# POKER PROBABILITY β YOUR CHANCE TO WIN IN POKER

Levelling up in poker is about more than just having the rules down. By understanding odds and probabilities, you could be the next poker player to get a nice piece of a larger pool!

It’ll take some time to get incredibly good at this skill. But everyone has to start somewhere, and you can start right here.

Read on to learn about poker odds and probability and how to calculate them.

Table of Contents

## WHAT IS PROBABILITY IN POKER?

Probability is a form of math that calculates the percentage chance of something occurring. Mathematicians often express this number as a portion of 100%. All of the possibilities must equal one or 100% together.

Keep in mind that an occurrence’s probability is a percentage. An occurrence’s odds are a ratio of 1:3 or 1-out-of-3. The measurement is pretty much the same, but it’s good to know the difference.

The simplest way to show probability is through a coin flip. A fair coin flip only has two outcomes: heads or tails. Each outcome takes up one-half of the total possibilities, so you have a 50% chance you’ll get heads or tails.

From there, you have to dive into more complex mathematics. What are the odds that you’ll get a certain number out of a six-sided dice? If each possibility gets its share, you’re looking at 1/6 or around 16.667%.

You can apply this same style of math when playing poker.Β

### HOW DOES POKER PROBABILITY WORK?

Poker is a game where you have to get a certain set of cards to win. How you get your set of cards varies from game to game. But most of the known games use a full 52-card deck.

You have a 1/52 chance of getting each type of hole card at the start. But so do the other poker players. The correct strategy is to approximate probabilities for the hole cards.

In a game like Texas hold ’em, the flops, turns, and rivers can help you get closer to a correct math estimate. But many games only have a certain number of outs that the players hold. How many outs these players have can change your poker odds.

You can probably see how poker math can become complicated. But that’s what leaves most poker players with a poor grasp and gives you the advantage. Trust us: learning this poker strategy is worthwhile.Β

## HOW DO YOU CALCULATE POKER ODDS?

One part of poker math is just calculating a ratio or percentage. Say that you want to get a two in any suit for your first hole card. So you want one out of four possible cards in a 52-card deck.

4:52 (or 4/52) = 1:13

So your poker odds for getting a two are 1-out-of-13. But things get more complicated when you want a pocket pair of twos for your hole cards. At that point, you’ll have to start doing some multiplication.

4/52 (or 4:52) x 3/51 = 12/2652 = 1/221 or 1:221 odds

You can’t use 3/52 on the second ratio/fraction because you’ve already gotten one-half of your intended pocket pair. You shouldn’t include that card because you already have it.

The calculations for any specific pocket pair of two out in games like Texas hold ’em should work this way. If you’re looking for two pairs (such as in games with eight outs or nine outs), you need to make a longer formula:

4/52 x 3/51 x 2/50 x 1/49 = 184689/50000000000

And these are just the calculations at the start of the game when you’re looking for one pair or more.Β

### WHAT POKER ODDS ARE GOOD?

You don’t have to calculate your poker odds every time you sit down to a game. You can memorise the odds that someone else has calculated for you.

Just find a poker probability chart online or make your own. You can then use this knowledge to control how you bet during a cash game.

But which odds should lead you to bet higher? Usually, the smaller the ratio, the higher you should bet. The rarer the card combination, the more likely your opponent will have the wrong card for winning.

Getting a pocket pair of kings is 1:221, but getting two cards of identical suits is a 1:4 chance. You should bet higher if you have the two kings. As long as you avoid bad beats, you should play a game with the very lowest stakes.

The odds get even rarer with bigger card combinations. Getting a royal flush, for instance, is a one in several hundred thousand chance.

## WHAT IS THE PROBABILITY OF GETTING AN ACE?

Playing online poker is different from playing an online slot machine. The odds of you getting a certain card are the same throughout, and a card’s value doesn’t affect its rarity.

