The odds of flopping a Flush with a suited starting hand is 0.82% or 1 in 122
If you ever wanted to know some of the odds and probabilities of Texas hold'em poker, from the chances of flopping a flush (0.8%) or set (12%) to the odds of an overcard coming on the flop when.
Definition of Flush –
We make a Flush by having five cards of the same suit.
Example – AhJh7h3h2h
An Ace-High Flush is the strongest Flush in poker. However, the suits are all treated equally, and only the denominations are used to determine which Flush beats the other.
Flush Over Flush PokerOdds of Making a Flush on the Flop
Naturally, the odds of making a Flush on the flop depends on the type of starting hand we are dealt.
Odds of flopping a Flush with any starting hand = 0.2%
Odds of flopping a Flush with a suited starting hand = 0.82%
Odds of flopping a Flush with an unsuited starting hand = 0%
The type of suited hand we have does not affect the odds of making a Flush, but higher ranked cards will make stronger Flushes. Also, although the type of suited hand does not affect the odds of making a Flush, it will affect the odds of making a Flush or better.
Odds of flopping a Flush or better with any starting hand = 0.37%
Odds of making a Flush or better with a suited connector = 0.94%
Odds of making a Flush or better with a pocket pair = 1.22%
Odds of making a Flush or better with AKo = 0.1%
Odds of making a Flush or better with T9s = 0.94%
Odds of Making a Flush Draw on the Flop
Flopping a Flush is most unlikely and requires us to have two suited cards in the hole already. However, Flush draws are a lot more common, so it’s worthwhile knowing the odds of flopping four of the five cards required to make a Flush.
Odds of flopping a two card Flush draw with any starting hand – 2.58%
Odds of flopping a Flush draw with two suited cards – 10.9%
Odds of flopping a one card nut Flush draw with any starting hand – 0.17%
Odds of flopping a one card nut Flush draw with an Ax holding – 1.12%
Odds of flopping any one card Flush draw with an unsuited starting hand – 2.24%
The most useful piece of information here is that we will flop a Flush draw around 11% of the time when starting out with a suited hand.
While the probability of flopping a one card Flush draw with an unsuited starting hand is always 2.24%, it’s worth remembering that non-nut one-card Flush draws are not especially valuable holdings.
For the most part, we prefer our one card Flush draws to be to the nuts.
Odds of Making a Flush on the Later Streets
Let’s assume that we have flopped a Flush draw. How likely are we to make a Flush on the later streets?
Odds of making a Flush on the turn or river
When holding a Flush draw, there are always 9 cards remaining in the deck that can complete our Flush draw.
Hence -
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% 888 poker reload bonus code list.
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%.
Probability of not hitting a Flush draw on the turn – 38/47
Probability of not hitting a Flush draw on the river – 37/46
Probability of not hitting by the river is 38/47 * 37/46 = 0.6503 or roughly 65%
Therefore the odds of making a Flush by the river is (100% - 65%) roughly 35%.
Implied Odds Analysis of a Flush
The implied odds of a Flush depend on two main factors.
Two-Card or One-Card – Two-card Flushes (made with both hole cards) always carry better implied odds than one-card Flushes. A two-card Flush on non-paired board texture is always strong enough to play for 100bb stacks with. Non-nut one card Flushes, on the other hand, are little more than bluff-catchers in many situations.
Paired or Unpaired Board – Flushes always carry the best implied odds on unpaired board textures. When the board is paired, Flushes need to be treated with more caution since our opponent may have already made a Full House.
Basic Strategy Advice
Two-card strong Flushes are very powerful holdings in Hold’em and are good enough to play for 100bb stacks.
Two-card Flushes on paired textures are still relatively strong, although it might be safer to avoid getting all of our stack in where possible.
One-card Flushes are only worth playing for stacks with when it’s the nut Flush. 2nd nut one-card Flushes and lower are not overly strong in Hold’em.
If Villain wants to get the stacks in, he likely has a stronger one-card Flush. Mid-strength one-card Flushes are, therefore, little more than bluff-catchers in Hold’em.
The odds of flopping a straight flush with a premium suited connector such as T9s is 0.02% or 1 in 4,900
Definition of the Straight Flush –
Five cards of consecutive rank, all of the same suit.
Example – 5d6d7d8d9d
The Ten to Ace Straight Flush is the strongest hand in poker and is referred to as the “Royal Flush”.
Odds of Making a Straight Flush on the Flop
Flopping a Straight Flush seldom happens in poker. We specifically need to start out with two suited connected cards for this to be possible.
The odds of flopping a Straight Flush are so unlikely (0.02% or less) that the majority of poker equity calculators don’t even show the precise odds.
We’ll need to do some maths of our own.
Calculation of Straight Flush Odds
Let’s start with a very specific example -
We hold A2s. What are the odds of flopping the Ace to Five Straight Flush?
Why do we choose this example? It’s the easiest one because it provides only one way of making the Straight Flush. The flop has to come down precisely Three, Four, Five of the correct suit.
