em tournaments at live venues all over the United States.
Related Lessons
Related Lessons
Royal Flush
Ace high Straight Flush.
Ace of Spades King of Spades Queen of Spades Jack of Spades 10 of Spades in a single suit. Also frequently referred to as 'Broadway'.
Straight Flush
Five consecutive cards of the same suit.
Five sequential cards in the same suit. The highest type of Straight Flush is a Royal Flush, and the lowest is an A-2-3-4-5 hand (if Aces are low or high/low). This type of hand is referred to as a 'Steel Wheel'. Other Straight Flushes with special names include:
- King of Clubs Queen of Clubs Jack of Clubs 10 of Clubs 9 of Clubs - Off Broadway (because it's shifted down one rank from a Royal Flush, or 'Broadway').
Four of a Kind
One of each suit in a single rank.
Also known as Quads. Many of the Four of a Kind hands have their own nicknames:
- King of Clubs King of Diamonds King of Hearts King of Spades - Four Horsemen (of the Apocalypse)
- Queen of Clubs Queen of Diamonds Queen of Hearts Queen of Spades - Village People (four Queens)
- 10 of Clubs 10 of Diamonds 10 of Hearts 10 of Spades - Larry, after Larry Fortensky (four-ten-sky), Elizabeth Taylor's eighth husband
- 4 of Clubs 4 of Diamonds 4 of Hearts 4 of Spades - Yacht Club (because the 4 resembles a sail)
- 3 of Clubs 3 of Diamonds 3 of Hearts 3 of Spades - Forest (four 'trees')
- 2 of Clubs 2 of Diamonds 2 of Hearts 2 of Spades - Mighty Ducks (because the 2 resembles a duck)
Full House
Three of a Kind and One Pair.
A Full House is called as 'X over Y' where X is the Three of a Kind and Y is the Pair (e.g., in a A-A-A-Q-Q hand, you would call it as 'Full House, Aces over Queens').
A Full House is sometimes called a boat or a full boat. When called a Boat/Full Boat, the hand is announced as 'X full of Y' (e.g., the same A-A-A-Q-Q hand would be called a 'Full Boat, Aces full of Queens'). Some Full House hands have special nicknames:
- Ace of Clubs Ace of Diamonds 2 of Clubs 2 of Diamonds 2 of Hearts - Marksman (bows and arrows)
- 7 of Clubs 7 of Diamonds 7 of Clubs 4 of Diamonds 4 of Hearts - Sailing rednecks
- 3 of Clubs 3 of Diamonds 3 of Clubs 2 of Diamonds 2 of Hearts - Nits and Lice, Mites and Lice
Flush
Does Ace Play High And Low In Texas Holdem
Five cards of the same suit.
Any five cards, all of which are in the same suit. A Flush all in hearts is referred to as 'Valentine's' while a flush all in clubs is known as a 'Golf Bag'.
Straight
Five consecutive cards.
Five cards in sequential order (but not all in the same suit, or it would be a Straight Flush). Also known as a Run (in many melding/counting games, such as gin and its variants, cribbage, and canasta, a Straight is referred to as a Run, and the name has carried over into poker).
- 6 of Clubs 5 of Diamonds 4 of Hearts 3 of Spades 2 of Clubs - Rabbit (the lowest Straight Flush if Aces are high)
- 5 of Clubs 4 of Diamonds 3 of Hearts 2 of Spades Ace of Clubs - Wheel, Bicycle, Bike, Spike, First Street, Little Wheel (the lowest run if Aces are low or high/low)
Three of a Kind
Three cards of the same rank. Also known as Trips, a Set, or Triplets. Three-card combinations that have special names include:
- Ace of Clubs Ace of Diamonds Ace of Hearts - Beatles reunion
- King of Clubs King of Diamonds King of Hearts - Three Wise Men, Christmas Special (both references to 'Three Kings'), Alabama Night Riders, Ku Klux Klan (KKK is an abbreviation for the Ku Klux Klan, and 'Alabama Night Riders' is a colloquial term used to refer to this group, which has a history of carrying out their acts at night in rural ateas)
- Queen of Clubs Queen of Diamonds Queen of Hearts - Six Tits
- Jack of Clubs Jack of Diamonds Jack of Hearts - Hart, Schaffner, and Marx (Three Jacks)
- 10 of Clubs 10 of Diamonds 10 of Hearts - Dallas to Fort Worth (the I-10 connects these two Texas Cities), San Jose to Gilroy, Gilroy, Thirty Miles of bad road (the distance between San Jose and Gilroy, California, used to be 30 miles, although the two cities are now adjoining)