The odds of getting an ace in your hole cards are the same as getting a two or three. Using the above rule, you can easily calculate that your odds of getting an ace are 1:13. If you want a particular ace, your odds would be 1:52.

But the odds would be far rarer if you play with two decks instead of just one. They’ll also be different if you’re using a poker deck of a different size.Β

### PLAYING POKER WITH ONE DECK

A typical poker deck consists of 52 suited cards. You need to use that number in your calculations. Most poker odds charts refer to this type of poker deck.

Some tables don’t always use a full deck, but these instances are not super common. On top of that, unfortunately, you won’t be able to refer to a memorised poker odds chart in this situation. You’ll have to make calculations independently to learn your chances of getting pocket aces or other specific cards. You could be spending ages determining these odds.

In short, calculating odds is much easier with one full deck as opposed to an incomplete one or multiple decks.

### PLAY POKER WITH MORE DECKS

You may end up playing a poker game with two or more decks.

If the dealer allows you to do so, make sure to count the cards. You then need to use the deck number in your calculations. However, card counting has become forbidden at most casinos, so you’d be better off using an odds chart to discern the chances of earning certain hands. Remember that since you’re using more decks, the odds would be much lower than if you had to use one.

## POKER PROBABILITY β POKER HAND TABLE

You can get a variety of winning hands, and each of them has a unique strength level. The player with the strongest hand value is the one who wins. All of the different types of poker games use the same hands unless you’re playing Three-Card Poker.

Different winning poker hands, from strongest to weakest, are the following:

1. Royal Flush β Ace, king, queen, jack, and 10 suited cards of identical suits.
2. Straight Flush β Five sequential cards of identical suits.
3. Four-of-a-kind β Four suited cards of the same value.
4. Full House β Three-of-a-kind and a pair.
5. Flush β Five suited cards of identical suits.
6. Straight β Five sequential cards of different suits.
7. Three-of-a-kind β Three cards of the exact same position in ranking.
8. Two pair β Two sets of cards of the same value.
9. One pair β One set of cards of the exact same position.
10. High card β One card of a high rank (ace, king, queen, etc.), or a combo that does not conform to any of the above combinations.

You can calculate the approximate probabilities of getting each winning hand at the beginning of a round. But your hand odds will vary at different points of the game. So you’ll have, say, a different ratio after both the turn and river cards are flipped than the pre-flop.

To keep up, you need to change your calculations as you go. This is why you’ll likely see a poker table or chart for each street of a typical Texas hold’em poker game.

## PROBABILITY OF GETTING A HAND PREMIUM FROM THE DEALER

Premium poker hands are the strongest hole cards you can get on the pre-flop. Luckily, you’ll only have to memorise one percentage for each premium hand. By definition, they stop being premium hands post-flop.

Below you’ll find a list that tells you the probability of getting some hand premiums during the first stages of a game:

• A-A (pocket aces) or pocket pairs β 0.452%.
• A-K of the same suit β 0.301%.
• A and less than J of identical suits β 2.714%.
• A and less than J of differing suits β 8.144%.
• Suited sequential cards β 3.318%.

## PROBABILITY THAT YOUR OPPONENTS WILL HAVE STRONGER A HAND

As mentioned above, the rarer the hand, the less of a possibility that your opponent will also have it. You can see this rule reflected in the list poker odds below.

The author calculated these odds using a poker hand probability calculator. The number of outs is seven (Texas hold’em style).

Pre-flop stage odds include:

• Pair of A’s = 15% opponent winning chance (OWC).
• AK of identical suits = 31.9% OWC.
• Same Suit 9 and 10 = 43.7% OWC.
• Same suit 3 and 4 = 58.3% OWC.
• 2 and 3 of different suits = 65.1% OWC.

