Probability Of Straight Flush Texas Holdem

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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. The worst case for a possible straight flush is holding something like A2s, AKs, A5s, etc., where there's only one possible way to flop the straight flush. In that case, the probability is one in 50C3, or 19600. The best case is 45s.TJs, which is 4 in 19600, because there are 4 ways to flop the straight flush. Let’s assume that you are playing 5-card poker, and that you don’t get to discard. Then your question is equivalent to asking, “What is the probability of being dealt 5 cards that are a straight flush?”.

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.

If you've got a flush draw (one card short of a full flush) after the flop, you'll make your hand 34.97% of the time. That's just over a third. Probability in% Odds: Royal flush: 4: 0.: 649737:1: Straight flush: 36: 0.: 72193.5:1: Four-of-a-kind: 624: 0.: 4163.99:1: Full house: 3744: 0.144057623: 693.17:1: Flush: 5108: 0.: 507.8:1: Straight: 10200: 0.: 253.8:1: Three-of-a-kind: 54912: 2.: 46.3:1: Two pair: 123552: 4.: 20:1: Pair: 1098240: 611: 1.366:1: High card: 1202540: 035.

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:

  1. Find out how many unknown cards there are in total.
  2. Find out how many outs we have.
  3. Make ratio of outs to non-outs.
  4. 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.

  1. 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.
  2. 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.
  3. Ratio = 37:9
    • Out of 46 unknown cards, if we take away 9 outs we are left with 37 unwanted cards.
  4. Simplified ratio = 4.1:1
Straight

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.

  1. Total number of unknown cards = 47
    • 52 minus 5 cards we can see (2 in our hand and 3 on the flop).
  2. 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.
  3. Ratio = 35:12
    • 47 - 12 = 35.
  4. 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).

  1. Total number of unknown cards = 46
  2. Total number of outs = 11
    • 9 hearts left in the deck.
    • 2 twos.
  3. Ratio = 35:11
    • 46 - 11 = 35.
  4. 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.

  1. Total number of unknown cards = 47
  2. Total number of outs = 6
    • 8 straight draw outs in total (4 nines and 4 aces).
    • Minus the A and 9 = 6.
  3. Ratio = 41:6
    • 47 - 6 = 41.
  4. 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:

  1. Find out how many outs you have.
  2. 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.

Still struggling with playing flushes (and flush draws) in cash games? Try watching SplitSuit's strategy video on playing Flushes and Flush Draws.

Go back to the interesting Texas Hold'em Articles.

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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% 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?

    Probability Of Straight Flush Texas Holdem Tournaments

    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.

    Chance Auf Royal Flush Texas Holdem

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

    Probability Of Straight Flush Texas Holdem Rules

    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 3rd 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 3rd 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 2nd nut straight, just less.

    Probability Of Straight Flush Texas Holdem Odds

    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?

    Probability Of Straight Flush Texas Holdem Poker

    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)

    Chances Of Royal Flush Texas Holdem

    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.