Dec 25, 2019 Poker Tips & Strategy The Odds of Different Rare Card Hands Author: Ivan Potocki December 25, 2019. There are very few feelings in poker that beat the one of flopping quads or a straight flush. There you are, sitting with the absolute nuts and your only job is to figure out how to milk your opponents most money you can. As you can see in the above table, if you’re holding a flush draw after the flop (9 outs) you have a 19.1% chance of hitting it on the turn or expressed in odds, you’re 4.22-to-1 against. The odds are slightly better from the turn to the river, and much better when you have both cards still to come.

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.

Royal Straight Flush Odds

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

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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.

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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 Flopping Two Pair

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

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Poker Odds Of Flopping A Straight Flush