Post-flop odds include:

• Four A’s = 0% OWC.
• Royal flush = 0% OWC.
• Low four-of-a-kind = 0% OWC.
• Low straight flush = 0.4% OWC.
• Low full house = 4.7% OWC.
• Low three -of-a-kind = 8.3% OWC.
• High two pair = 19.5% OWC.
• Single high card = 45.6% OWC.
• Low two pair = 52.2% OWC.

Post-turn odds:

• Royal flush = 0% OWC.
• Low four-of-a-kind = 0% OWC.
• Low straight flush = 0.4% OWC.
• Low full house = 1.6% OWC.
• High straight flush = 9.3% OWC.
• Low three-of-a-kind = 9.8% OWC.
• High three of a kind = 14.6% OWC.
• High two pair = 19.5% OWC.
• Low two pair = 53.7%
• Single high card = 66.9% OWC.

Post-river odds:

• High straight flush = 0% OWC.
• High and low four-of-a-kind = 0% and 0.1% OWC, respectively.
• Low full house = 0.5% OWC.
• High two pair = 16.5% OWC.
• Low three of a kind = 39.6% OWC.
• Low two pair = 95% OWC.

## PROBABILITY OF GETTING A THREE, A STRAIGHT OR A FLUSH

A three-of-a-kind, a straight, and a flush are some of the most powerful hands. What is the probability of getting any of these sets in a game? Take a look:

• Three-of-a-kind = 0.0211284514 or 2.1% chance.
• Straight = 0.0039246468 or 0.3% chance.
• Flush = 0.0019654015 or 0.1% chance.
• Straight Flush = 0.00001385169 or a nearly 0% chance.
• Royal Flush = 0.00000153907 or a nearly 0% chance.

## WHAT ARE CHANCE SETS?

After players get their first two cards, the dealer will flip over the three remaining cards on the poker table. This is referred to as the flop, and they change the number of outs to five. Ideally, the cards in the players’ hands will create sets with the flop cards.

You can also earn sets from not only the river but both the turn and the post-flop as well. But this section will focus on some of the odds of flopping sets.

Odds after having any pocket pairs:

• Any set = 10.8%.
• A full house = 0.73%.
• Four-of-a-kind = 0.25%.

Two suited cards:

• A flush = 0.84%.
• Flush draw = 10.8%.
• Backdoor flush draw = 41.6%.

Two non-paired cards:

• A pair = 32.4%.
• Two pair = 2.02%.
• Full house = 0.9%.
• Four-of-a-kind = 0.1%.

### POT ODDS

Another set of odds that players often use is pot odds. Players often use pot odds to learn how profitable a game will be for them. Pot odds are a ratio between the total pot size and the amount a player bets.

You can calculate a game’s pot odds in three steps. The first step is to calculate the total pot, including the bet that you need to call. So if the pot is β¬150 and you need to call a β¬50 bet, the total pot would be β¬200.

You should then divide the total pot by the amount of your call. In this case, this would be β¬50/β¬200 or 0.25. If we had to turn this value into a percentage, these odds would become 25%.

This means you need to win 25% of the time to profit. But you also want to consider your odds of hitting the set. If you have an 80%+ chance of hitting a set, you can go over the top with your betting.

### IMPLIED ODDS

Implied pot odds are another type of pot odds. It helps players calculate how much money they may win if they hit a set on the flop, river, or turn. And pot odds would also be combined with hand odds.

After calculating your pot odds as above, you need to use another formula to get your implied odds:

β¬50/β¬50 + β¬100 + β¬50 + X = 0.25

The ‘x’ in this case is the amount you’ll need to win on the river. The two β¬50 numbers are yours and your opponent’s bets. The β¬100 is the total pot amount.

To solve for x, here’s what you need to do:

β¬50/β¬200 + X = 0.25

0.25 x β¬200 + 0.25 Γ X = β¬50

β¬50 + 0.25 x X = β¬50

0.25 x X = 0

X = 0

In this case, you would want to fold at this point, as placing a bet won’t be worth it.

