Odds Of Getting Straight Flush In Texas Holdem

Posted By admin On 13/04/22
  1. Odds Of Flopping Royal Flush In Texas Holdem
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  4. Odds Of Getting A Royal Flush In Texas Holdem Poker
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Martin HarrisMo Nuwwarah

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Odds of flopping royal flush in texas holdem

Table Of Contents

In this series we are offering various strategy advice for short deck hold'em, also sometimes called six plus hold'em (or 6+ hold'em), including sharing tips from some of the pros who have found the game a fun and challenging poker variant to play.

Before we delve any further into strategy, with this article we're going to highlight some of the more interesting and notable odds and probabilities in short deck hold'em. In particular, we'll point out how those odds and probabilities differ from what you encounter in regular, full deck hold'em, which in turn creates some important differences when it comes to strategy.

Short Deck Hold'em (Six Plus Hold'em): Rules and Hand Rankings

As discussed last week, short deck hold'em tosses out all of the fives, fours, threes, and twos, creating a 36-card deck with which to play. The game is played just like regular hold'em, with players being dealt two hole cards and making hands with the five community cards dealt as a flop, turn, and river. Also, as in regular hold'em the ace can be high or low, meaning in short deck A-6-7-8-9 makes a straight.

The big change from regular hold'em comes from the hand rankings being altered. In short deck, flushes rank above full houses, and depending on the game it is sometimes the case that three of a kind beats straights.

Regular hold'emShort deck (straights beat trips)Short deck (trips beat straights)
Royal FlushRoyal FlushRoyal Flush
Straight FlushStraight FlushStraight Flush
Four of a KindFour of a KindFour of a Kind
Full HouseFlushFlush
FlushFull HouseFull House
StraightStraightThree of a Kind
Three of a KindThree of a KindStraight
Two PairTwo PairTwo Pair
One PairOne PairOne Pair
High CardHigh CardHigh Card

The reason for these changes has to do with the fact that in short deck the probabilities of making certain hands are different. In short deck, it is actually easier to make a full house than a flush, which is why flushes rank higher than full houses. (The opposite is true in regular hold'em.) It is also easier to make a straight than to make trips in short deck, which is why some rank three of a kind higher than a straight.

While some short deck games use small and big blinds just like in regular hold'em (with or without antes), others have introduced another twist by removing the blinds and having all players ante, with the button putting in a double-ante and play beginning before the flop with the player left of the button having an option to call, fold, or raise.

Short Deck Hold'em (Six Plus Hold'em): Preflop Probabilities

If you're a regular hold'em player, you're probably well acquainted with probabilities related to starting hands, and therefore know the chances of getting dealt pocket aces (1 in 221), a pocket pair (1 in 17), or two cards of the same suit (1 in 4.25). But what happens to those preflop probabilities after the fives through deuces are removed from the deck?

As you might imagine, reducing the deck from 52 cards down to 36 cards also reduces the number of different starting hand combinations there are.

Whereas in regular hold'em there are 1,326 distinct starting hands, in short deck hold'em there are only 630 distinct starting hands — less than half (about 47.5 percent). That's counting suits as distinct, which isn't generally done when valuing starting hand strength.

If we don't consider suits as distinct, in regular hold'em there are just 169 combinations of starting hands (13 pocket pairs, 78 non-paired suited hands, and 78 non-paired unsuited hands). Meanwhile when not considering suits as distinct, in short deck hold'em there are just 81 combinations of hands (9 pocket pairs, 36 non-paired suited hands, and 36 non-paired unsuited hands) — again, less than half as many in short deck versus regular hold'em (about 47.9 percent).

Fewer starting hand combos obviously affects the frequency with which you are dealt specific hands. For example, when it comes to being dealt pocket aces, that happens about twice as often in short deck hold'em — once every 105 hands (just under one percent of the time).

Pocket pairs come around more frequently in short deck, too — once every 11.66 hands (about 8.6 percent of the time). That's almost 1.5-times as often as in regular hold'em.

Meanwhile in short deck you're dealt suited hands at just about the same frequency as in regular hold'em — once every 4.375 hands (or about 22.8 percent of the time).

Here is all of that in table form, with a couple more comparisons of probabilities added to the list:

Regular hold'emShort deck (Six Plus) hold'em
Number of cards used5236
Distinct starting hands1,326630
Distinct non-equivalent starting hands16981
Probability of being dealt pocket aces0.45% (1 in 221)0.95% (1 in 105)
Probability of being dealt any pocket pair5.9% (1 in 17)8.6% (1 in 11.66)
Probability of being dealt any suited hand23.5% (1 in 4.25)22.9% (1 in 4.4)
Probability of being dealt connectors15.7% (1 in 6.4)22.9% (1 in 4.4)
Probability of being dealt ace-king1.2% (1 in 83)2.5% (1 in 39)
Probability of being dealt two Broadway cards14.3% (1 in 7)30.2% (1 in 3.3)

It’s obvious players have to adjust their thinking when it comes to starting hands and their value in short deck hold’em. Hand values go up in short deck, so what might seem like a decent starting hand in regular hold’em is going to be average or worse in short deck.