- 7 of Clubs 7 of Diamonds 7 of Hearts - 21, Slot Machine, Jackpot (all named after results in other casino games like Blackjack and Slots)
- 6 of Clubs 6 of Diamonds 6 of Hearts - The Devil, The Beast, Lucifer, Devil's Area Code
- 5 of Clubs 5 of Diamonds 5 of Hearts - Washington Monument, Pork Chop Sandwiches
- 4 of Clubs 4 of Diamonds 4 of Hearts - Grand Jury
- 2 of Clubs 2 of Diamonds 2 of Hearts - Huey, Dewey, and Louie (three ducks)
Two Pairs
Two pairs, each with two cards of the same rank. Notable named two pair combinations include:
- Ace of Clubs Ace of Diamonds 8 of Clubs 8 of Diamonds - Dead Man's Hand (Arrows and Nooses)
- King of Clubs King of Diamonds Queen of Clubs Queen of Diamonds - Mommas and Poppas
- King of Clubs King of Diamonds 9 of Clubs 9 of Diamonds - Pair of Dogs (because it's K9K9-- two canines)
- Queen of Clubs Queen of Diamonds 3 of Clubs 3 of Diamonds - San Francisco Waiters (Queens with Trays/Treys)
- Jack of Clubs Jack of Diamonds 5 of Clubs 5 of Diamonds - Jackson Five (Jacks and Fives), Motown, Rock and Roll
- Jack of Clubs Jack of Diamonds 3 of Clubs 3 of Diamonds - Hookers with Crabs (because the Jacks hook and the 3 is like a sideways crab)
- 9 of Clubs 9 of Diamonds 8 of Clubs 8 of Diamonds - Oldsmobile
- 9 of Clubs 9 of Diamonds 6 of Clubs 6 of Diamonds - Dinner for Four
- 3 of Clubs 3 of Diamonds 2 of Clubs 2 of Diamonds - Socks and Shoes, Mites and Lice, Mits and Mites, Nits and Lice
One Pair
Two cards of the same rank. The poker hand that contains a single pair that is the most worth noting is the Princess Leia (an A-A-2-3), so called because the room in which Leia was imprisoned in Star Wars was room A-A-2-3. The best known names given to (pocket) pairs include:
- Ace of Clubs Ace of Diamonds - Pocket Rockets, Bullets, American Airlines
- King of Clubs King of Diamonds - Cowboys, King Kong
- Queen of Clubs Queen of Diamonds - Bitches, Double date, Canadian Aces, Siegfried and Roy
- Jack of Clubs Jack of Diamonds - Fish Hooks
- 9 of Clubs 9 of Diamonds - German Virgin (no, we don't know why.)
- 8 of Clubs 8 of Diamonds - Snowmen
- 7 of Clubs 7 of Diamonds - Sunset Strip, Hockey Sticks
- 6 of Clubs 6 of Diamonds - Route 66
- 5 of Clubs 5 of Diamonds - Speed limit
- 4 of Clubs 4 of Diamonds - Magnum, Sail Boat
- 3 of Clubs 3 of Diamonds - Crabs
- 2 of Clubs 2 of Diamonds - Ducks
High Card
While the high card is the lowest possible hand in poker (every poker hand automatically has a 'high card' in it-- the card with the greatest value), it comes into play in some poker variants more than others. Poker rookies often underestimate the value of the high card.
Ace High Low Texas Holdem Game
Texas Hold'em, for instance, is frequently referred to as a game of high cards because a player with higher cards always has an advantage. If player 1 holds K-Q and player 2 holds J-10, there are three possible outcomes:
Is Ace High Or Low In Texas Holdem Poker
- The flop makes player 1's hand, and player 1 wins.
- The flop makes player 2's hand, and player 2 wins.
- The flop doesn't make either player's hand, and player 1 wins again.
The player with high cards has a statistical advantage and will win 63% of the time.
Well known nicknames given to pocket hands are:
- Ace of Clubs King of Diamonds - Big Slick, Anna Kournikova (looks great, never wins!)
- Ace of Clubs Queen of Diamonds - Big Chick
- Ace of Clubs Jack of Diamonds - Black Jack, Jack-Ass
- King of Clubs Queen of Diamonds - Royalty, Marriage
- King of Clubs Jack of Diamonds - Kojak
- Jack of Clubs 5 of Diamonds - Jackson Five
- Queen of Clubs 3 of Diamonds - Gay Waiter
- 9 of Clubs 5 of Diamonds - Dolly Parton
- Ace of Clubs 8 of Diamonds - Dead Man's Hand (player Wild Bill Hickok was shot in 1876 after winning with it!)
- King of Clubs 9 of Diamonds - Canine
- Jack of Clubs 4 of Diamonds - Flat Tire