Keep in mind, though, that your implied odds can’t be completely accurate. The complex mathematics required here is often too much for one person to handle, especially if you’re still a rookie.

### OTHER

There are a few other types of odds than just regular pot odds and implied odds. But these are more advanced.

It’s best to start with the two types of pot odds stated in this article. Once you get the hang of them, you can do some more research to learn about the other styles.Β

## WHAT IS THE POKER CHANCE CALCULATOR AND WHERE CAN I FIND IT?

A poker hands probability calculator is one of the best poker tools. This software can easily help you find the poker hand odds in any player’s game. For example, you can find the odds of winning with bad beats, a paired board, etc.

Some poker probability calculators will only show the odds for Texas hold’em. But, many offer a variety of games with a various number of outs.

All you have to do is enter your pre-flop and post-flop poker hand. Then you can create the poker hand of each of your opponents. The calculator will then show you your poker hand probability and the chance of you winning.

You can’t use this poker software to win a game. But you can use it to build your own poker hand odds chart and boost your knowledge.

You can find poker software that can give you these calculations on a variety of online poker platforms. There are also several phone applications that you can use. Just keep in mind that a poker probability calculator won’t help you win a game while you’re in the middle of it.

## CONCLUSION β READY TO PLAY POKER?

Now that you know how to calculate poker odds, you should be all set and ready to go! Keep in mind that it will take a lot of practice to get these poker calculations just right. We recommend you practice playing online for free first before raising the stakes.

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## FAQ

### β DOES KNOWLEDGE OF MATH HELP IN PLAYING POKER?

Yes, having math skills can help you with calculating odds. But having these skills doesn’t guarantee that you’ll end up getting a winning hand. A poker game is still very much a game of luck with very few ways to draw high.Β

### β CAN YOU CALCULATE THE PROBABILITY YOURSELF IN POKER?

Calculating poker odds yourself is possible, but it’s very difficult to do. You can end up spending ages determining the right calculations. You should use a calculator to calculate poker hand odds.

Just keep in mind that another poker player may frown upon you bringing a calculator to physical games. You may want to use the calculator for online or video poker probability.Β

### β WHAT’S THE FASTEST WAY TO CALCULATE POKER ODDS?

It’s best to memorise a poker odds chart. You can also make a chart as well. This way, you can pull up your poker odds right away.Β

### β WHAT ARE OUTS IN POKER AND HOW TO FLOP A SET WITH A POCKET PAIR?

The outs in poker are the cards that make up each player’s poker hand. So if all the players have eight outs, they have eight cards on their hands. If the players have nine outs, they have nine cards in their hands.

Flopping a set means that you will complete a set with the flop cards. The flop cards are a set of cards in Texas hold’em that the dealer turns over after the first round. If you have a pocket pair, you can match them with the flops to get a straight flush, royal flush, three-of-a-kind, etc.Β

### β DO POKER ODDS CHANGE WITH MORE PLAYERS?

Yes, the number of players in a game is something to consider when you’re calculating odds. However, the number of players in a game can decrease your odds of winning.Β

### β WHAT IS THE PROBABILITY OF A DRAW IN POKER?

A poker draw is an incomplete set. You need to draw a certain card or use a flop, turn, or river to complete your set.

There are a few different types of draws in poker. For example, you can get a higher flush draw, an open-ended straight draw, etc.

Each of them has a different probability of occurring. You can look at the sections below to get a better idea of their probability.

Gunshot straight draw (four outs to get a straight):

• Hitting gunshot straight draw on the turn = 8.5%.
• Hitting gunshot straight draw on the river = 8.7%.

Open ended straight draws (eight outs to get a straight):

• Hitting open ended straight draw on the turn = 17%.
• Hitting open ended straight draw on the river = 17.4%.

Flush draw (four cards to a flush):

• Hitting a flush draw on the turn = 19.1%.
• Hitting a flush draw on the river = 19.6%.