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Mathematics: Flushes & Straights : Simple Pot Odds : Implied Odds : Reverse Implied Odds

A flush is a relatively strong hand in Texas Hold’em with the highest possible flush being ace-high with all 5 cards in the same suit. The best Flush possible is the ace-high Flush: A♠J♠10♠3♠2♠ When it comes to flushes, the suits don’t matter. High Hand Rankings. There are 10 different high hand rankings in Poker. These are detailed below with number 1 being the best poker hand possible and number 10 being the lowest ranking hand. You’ll never not know the winning poker hand again! This is the highest poker hand. It consists of ace, king, queen, jack and ten, all in. In Texas Hold'em, where players have a total of seven cards available for making the strongest hands of five cards, a Flush can occur pretty frequently. There are more than 5,000 ways to get a. You could call Alice's hand - in this context - a 'Ten-Nine-Eight-Seven-Five-High Flush' and Bob's hand a 'Ten-Nine-Eight-Seven-Four-High Flush'. By the way: the only way that a flush leads to a split pot in Texas Hold'em is if all players play the whole flush from the community cards. The Royal Flush. The Royal Flush, as the name suggests, is the best possible hand in Texas Holdem. This hand combination is made up of the five highest cards in a deck – the Ace, King, Queen, Jack and the number 10. The royal flush must have all these characters of the same suit.

Watch SplitSuit's video on Flushes and Flush Draws for 8 hand histories involving strategy on playing flushes in Texas Hold'em.

You are on the flop with a pretty decent flush draw. You have two hearts in your hand and there are another two on the flop.

Unfortunately, some cool cat has made a bet, putting you in a tricky situation where you have to decide whether or not it is in your best interest to call to try and make the flush, or fold and save your money.

This is a prime example of where you are going to take advantage of 'pot odds' to work out whether or not it is worth making the call.

What are pot odds? What about flushes and straights?

Basically, just forget about the name if you haven't heard about it before, there's no need to let it throw you off. Just think of 'pot odds' as the method for finding out whether chasing after a draw (like a flush or straight) is going to be profitable. If you're on your toes, you might have already been able to guess that it is generally better to chase after a draw when the bet is small rather than large, but we'll get to that in a minute...

Pot odds will tell you whether or not to call certain sized bets to try and complete your flush or straight draw.

Why use pot odds?

Because it makes you money, of course.

If you always know whether the best option is to fold or call when you're stuck with a hand like a flush draw, you are going to be saving (and winning) yourself money in the long run. On top of that, pot odds are pretty simple to work out when you get the hang of it, so it will only take a split second to work out if you should call or fold the next time you're in a sticky drawing situation. How nice is that?

How to work out whether or not to call with a flush or straight draw.

Now, this is the meat of the article. But trust me on this one, the 'working-out' part is not as difficult as you might think, so give me a chance to explain it to you before you decide to knock it on the head. So here we go...

Essentially, there are two quick and easy parts to working out pot odds. The first is to work out how likely it is that you will make your flush or straight (or whatever the hell you are chasing after), and the second is to compare the size of the bet that you are facing with the size of the pot. Then we use a little bit of mathematical magic to figure out if we should make the call.

1] Find out how likely it is to complete your draw (e.g. completing a flush draw).

All we have to do for this part is work out how many cards we have not seen, and then figure out how many of these unknown cards could make our draw and how many could not.

We can then put these numbers together to get a pretty useful ratio. So, for example, if we have a diamond flush draw on the flop we can work out...

The maths.

There are 47 cards that we do not know about (52 minus the 2 cards we have and minus the 3 cards on the flop).

• 9 of these unknown cards could complete our flush (13 diamonds in total minus 2 diamonds in our hand and the 2 diamonds on the flop).
• The other 38 cards will not complete our flush (47 unknown cards, minus the helpful 9 cards results in 38 useless ones).
• This gives us a ratio of 38:9, or scaled down... roughly 4:1.

So, at the end of all that nonsense we came out with a ratio of 4:1. This result is a pretty cool ratio, as it tells us that for every 4 times we get a useless card and miss our draw, 1 time will we get a useful card (a diamond) and complete our flush. Now all we need to do is put this figure to good use by comparing it to a similar ratio regarding the size of the bet that we are facing.

After you get your head around working out how many cards will help you and how many won't, the only tricky part is shortening a ratio like 38:9 down to something more manageable like 4:1. However, after you get used to pot odds you will just remember that things like flush draws are around 4:1 odds. To be honest, you won't even need to do this step the majority of the time, because there are very few ratios that you need to remember, so you can pick them off the top of your head and move on to step 2.

2] Compare the size of the bet to the size of the pot.

