This leaves 9 cards of your suit, and 38 of a different suit; your odds of completing your flush on the turn are thus 9/47, or 19.14%. If the turn hasn't completed your flush, your odds of completing it on the river are 9/46, or 19.5%.
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Once you familiarize yourself with basic Texas Hold ‘em play, hand rankings and dealing, you should learn about the odds and probabilities associated with different aspects of the game. While it may be impossible to calculate precise odds mid-hand, particularly given you’ll never see your opponents’ cards until all decisions have been made, knowing when to play (and when not to play) different hands typically requires more than just good instinct.
In Texas Hold ‘em, winners are often decided before the community cards are even laid out, so the chances of being dealt a strong starting hand is something many players think.
Calculating Texas Hold ‘em Odds
To understand the odds of drawing any particular starting hand, you’ll have to consider all of the factors that go into the deal of a hand. Considering a shuffle to completely randomize the order of the cards, the biggest factors that will affect a draw are the number of players at the table and your own position relevant to the dealer. Also consider that there are four cards of any given value in each deck and there are 169 different hole card combinations. That being said, there’s a roughly one in 1326 chance that players will be dealt any specific hand, so it’s important to know what kind of odds you should keep in mind whenever you step to the poker table.
Pre Flop
You have a 55:1 chance of being dealt a pair of Jacks or higher.
Your Texas Hold’em experience will begin with your hole cards, and while you cannot change the cards that are dealt your way, it’s good to know what to expect. While World Series of Poker reruns may make it seem like someone at the table will be dealt pocket kings every hand, starting with a monster hand is rarer than you may imagine. For more on Pre Flop strategy see our guide here.
Quick Odds
While an extensive list of the probabilities for preflop hands could fill a book, here are some quick odds to consider when you’re peeking at your cards for the first time.
- Being dealt a pocket pair: 16:1
- Being dealt suited cards: 3.2:1
- Being dealt suited connectors: 24:1
- Being dealt AK: 82:1
- Being dealt two cards of jack or higher: 10:1
- Being dealt AA, KK, QQ or JJ: 55:1
The Flop
The flop is a game changer in every sense of the words. With more cards in your hand, players will get their first real taste of what the final outcome will look like. That being said, players will want to think about the odds for how their hand could turn out before they start placing or calling bets. For more on Post Flop strategy see our guide here.
Quick Odds
Though the presented odds may be mathematically accurate, they do present a best case scenario that you won’t always find yourself in at the table. These calculations don’t take into account the probabilities of the card or cards you are looking for turning up as burn cards or in your opponents’ hands, so keep that in mind when considering your next move.
- Hitting a pair on the flop: 2:1
- Pocket pair improving to three of a kind on the flop: 7:1
- Flop being three of a kind: 424:1
- Odds of flopping a flush with suited hole cards: 118:1
The odds of flopping a straight can be a bit harder to pin down. Depending on your starting hand, there are any number of card combinations that could lead to a flopped straight. Those hands that have the more flexibility when it comes to straight draws, particularly middling connectors (those between 5 and 9), have the strongest chances of hitting on the flop because there are more cards that could allow for their straight to hit. The wider the gap between your starting cards, the worse your chances are.
The Turn and River
Naturally, as the hand progresses and fewer cards remain to be dealt, the odds of making any particular hand become slimmer and slimmer. That being said, you’ll want to look at the odds for a hand from beginning to end as well as those from stage to stage.
Quick Odds
Your odds change as each new card is dealt.
Texas Holdem Odds And Probabilities
Over the course of a full hand, these scenarios could play out
- One pair on flop improving to two pair or a set by the river: 4:1
- Catching an ace on the turn or river: 7:1
- Open ended straight hitting by the river: 2:1
- Gutshot straight draw hit by the river: 5:1
- Pocket pair improving to set by river: 10:1
- Going runner runner for a flush: 23:1
- Going runner runner for a straight: 67:1
Pot and Implied Odds
In addition to the odds that your cards will pair or better, experienced players know that pot odds, that is, the ratio of the size of the pot to the cost of a call, play an important role in proper Hold’em strategy. With all of the risks that are inherently involved in games like poker, players won’t get far if they don’t decide to gamble every so often – and pot odds allow you to make smarter decision when it comes time to place your money on the line. Pot odds take into consideration the likelihood of making a hand to establish a decent risk vs. reward ratio.
Another important statistic for players to keep in mind is ‘implied odds,’ which factor in the likely size and frequency of any betting that may come in later rounds of play. These come into play post flop and will be a factor until the river is dealt, and unlike most other Texas hold ’em odds, implied odds will be entirely based on your read on your opponents’ betting habits and aggression.
To calculate effective pot odds, consider your position in the hand and relative strength, then make a note of the amount of money currently in the pot. If you’re in a position to call, think of how much you stand to win should your hand come out ahead, as establishing a solid return on investment can help turn a questionable call into a big win. If no one has bet, then pot odds can help you deduce what size bet you will want to make in order to shift the statistical probabilities in your favor. With a sound bet, you could either make the continued investment not worth the potential gain or place a value wager designed to elicit a call from any remaining opponents. You will have to decide whether or not your chances of winning are worth risking the amount you could lose if you are wrong – a fine line for some players, but one that must be crossed often. For more on Texas Hold’em pot size and strategy see our guide here.
Mathematics: Flushes & Straights : Simple Pot Odds : Implied Odds : Reverse Implied Odds
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...
Odds Of A Royal Flush In Texas Holdem
- $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.
Texas Holdem Odds Calculator
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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