So, how likely is this?
In order to calculate, we’ll first need to know how many combinations of three cards are possible on the flop.
Basic Combinations and Permutations
Firstly, how many different combinations of three cards can be dealt on the flop? Assuming we care about the order of the three cards (and that our two hole cards are already known), the answer is 117,600 (50 * 49 * 48).
In statistics, this type of calculation is referred to as a permutation and accounts for the order of the flop cards.
Of course, in Hold’em, the order of the cards on the flop doesn’t matter (i.e. a 3,4,5 flop is the same as a 5,3,4 flop, for all intents and purposes). What we are interested in is the number of possible combinations of three cards.
A combination is similar to a permutation but doesn’t account for the order. Since there are 6 possible ways of arranging three cards, we can simply divide our number of permutations (117,600) by 6 to establish the number of possible three-card combinations on the flop.
117,600 / 6 = 19,600 possible combinations of three cards on the flop (given two cards are known)
In other words, there are 19,600 different possible sets of three cards that may fall on the flop given that our two hole cards are already known.
Guess what?
To make the exact Straight Flush in question, only one of these 19,600 combinations will do the job.
Armed with that information, we can now establish a range of different probabilities.
Odds of flopping the Straight Flush with A2s = 1/19,600 = 0.00005 or roughly 0.005%
That’s an insanely small likelihood!
Thankfully, the odds with different types of starting hands are usually a little better.
It all depends on the number of different combinations of three cards that provide a Straight Flush.
For example, think about T9s.
How many different ways are there to make a Straight Flush with 9Ts?
Ways of making a Straight Flush with T9s
JQK
QJ8 J87 678
So that’s four different ways. We are hence four times as likely to make a Straight Flush with 9Ts as we are to make a Straight Flush with A2s.
Odds of flopping the Straight Flush with 9Ts = 4/19,600 = 0.0002 or roughly 0.02%
Ways of making a Straight Flush with T8s
QJ9
J79 679
Odds of flopping the Straight Flush with T8s = 3/19,600 = 0.00015 or roughly 0.015%
Ways of making a Straight Flush with T7s
J89
689
Odds of flopping the Straight Flush with T7s = 2/19,600 = 0.0001 or roughly 0.01%
Only suited connectors (or gappers) can make Straight Flushes on the flop. All other holdings such as pocket-pairs and off-suit combos can never flop a Straight Flush.
We are, naturally, more likely to flop a Straight Flush draw as opposed to the Straight Flush itself. To see examples of calculating the odds of hitting a Straight Flush draw on the flop, check out the 888poker article on Royal Flush odds in poker.
Odds of Making a Straight Flush on the Later Streets
There will be two primary types of Straight Flush draw we’ll flop. The gutshot Straight Flush draw and the open-ended Straight Flush draw.
Gutshot Straight Flush draws have 1 out in the deck, while open ended Straight Flush draws have 2 outs in the deck.
Odds of Hitting on the Turn or River
Odds of catching the gutshot Straight Flush on the turn 1/47 = 0.0213 or roughly 2.1%
Odds of catching the open-ended Straight Flush on the turn 2/47 = 0.426 or roughly 4.3%
Odds of catching the gutshot Straight Flush on the river 1/46 = 0.0217 or roughly 2.2%
Odds of catching the open-ended Straight Flush on the river 2/46 = 0.0435 or roughly 4.4%
Odds of Hitting by the River
To calculate the probability of hitting by the river, we’ll employ the trick of calculating the possibility of not hitting and then subtracting from 100%.
Odds of not catching the gutshot Straight Flush on the turn 46/47
Odds of not catching the open-ended Straight Flush on the turn 45/47
Odds of not catching the gutshot Straight Flush on the river 45/46
Odds of not catching the open-ended Straight Flush on the river 44/46
Odds of not catching the gutshot Straight Flush on the turn or river = 46/47 * 45/46 = 0.9574 or roughly 95.7%
Odds of not catching the open-ended Straight Flush on the turn or river = 45/47 * 44/46 = 0.9158 or roughly 91.6%
Odds of hitting the gutshot Straight Flush by the river = (100- 95.7%) roughly 4.3%
Odds of hitting the open-ended Straight Flush by the river = (100 – 91.6%) roughly 8.4%
Implied Odds Analysis of a Straight Flush
A Straight Flush always carries excellent implied odds when hitting. This is because our opponent is usually forced into stacking off with very strong worse hands such as worse flushes and full houses.
Straight Flushes made with two of our hole cards always carry better implied odds than Straight Flushes made with one of our hole cards.
When using just one of our hole cards, it means there will be four cards to the Straight Flush already on the board. This decreases the chance that our opponent will pay us off with worse holdings.
Although Straight Flushes should hardly ever be folded, their implied odds are the best when no higher Straight Flush is possible on the board.
Basic Strategy Advice
It’s basically the nuts. Play aggressively and make big bets! Even if a higher Straight Flush is possible, it’s usually just a cooler if we are beat. We’d have to be really deep to find an exception.
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