Anyone who has ever played poker knows that a great deal of chance is involved in the game. However, there is also a good deal of mathematical probability at work. Let’s take a look at the different ways the odds can work in your favour or against you.
WHAT IS PROBABILITY IN POKER?
Probability in poker is kind of like poker math. It predicts the likelihood of hitting a specific hand or the likelihood of certain events occurring during a poker hand.
However, you can also use probability to predict how often certain events will occur over the long run. For example, if you’re handed AA in Texas hold ’em, the chances of flopping a set are about 12%. This means that, you can expect to flop once every eight times you’re given AA.
While probability can’t tell you what will happen in any given hand, it can give you an idea of what to expect over the long term.
POKER HANDS PROBABILITY
Aside from understanding the basic rules of poker, understanding the poker probability of various hands is what can help take you from a novice player to a poker pro in no time.
Ready to put your brain to work? Lucky for you, you won’t have to do much math. We’re here to explain everything there is to know in relation to various poker hands.
ROYAL FLUSH
A royal flush features an ace, king, queen, jack, and 10 all in the same suit (hence the name as they’re all royal and all part of the exact same card category, like clubs or diamonds).
Because the combo needs to be of the same category, it makes this hand the least probable of all of the poker hands listed here. This is why it has a probability of less than 0.0000154.
STRAIGHT FLUSH
A straight flush is similar to the hand above in that you need to have five consecutive cards, so there isn’t much of a difference between the two. However, straight flushes can form combinations of different numbers. For example, you could have a five, six, seven, eight and nine of clubs and that would be a straight flush. This means that this combo is still somewhat difficult to draw, but slightly more probable than a royal flush.
There are 40 possible combinations possible within any 52-card stack. This means that the chances of drawing this hand are 0.0000139%.
FOUR-OF-A-KIND
A four-of-a-kind contains four cards of the exact same rank, and is ranked above a full house. It is also sometimes known as quads.
Four-of-a-kinds are relatively rare, but they do happen from time to time. There are over 600 ways for you to form this hand, which adds to a 0.00024% chance of drawing it.
FULL HOUSE
A full house contains three cards of one rank and two of another rank, like, for example, a hand containing three kings and two queens. Full houses are ranked by the value of their first three cards, and then by the rank of next two.
So, in the situation above, the hand containing three kings would be higher than a hand containing three queens. Full houses are fairly rare hands, with a full house poker probability of 0.001441%.
FLUSH
A flush is a hand where the whole combo belongs to the same card category. A flush is often considered a strong hand since a flush is fairly difficult to make. However, there are some instances in which a flush can be beaten by other hands.
The chances of forming a flush is 0.001965%.
STRAIGHT
Straights contain five cards of sequential rank, not of the same house, like, for instance, a hand containing a six, seven, eight, nine and 10.
When you look at the mathematical equation for earning this hand, you will see that the number of five-card hands in a sequence totals well over 10,000. This increases the chances to 0.003925%.
THREE-OF-A-KIND
Three-of-a-kinds are hands that contain three cards of the same rank, such as three kings or three queens. They are also known as ‘trips’ or ‘a set’.
When multiple players earn this hand, the highest-ranking card in the hand (known as the kicker) is used to determine the winner.
The mathematical probability of earning this hand is 0.021128%.
TWO PAIR
A two pair is where you have two cards of the same rank, and two more of the same rank (and one additional card of a different rank). For example, if you have two eights and two fives, that’s two pairs. The hand with the highest set wins, so in this case, the eights would beat the fives.
What is the probability of having two pairs in an online poker game? It’s 0.047539%.
ONE PAIR
One pairs contain two cards of the same rank, plus three unpaired cards. If two or more players gained this hand, the highest-ranking pair wins.
One pairs are the second-weakest hands in poker, so the chances of gaining these hands go up to 0.422569%.
HIGH CARD
A high card is a hand that does not meet any of the criteria of the previous hands, but your hand contains the card that is valued the highest. The value of this card determines which poker player wins the pot if two or more players earn a high card as well.