The title pretty much says it all here. Use your skills from the last step to work out a ratio for the size of the bet in comparison to the size of the pot. Just put the total pot size (our opponent's bet + the original pot) first in the ratio, and the bet size second. Here are a few quick examples for you...

• $20 bet into a $100 pot = 120:20 = 6:1
• $0.25 bet creating a total pot size of $1 = 1:0.25 = 4:1
• $40 bet creating a total pot size of $100 = 100:40 = 2.5:1

That should be enough to give you an idea of how to do the second step. In the interest of this example, I am going to say that our opponent (with a $200 stack) has bet $20 in to a $80 pot, giving us odds of 5:1 ($100:$20). This is going to come in very handy in the next step.

This odds calculation step is very simple, and the only tricky part is getting the big ratios down into more manageable ones. However, this gets a lot easier after a bit of practice, so there's no need to give up just yet if you're not fluent when it comes to working with ratios after the first 5 seconds. Give yourself a chance!

To speed up your pot odds calculations during play, try using the handy (and free) SPOC program.

3] Compare these two ratios.

Now then, we know how likely it is that we are going to complete our draw, and we have worked out our odds from the pot (pot odds, get it? It's just like magic I know.). All we have to do now is put these two ratios side to side and compare them...

• 5:1 pot odds
• 4:1 odds of completing our draw on the next card

The pot odds in this case are bigger than the odds of completing our draw, which means that we will be making more money in the long run for every time we hit according to these odds. Therefore we should CALL because we will win enough to make up for the times that we miss and lose our money.

If that doesn't make total sense, then just stick to these hard and fast rules if it makes things easier:

If your pot odds are bigger than your chances of hitting - CALL
If your pot odds are smaller than your chances of hitting - FOLD

So just think of bigger being better when it comes to pot odds. Furthermore, if you can remember back to the start of the article when we had the idea that calling smaller bets is better, you will be able to work out that small bets give you bigger pot odds - makes sense right? It really comes together quite beautifully after you get your head around it.

What if there are two cards to come?

In this article I have shown you how to work out pot odds for the next card only. However, when you are on the flop there are actually 2 cards to come, so shouldn't you work out the odds for improving to make the best hand over the next 2 cards instead of 1?

No, actually.

Even if there are 2 cards to come (i.e. you're on the flop), you should still only work out the odds of improving your hand for the next card only.

The reason for this is that if you work using odds for improving over two cards, you need to assume that you won't be paying any more money on the turn to see the river. Seeing as you cannot be sure of this (it's quite unlikely in most cases), you should work out your pot odds for the turn and river individually. This will save you from paying more money than you should to complete your draw.

I discuss this important principle in a little more detail on my page about the rule of 2 and 4 for pot odds. It's also one of the mistakes poker players make when using odds.

Note: The only time you use odds for 2 cards to come combined is when your opponent in all-in on the flop. In almost every other case, you take it one card at a time.

Playing flush and straight draws overview.

I really tried hard to keep this article as short as possible, but then again I didn't want to make it vague and hazy so that you had no idea about what was going on. I'm hoping that after your first read-through that you will have a rough idea about how to work out when you should call or fold when on a flush or straight draw, but I am sure that it will take you another look over or two before it really starts to sink in. So I advise that you read over it again at least once.

The best way to get to grips with pot odds is to actually start working them out for yourself and trying them out in an actual game. It is all well and good reading about it and thinking that you know how to use them, but the true knowledge of pot odds comes from getting your hands dirty and putting your mind to work at the poker tables.

It honestly isn't that tough to use pot odds in your game, as it will take less than a session or two before you can use them comfortably during play. So trust me on this one, it is going to be well worth your while to spend a little time learning how to use pot odds, in return for always knowing whether to call or fold when you are on a draw. It will take a load off your mind and put more money in your pocket.

To help you out when it comes to your calculations, take a look at the article on simple pot odds. It should make it all a lot less daunting.

Go back to the sublime Texas Hold'em guide.

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Is There A High Flush In Texas Holdem Odds

In this lesson you’re going to learn the first and most important step about how to play poker by learning the all important poker hand rankings.

• A standard poker hand consists of five cards.
• Each poker hand is ranked in a set order.
• The higher the rank, the less chance statistically you have of getting it.
• The higher the rank of your hand the better, because two pairs always beats one pair, and a flush always beats a straight.
• When two or more players have a hand of the same rank, then there are more ways to determine the best hand.

Hopefully all these points will make perfect sense by the end of this lesson.

Poker Hands (from Best to Worst)

Be sure to pay close attention and memorize the poker hand rankings. Let’s start with the best possible hand in poker….

Royal Flush

A Royal flush consists of five cards of the same suit, in sequence from 10 through to Ace. Remember that all suits are equal in poker. If two or more players hold a royal flush (highly unlikely) then the pot is split, i.e. the players share the winnings.

