Poker Probability Of Getting A Flush

The odds of being dealt a Flush on the flop is only the tip of the iceberg. To view a wider range of odds and probabilities of being dealt different hands then check out our very own poker odds. The royal flush is a case of the straight flush. It can be formed 4 ways (one for each suit), giving it a probability of 0.000154% and odds of 649,739: 1. 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). 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. The probability of collecting royal flush in poker is 1 to 649 740. The odd to catch this combination on the flop with pocket broadway cards is equal to 0.0008%. If there is a potential royal flush on the board, the probability that it will be collected on the turn is 2%, and till the river – 4%. I know that probability of getting flush (contains five cards all of the same suit) in 5 card poker is 0.196. But what if we have the option to replace a card with a new one on second turn? Suppose 'X' is dealt five cards. That contains 4 hearts and another card of different suit.

1. Poker Probability Of Getting A Flush System
2. Royal Flush
3. Poker Probability Of Being Dealt A Flush

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It is a common misconception that flush is more likely to hit. If you also believe that to be the case, then you are wrong. Well, maybe you are right, but it depends on which perspective you look at it. Let me explain.

As long as you start counting the hand from preflop, then you will hit the straight more often than flush. But if you have a flush draw on flop or turn, then you will hit a flush more often compared to when you have an open-ended straight draw, and you hit a straight.

There is a reason why flush has a higher ranking in poker than straight. It will hit less often. Look at this chance to win a straight and to hit a flush – from Wikipedia.

You will hit a flush every 0.20% of the time. So once every 509 hands. While you will hit a straight about 0.40%

Poker Probability Of Getting A Flush System

of the time or once every 255 hands, so you will hit almost 2 straights for every 1 flush that you hit.Table of Contents

Why is it easier to make a flush than astraight?

But after all that I have written, why is it easier to hit a flush than a straight?
Well postflop, if you hold a flush draw, you have more outs to hit the draw than holding the open-ended straight draw and hitting the straight. You will have 9 outs to hit a flush on the flop or turn if you have a flush draw.
From flop to the river, we have 9 outs twice to hit a flush, which is roughly 38%, from turn to the river we have about 18% (9 outs once). On the other hand, if you hold an open-ended straight draw, you will have only 8 outs to hit it.

What many people are forgetting is that you will get the flush draw less often than you will open-ended straight draw. Getting a suited hand preflop doesn’t happen super often. You will have a flush draw on the flop only 5.1% of the time.

One thing that is often neglected is you not accounting in the times when you have a gutshot, and you hit it. It seems it doesn’t happen often, but you will usually have 4 outs to hit a straight, which is around 16% from flop to river. Not something we should forget about. On top of that, there are also some double gutters, which also gives you 8 outs to hit your straight.

So only looking from the postflop perspective, it can feel that it is easier to hit a flush than a straight, but as I explained, that can often be misleading. Straight will happen more often.

Let’s say you usually play connectors and therefore your chances to hit your straight draw increase. You would have flopped 8 outs straight draw (either open-ended or a double gutter straight draw) about 10.5% of the time on the flop.

How often will an opponent flop a flush draw?

A player will have a flush draw on the flop about 5.1% of the time strictly math speaking and accounting in all the hands. But we know that players don’t play every single hand, and they are more likely to fold more off suited hand than suited hands preflop.

All this makes an opponent hit a flush draw roughly 10% of the time on the flop.

Which makes more money: Flush vs. straight?

As expected, flush will make you more money. In my case, not double the amount, but you will make more money with it. Why not the double, you might wonder? Well, if you have a straight, usually you will be willing to stack off with top straight or second nut straight sometimes 3^rd nut straight. But when it comes to flush, you will lose quite some money even if you hold a low flush, and it can be less than 3^rd nuts. On top of that, not many players will be willing to stack off with the top two or a set on a possible flush board, while the same players don’t have a problem committing with the same hands on possible straight board.

All this reduces your winrate by a little. But you, as you can see from my graph, will still make substantially more profit with a flush compared to straight. They are both great hands; it is just that a flush is stronger.

Now your winrate will, of course, differ a bit. If you have nut flush yo will win more than my 2,000bb/100 hands. If you have a lower flush, then it will be lower. Now sometimes higher flushes will beat us. A scenario of when we hit a flush, and our opponent also hits a flush is not that uncommon, and if you multi table, it will happen on semi-frequent occasions.

The same goes for a straight. Nut straight will give you the most money of any straight. You will still make decent money with 2^nd nut straight, just less.

Scenarios, where we hit backdoor straight, will be nicely profitable since it will be harder for an opponent to put us on a straight, as there was no apparent straight draw present when we started betting on the flop. If you want to read more about straight backdoor draws, I have this article I have for you.

What are the odds of getting straight flush?

Odds of hitting a straight flush is so low that it almost doesn’t make sense to write it in percentages. It is a 0.00139% chance you will hit a straight flush. This is 72,192:1 odds against hitting it. SO only once every 72,000 hands you will hit the second most powerful hand in poker.

What are the odds of getting a royal flush?

Hitting a royal flush is even harder than a straight flush. The royal flush is the strongest hand you can get in poker. Your chances of hitting it are 0.000154% of the time, or once every650,000 hands (odds against of 649,740:1 to be precise).

I have been dealt quite many royal flushes in my poker career, and frankly, hitting one doesn’t feel special anymore. But I remember that when I hit it for the first time, I was ecstatic for some time. That is how rare the royal flush is.

Does a straight beat a flush?

Poker hand rankings go from strongest to weakest:

1. Royal flush
2. Straight flush
3. Four of a kind
4. Full house
5. Flush
6. Straight
7. Three of a kind
8. Two pair
9. One pair
10. No pair (high card)

You can see that straight doesn’t beat a flush, but it does beat many other hands, making it a powerful hand on right boards. When the board is not paired, and no flush can be present, then if you hold the highest straight, you will have the best hand.

What are the odds of getting pocket aces?

Chances of being dealt pocket aces are slightly less than 0.5%. Exactly once every 221 hands, you will get the rockets. The number of players on the table doesn’t matter. There are still 52 cards in the deck, no matter how many players are at the table.

If you wonder how often you can expect to win with AA depending on the number of opponents and different hands you are up against, then read this post.

What are the odds of an ace flop?

We all know it, that horrible feeling when you hope ace doesn’t show up on the flop, but it seems like it always does. It doesn’t always come. But you will see ace on the flop 42% of the time, which is quite often. But don’t worry on some occasions you will also hit two flushes, sets or straights yourself. That is why pocket kings have around 70% (and not only 58%) to win against Ax.

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.

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?

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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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.

Royal Flush

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.

Poker Probability Of Being Dealt A Flush

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.

A big part of strong decision making is understanding how often you should be betting, raising, and applying pressure.
The good news is that there is a simple system, with powerful shortcuts & rules, that you can begin using this week. Rooted in GTO, but simplified so that you can implement it at the tables, The One Percent gives you the ultimate gameplan.

This 7+ hour course gives you applicable rules for continuation betting, barreling, raising, and easy ratios so that you ALWAYS have the right number of bluffing combos. Take the guesswork out of your strategy, and begin playing like the top-1%.

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.

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.