For example, if Player A has a king high and their opponent has a queen high, then Player A would win the pot. The likelihood of hitting this hand is high at 0.501177%.
POKER HAND PROBABILITY CHART
To make things easier for you here is a helpful chart so you can quickly view the probability of various poker hands:
| Poker Hand | Probability (%) |
| Royal Flush | 0.00000154 |
| Straight Flush | 0.0000139 |
| Four-of-a-Kind | 0.00024 |
| Full House | 0.001441 |
| Flush | 0.001965 |
| Straight | 0.003925 |
| Three-of-a-Kind | 0.021128 |
| Two Pair | 0.047539 |
| One Pair | 0.422569 |
| High Card | 0.501177 |
Take note that these are percentages. You might see percentages listed online when learning about poker odds. However, these are simply the mathematical chances you will have any specific hand when playing poker online (or in person at a real table).
HOW TO CALCULATE POKER PROBABILITY
The most common way to analyse probabilities is to use the ‘52-card method.’ This involves breaking down the deck into its parts (suits, ranks, and combinations) and then calculating the likelihood of hitting certain combinations. For instance, a coin flip has two possible outcomes, so the chances of one occurring is 50%.
However, this method only provides a rough estimate of probability; for more accurate results, you’ll need to use Monte Carlo simulations or other more advanced methods.
To analyse probabilities, you ultimately need to know the number of ways that each hand can be made. For instance, there are four ways to make a straight flush. The more ways a hand can be made, the more likely it is to occur.
So, if you want to compute the chances of hitting a straight flush, you would divide four (the number of ways it can be made) by 2,598,960 (the total number of possible hands). This would give you a probability of 0.00015%.
WHY DOES PROBABILITY IN POKER MATTER?
Some people argue that probabilities in poker don’t matter because the outcome of any hand is completely random. If that were the case, why would professional poker players work so hard to understand the dynamics of probabilities in every poker game?
Understanding probabilities can be very useful when making decisions in an online poker game or a land-based one. By understanding the odds of certain combinations forming/certain hands winning, players can make more informed choices about when to bet and how much to bet. Additionally, probabilities can help them spot patterns in their opponents’ betting behaviour, so probabilities easily tie into their strategy.
For instance, if a player always bets when they have a high chance of winning, they are likely to be a tight player. Conversely, if a player frequently makes risky bets with low-probability hands, they are probably a loose player. While probabilities can’t guarantee success at poker, it can give you an important edge in making decisions.
POKER PROBABILITY TIPS
If you’re serious about winning at poker, then you need to understand poker odds. Here are a few other tips to take note of:
- Look at poker odds — These are the chances of forming certain card combinations. For instance, the odds of hitting a flush are approximately one in 508. Knowing your odds of winning can help you make better decisions at the table. We’ll get into this in a bit, so sit tight if this sounds confusing to you.
- Practise calculating probabilities — One great way to practise calculating your chances is by using a stack of cards. This will help you get a feel for how to do it in your head during a standard game. Online poker tables also come with a demo mode that allow you to play online poker using virtual funds instead of your actual bankroll.
- Pay attention to table trends — This can help you predict what is likely to be dealt next. For example, if you notice that a lot of low cards have been showing up, then it’s likely that high cards will be dealt soon. Just keep in mind that this is never a guarantee.
- Keep track of the cards that are handed out — It’s not wrong to keep track. This information can be useful for making calculations about future hands. For example, if you know that there are only a few high cards left in the deck, then you can adjust your play accordingly.
The most important thing is to have a solid understanding of basic math. You’ll also need to know the likelihood of certain hands being hit. Once you have a firm grasp of these concepts, you can use them to your advantage.
WHAT ARE THE ODDS OF HITTING SPECIFIC HOLE CARDS?
A hole card in poker is a card placed face down and not seen by other players. Hole cards are dealt to each player at the beginning of each hand, and five community cards are dealt face-up in the middle of the table.