Straight Flush

Five cards of the same suit, in sequence. This example shows a Jack high straight flush. If two or more players hold a straight flush then it is the highest that wins. For example, a Queen high straight flush beats a Jack high straight flush. You will notice that this is very similar to a Royal flush, and that’s because a Royal flush is in fact an ace high straight flush – but it’s given its very own ranking.

Four of a Kind

This hand contains four cards of the same rank/value. This example shows four 8’s, plus a 5 (remember that all poker hands must have five cards). If two or more players have four of a kind, then the highest value wins (e.g. four 9’s beats four 8’s). If two or more players share the same four of a kind, which can happen when using community cards (more on that later) then the winner is decided by the fifth card. So a player with four 8’s and a 6 would beat a player with four 8’s and a 5.

Full House

A full house contains three cards of the same rank, plus a pair. In our example you can see three 10’s and a pair of 7’s. The value of the three matching cards determines the strength of a full house. So three Jack’s with a pair of 7’s would beat our example hand. If players share the same three cards, which is possible when using community cards, the strength of the pair is then taken into account. So, three 10’s and a pair of 8’s would beat our example hand.

Flush

Five cards of the same suit in any order. Our example shows a Queen high flush. If two or more players have a flush then the player with the highest ranked card wins. If the players share the same high card then it’s determined by the value of the 2nd, 3rd, 4th, and 5th card respectively.

Straight

This hand contains five unsuited cards in sequence. Our example shows a King high straight. In the event of a tie, the best straight is determined by the highest ranked card. A straight consisting of 8, 9, 10, J, Q, would lose to our example hand. But a straight consisting of 10, J, Q, K, A, would win. Also note that an Ace can be used as the low card for a straight of A, 2, 3, 4, 5. This would lose to a straight of 2, 3, 4, 5, 6.

Three of a Kind

Three cards of the same rank, and two unrelated cards. Our example shows three 4’s. Three 5’s would beat our example hand, three 6’s would beat three 5’s, and so on. If players share the same three cards, then the value of the highest unrelated card would count and if necessary, the value of the second unrelated card. So, three 4’s with Jack, 8, would beat our example hand. As would three 4’s and 10, 9 (because 9 is higher than 8).

Two Pair

Two cards of matching rank, with another two cards of another rank, plus an additional card. In the event of a tie, the highest pair wins. If players share the same highest pair, then the value of the next pair wins. For example, a pair of Aces, and a pair of 6’s would beat our example hand, as would a pair of Kings and a pair of 7’s. If two or more players share the same two pair, then the value of the fifth card counts. So, a pair of Kings, a pair of 6’s, with a 4, would beat our example hand.

One Pair

A paired hand contains two cards of matching rank, plus three additional cards. The value of the pair determines who wins in the event of a tie. For example a pair of 10’s beats our example hand. If players share the same pair then the best hand is determined by the value of the highest additional card. If this is the same then it goes to the second card, and if necessary the third. So, a pair of 9’s with an Ace, 2, and 10, would beat our example hand. As would a pair of 9’s, King, 10, and a 3.

High Card

If a hand doesn’t fall into any of the above categories, then it is judged on the value of the highest ranked card among the five. In this example we have a hand which is Queen high. If players share the same highest card, then it goes to the value of the 2nd, 3rd, 4th, and even 5th card if necessary. A hand of Queen, 10, 9, 5, 4, would beat our example hand.

Community Cards

As you already know, a poker hand consists of five cards. In many variations of poker, players receive or can choose from more than five cards. For example, in Texas Hold’em each player is dealt two private cards, but can also use the five community cards that are available for all the players to use. This makes a total of seven cards, but each player must choose their best five cards to make their best possible hand. Here’s an example:

In the above example, the best five cards among total of seven (two private cards and five community cards) would be combined to make a flush.

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Conclusion

If you don’t fully understand the poker hand rankings then please read through the list again. It’s vital that you know which hand beats which. Of course, how good a poker hand is, is very dependent on which type of poker game you are playing and other factors such as the number of other players you are playing against. You will learn the true strength of a poker hand as you gain experience of playing the game.

We have created a printable poker hand rankings chart that you can use as a source of reference. Hopefully we’ve explained the poker hand rankings to you well enough whereby you don’t need this chart, but it still might be handy for some. The chart will load as a PDF (link opens in a new window) and you’ll need to have Adobe Acrobat installed on your computer to be able to view it.

Make sure that you memorize the poker hand rankings before moving onto the next lesson.

Is There A High Flush In Texas Holdem Tournament

By Tim Ryerson

Tim is from London, England and has been playing poker since the late 1990’s. He is the ‘Editor-in-Chief’ at Pokerology.com and is responsible for all the content on the website.

Is There A High Flush In Texas Holdem Rules