Texas Holdem Flush Draw Odds

Posted on 7/22/2022 by admin

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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.

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. In Texas Hold’em a hand where aces, kings and queens pair up preflop is very rare. At a 9 player table this scenario unfolds roughly every 17,000 hands. The odds are 1:16,830 and the probability is 0.006%. Queens does happen every now and then, for example during this hand at the Bike.

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.

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%. This means that the total odds for completing a flush - which should matter for example if you're going all in after the flop - are (19.14%) + (19.5%. (1-19.14%)) = 34.96% (the odds of completing on the turn, plus the odds of completing on the river times the. Odds of completing a Flush draw on the turn – 9/47 = 0.1915 or roughly 19.2% Odds of completing a Flush draw on the river – 9/46 = 0.1957 or roughly 19.6% Odds of making a Flush by the river Here we will use the simple trick of calculating the probability of not hitting our Flush draw and then subtracting from 100%.

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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Okay, so you know how to work out the odds for hitting a flush draw or a straight draw. In fact, every pot odds article you've ever read uses either a flush or a straight draw (or both if you're lucky) as their main example to help explain how it all works.

The odds of hitting a flush draw on the turn are 4.2 to 1.
The odds of hitting a straight draw on the turn are 4.9 to 1.

Easy stuff. But what if you're draw isn't a straight or flush draw? What about if your draw is a combination of both? Or how about if you're drawing to something unusual/random like four of a kind?

In this article I'll show you the method for working out the odds for uncommon draws in Texas Hold'em. I'll also throw in a bunch of examples for good measure.

The method for working out odds of random draws.

The method for working out unusual draws is exactly the same as the method for working out standard flush or straight draws.

You find out how many outs you have, then compare that number of outs to the number of cards that won't help you (e.g. “non-outs” : ”outs”).

Note: “Outs” are cards that will complete the draw you are chasing after. (e.g. if you are after the last Ace to make 4-of-a-kind, you only have 1 out).

The important part here is just find the number of outs you have. After you've figured that out, the rest is a doddle. If you're not familiar with the basic process, I'd highly recommend you have a read through the main pot odds article first. But for the rest of you, I'm going to use the following steps:

Find out how many unknown cards there are in total.
Find out how many outs we have.
Make ratio of outs to non-outs.
Simplify that ratio to make it easier to work with.

Examples of working out odds for different types of drawing hands.

1) Flush draw on the turn.

We'll start with something simple.

Our hand: A 2
Board: K 9 7 3

In this example, we have a flush draw, but we're on the turn instead of the flop. Therefore, there will be one less unknown card than usual to include in our workings out.

Total number of unknown cards = 46

2 cards in our hand.
4 cards on the board.
52 (total number of cards in a deck) minus 6 = 46.

Total number of outs = 9

There are 13 hearts in the deck.
2 of them are in our hand.
2 of them are on the board.

Ratio = 37:9

Out of 46 unknown cards, if we take away 9 outs we are left with 37 unwanted cards.

Simplified ratio = 4.1:1

Easy! The only difference that you have to remember in this example is that we are on the turn and not the river. As a result, there is one less “unknown” card left in the deck due to the fact that we can now see the turn card.

The majority of examples work out odds for when you're on the flop waiting for the turn, so I thought I'd do one for when you're on the turn waiting for the river.

2) Flush draw + inside straight draw on the flop.

Our hand: A 2
Board: K T Q

In this example we have a standard nut flush draw, but we also have an inside straight draw to boot.

Total number of unknown cards = 47

52 minus 5 cards we can see (2 in our hand and 3 on the flop).

Total number of outs = 12

9 hearts left in the deck.
3 jacks. Don't forget that the J has been included in the 9 hearts above for the flush draw.

Ratio = 35:12

47 - 12 = 35.

Simplified ratio = 2.9:1

The important part here is to remember that one of the jacks has already been included as an out for our flush draw. Many players make the mistake of believing that they have 9 hearts + 4 jacks, thinking they have 13 outs instead of 12.

Always double check to make sure that you're not including your outs twice when they can overlap like in this example.

3) Flush draw + 3-of-a-kind draw on the turn.

Our hand: A 2
Board: K 9 7 2

Let's say that we are confident that our opponent only has a pair or two-pair at best. Therefore, if we can improve our pair of twos to 3-of-a-kind, we will be able to win the hand (as well as if we are able to make a flush).

Total number of unknown cards = 46
Total number of outs = 11

9 hearts left in the deck.
2 twos.

Ratio = 35:11

46 - 11 = 35.

Simplified ratio = 3.2:1

This one's pretty straightforward. There are 2 twos left in the deck, and neither of them are hearts so we don't have to worry about these 2 outs overlapping with our flush draw outs.

4) Straight draw on the flop, and flush cards do not help us.

Our hand: Q J
Board: K T 2

In this example we have a common open-ended straight draw. However, the problem is that there is also a flush draw on the flop. We are confident that our opponent has either top pair (or better) or a flush draw. This means that we are not interested in continuing with our hand if another spade comes on the turn. Therefore, the A and 9 are not going to be considered as outs.

Total number of unknown cards = 47
Total number of outs = 6

8 straight draw outs in total (4 nines and 4 aces).
Minus the A and 9 = 6.

Ratio = 41:6

47 - 6 = 41.

Simplified ratio = 6.8:1

Thanks to the flush draw cards our straight draw odds become a lot worse. We could just work out our normal straight draw odds including the spade cards (4.9:1) and then try to account for reverse implied odds as best as we can. However, this method is a lot simpler.

Final thoughts on working out odds for unusual draws.

Working out your odds of completing unusual draws and random types of hands all boils down to finding your total number of outs. After that, all you have to do is work through a small number of simple steps and you're done.

If you can figure out the exact number of outs you have, you'll never have a problem with odds.

Just remember:

Find out how many outs you have.
Make a ratio of non-outs to outs and simplify it.

Using this method you should be able to work out the odds in other random situations like:

When the dealer accidentally flips over a card and has to burn it in a live game.
When a player announces what cards they held before the hand is over.
When you want to work out the odds of improving from 3-of-a-kind to 4-of-a-kind, because I mentioned it at the start of this article but didn't actually give an example (hint: you only have 1 out).

Note: After working your odds out you can compare your results with the list of odds found in the ratio odds chart.

Also, throughout this “unusual draws and their odds” article I've just worked out the ratio odds for different types of draws. If you're more comfortable using percentage odds, you can just use the same number of outs as before and use the rule of 2 and 4 to get a rough idea of your percentage odds.