What’s important to know is that hole cards can only be seen by the player who is holding them, and they can be used in combination with the community cards to make the best five-card hand possible. Because you don’t necessarily draw a hole card, the odds are slightly different here.
What you’re trying to measure is the chance of being dealt a specific set of hole cards (if you’re playing poker games like Texas hold ’em, for instance). So you might be better off asking about your odds of hititng a pocket pair of AA as hole cards. In this case, your chances are 0.00452.
How did we get to that number? Since there are four aces in each deck, you have a 4/52 chance of getting this pocket pair. Once you do pick it up, then you now have a 3/51 chance of hitting the second card. This means that your first probability is one in 13, whereas your second probability is one in 17. If you multiply those, you get 221, meaning your odds are one in 221 or 0.00452 of hitting an AA pocket pair. This same reasoning can be applied to other pocket pairs.
FLOPPING A MADE HAND — WHAT ARE THE ODDS?
A made hand in poker is a hand that is likely to win, given the current card distribution. For instance, if you have a pair of aces in your hand and there are no others on the board, you have a made hand.
For instance, if you have two diamonds in your hand and four diamonds on the board, you have a flush draw. Made hands are typically easier to play than draws since they don’t require as much guesswork. But, seeing as nothing is certain in poker, what are your chances of flopping a made hand?
In general, it depends on the hand. The chances of flopping a weaker hand like a pair (11.8%) are much higher than your chances of flopping something as rare as a royal flush (0.005%).
Overall, it’s important to understand that of all possible hole card combinations in Texas hold ’em, 23.5% of combinations are suited. This can help you better understand how to determine the possibility.
POT ODDS AND PROBABILITY
Unfortunately, understanding probability in poker isn’t all about understanding the chances of earning distinct hands. You also need to take pot odds into account.
Put simply, pot odds are the ratio of the current size of the pot to the cost of a call. To make a mathematically correct call, you need pot odds to be greater than your hand odds. For example, if the pot is €100 and it costs €10 to call, then you are getting pot odds of 10-to-one.
Of course, to determine your hand odds, you need to know two things: the poker probability of making your hand and the total pot size. The likelihood of making your hand is easy to determine if you know what cards you have and how many outs are still in play.
The pot size is a little more tricky, but you can get a good estimate by looking at the number of chips in your opponent’s stack and subtracting your bet from that number. If pot odds are greater than hand odds, then you should call; if they are less, then you should fold.
Of course, there are other factors to consider when deciding on the poker table, but pot odds are a good starting point.
POKER ODDS OF EARNING A STRONG STARTING HAND
To answer this question we first need to define what a good hand is. There are a few things to consider. First, you want a starting hand with good cards, including kings, and queens. Additionally, you want a hand combination that works well.
Finally, a good hand is a hand that gives you options. If you have a hand with multiple possibilities for how to play it, you’re in good shape. Below you’ll find some examples of good starting hands along with an estimate of the probability of hitting that hand:
AA
To determine your chances of hitting a set of pocket aces, you first need to calculate the chances of getting your first A card, then multiply that by your chances of getting the second one. In this case, your chances of getting pocket aces are one in 221 or 0.00452.
SUITED AK
An AK hand is in the top 2% to 3% of all Texas hold ’em poker starting hands. That means it’s a great hand to start with, especially if they are suited cards. To work this out, you need to consider the chances of not only getting an A or a K but also the probability of getting them in the same category.
Your first card can be any of the four aces or any of the four kings, so the probability is 8/52. Then, your chances of being dealt two suited cards are 1/51 (because there is only one card to match the same suit you already have, and there are only 51 cards left since you already took one).
This means that your chances of hitting a suited A and K set are 0.3%.
SUMMARY
Poker is a game that requires not only luck but also quick thinking and skill. Playing poker is always going to be a little rocky, especially if you’re a new player. But, with a bit of poker math and a good understanding of pot odds, you’ll be able to build the best hand you possibly can and beat your opponent!
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