Another preflop issue to keep in mind — with fewer starting hands overall, that means the gap in equities between starting hands is narrower as well. For example, in a preflop all-in situation, is about a 78 percent favorite to beat in regular hold'em, but in short deck hold'em the aces are only about 63-67 percent to win depending on the rules being used. Search online for 'short deck hold'em calculator' or 'six plus hold'em calculator' if you're curious to test out some hand comparisons using some recently-built equity calculators.

We’ll talk more about preflop strategy in the next installment.

Short Deck Hold'em (Six Plus Hold'em): Postflop Odds

Postflop is where short deck hold'em introduces some surprises to new players, since the odds and probabilities can be quite different from regular hold'em.

Of course, if you just take a moment to think about it, it's obvious that when drawing to a certain number of outs, the chance of hitting your needed card changes when there are fewer cards left in the deck.

Let's say you hold and the flop comes to give you an open-ended straight draw. You have eight outs (the kings and the eights) to fill your straight, but instead of there being 47 unseen cards (as in regular hold'em), there are only 31 unseen cards in short deck. Whereas in regular hold'em you'd have an 8 in 47 chance of filling your straight on the turn (about 17 percent), in short deck hold'em your odds of turning the straight are 8 in 31 (nearly 26 percent).

I have seen discussions of short deck hold'em outs recommending players replace the 'Rule of 2 and 4' from regular hold'em with a new 'Rule of 3 and 6' for short deck. In regular hold'em, if you flop an open-ended straight draw with eight outs, you can roughly estimate your chance of filling the straight by multiplying those eight outs by two for the turn (~16 percent) and by four for the turn and river (~32 percent).

In short deck you can do something similar, multiplying your eight outs by three for the turn (~24 percent, which is close to the actual 25.8 percent) and by six for the turn and river (~48 percent, which is also close to the actual 45.6 percent).

Here's a table showing how your odds of hitting a certain number of outs change from regular hold'em to short deck:

Regular Hold’em OutsTurnTurn+RiverShort Deck Hold’em OutsTurnTurn+River
12.1%4.3%13.2%6.5%
24.3%8.4%26.5%12.7%
36.4%12.5%39.7%18.7%
48.5%16.5%412.9%24.5%
510.6%20.4%516.1%30.1%
612.8%24.1%619.4%35.5%
714.9%27.8%722.6%40.6%
817.0%31.5%825.8%45.6%
919.1%35.0%929.0%50.3%
1225.5%38.4%1238.7%63.2%
1531.9%54.1%1548.4%74.2%

By the way, don’t forget when you are drawing to a flush that there are fewer outs available to you in short deck than in regular hold'em. If you flop a flush draw in regular hold’em you have nine outs, but in short deck you only have five.

Short Deck Poker Strategy

As already noted, hand values tend to be higher in short deck hold’em, which means one-pair hands aren’t going to be as strong postflop in short deck as they are in regular hold’em. And thanks to the increased chance of players filling draws, those one-pair hands and other modest “made hands” are going to be more vulnerable, too.

Speaking of pairs, it's important to remember that pocket pairs in short deck should be valued drastically differently. Aces and kings are obviously strong hands in regular hold'em, and that stays true in short deck, except the difference between the two is even more pronounced.

Things change quickly after that as pairs below kings are unexciting holdings in short deck. The reason for this will be familiar to any pot-limit Omaha player of decent experience level: similar to PLO, the only easily dominated hands in short deck are pocket pairs.

Where traditional 'dominated' spots in hold'em — like ace-queen against queens — are much closer in equity in short deck, holding a pair versus a higher pair is still a pretty rough spot. And medium pairs are actually a slight dog against overcards, in contrast to regular hold'em. Pairing hole cards happens much more often in short deck, and it's far easier for connecting cards to make straights.

Because equities run much closer in short deck, it's important to maximize opportunities for high-equity spots like holding bigger pairs while minimizing the times you're on the wrong side of that.

A few other items related to postflop probabilities in short deck:

  • with suited cards you flop flush draws less often in short deck, and complete flushes less often as well
  • with connectors and one-gappers you flop straight draws more often in short deck, and complete them more often, too
  • with a pocket pair, you flop a set more often in short deck (about 17 percent of the time vs. 12 percent in regular hold’em

We'll be exploring postflop strategy in more detail going forward in the series as well. Blockers, bluffing opportunities and more will be examined in the coming weeks.

Meanwhile, take a look at the video below and listen to Tom Dwan, Patrik Antonius, Daniel Cates, Kane Kalas, Jason Koon, Phil Ivey, Wai Kin Yong, and Gabe Patgorski offer some general advice about how to approach short deck hold’em strategy.

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    cash game strategytournament strategyshort deck hold’emsix plus hold’emoddsprobabilitiespreflop strategypostflop strategydrawing handsstarting hand selection

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.

Odds Of Flopping Royal Flush In Texas Holdem

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.

Odds of getting straight flush in texas holdem rules

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?

Odds Of Getting Straight Flush In Texas Holdem Tournaments

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 Getting A Royal Flush In Ultimate Texas Hold Em

  • $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.

Odds Of Getting A Royal Flush In Texas Holdem Poker

Royal

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.

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Go back to the sublime Texas Hold'em guide.

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Odds Of Getting A Royal Straight Flush In Texas Hold Em

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