Common Flop Odds

There have been several posts asking for flop odds lately. This chart puts most of the important flop odds all together.

Texas Hold'em Flop Odds

Common odds when holding unpaired hole cards:

Code:

flopping EXACTLY one pair by pairing a hole card                                    26.939% 
flopping EXACTLY two pair by pairing a hole card AND pairing on the board            2.02%
flopping EXACTLY two pair by pairing EACH of your hole cards                         2.02% 
flopping EXACTLY trips by flopping two cards to one hole card                        1.347% 
flopping EXACTLY a full house, trips of one hole card and pairing the other          0.092%
flopping EXACTLY four of a kind, three cards to one of your hole cards               0.01%

Common odds when holding paired hole cards:

Code:

flopping EXACTLY two pair by pairing the board                                      16.163% 
flopping EXACTLY trips by flopping a set for your pocket pair                       10.775% 
flopping EXACTLY a full house, a set to your hole pair and pairing the board         0.735%
flopping EXACTLY a full house, by the board tripping up                              0.245%
flopping EXACTLY four of a kind, two cards to your hole pair                         0.245%

Common odds when holding two unsuited cards:

Code:

flopping a four flush                                                                2.245%

Common odds when holding two suited cards:

Code:

flopping a flush (including the slight chance of a straight flush in some cases)     0.842%
flopping a four flush                                                               10.944%

Common odds when holding connectors from 54 to JT

Code:

flopping a straight (including the slight chance of a straight flush in some cases)  1.306%
flopping an 8 out straight draw*                                                    10.449%

Common odds when holding one gapped connectors from 53 to QT

Code:

flopping a straight (including the slight chance of a straight flush in some cases)  0.980%
flopping an 8 out straight draw*                                                     8.08% **

Common odds when holding two gapped connectors from 52 to KT

Code:

flopping a straight (including the slight chance of a straight flush in some cases)  0.653%
flopping an 8 out straight draw*                                                     5.224% **

Common odds when holding three gapped connectors from A5 to AT

Code:

flopping a straight (including the slight chance of a straight flush in some cases)  0.327%
flopping an 8 out straight draw*                                                     2.612% ***

Notes

* An 8 out straight draw includes open ended straight draws and double barrelled gut shots.
** The odds are 0.327% less for the combinations on the edge as they have one less opportunity for a double barrelled gut shot.
*** Only the 95 and T6 three gappers have the posted 8 out draws, all the other three gappers have a lower chance. The closer the three gapper is to the edge, the lower the chance.

Where did you get these? I only glanced at a few and they were wrong...

They look about right to me...

They look wrong to me.

Odds of flopping one pair on unpaired hole cards is 41%, I am sure.

I'm certain that it is over 27%.

The key word here is EXACTLY...

Dwarfman I think you are talking about the odds of flopping AT LEAST one pair instead of EXACTLY one pair.

So what is the odds of flopping AT LEAST one pair? Lets see that would be 1 - the probability of neither of your two cards being paired on the flop. The probability of not pairing either of your cards is (44/50)*(43/49)*(42/48), subtract that from 1 and you get 0.3242857 or 32.42857%.

Add the following percentages and see what you get:

flopping EXACTLY one pair by pairing a hole card 26.939%
flopping EXACTLY two pair by pairing a hole card AND pairing on the board 2.02%
flopping EXACTLY two pair by pairing EACH of your hole cards 2.02%
flopping EXACTLY trips by flopping two cards to one hole card 1.347%
flopping EXACTLY a full house, trips of one hole card and pairing the other 0.092%
flopping EXACTLY four of a kind, three cards to one of your hole cards 0.01%

Originally Posted by dwarfman

Odds of flopping one pair on unpaired hole cards is 41%, I am sure.

Wrong, your odds of having a pair or better when all 5 cards are out are probably around 41%. Odds of flopping are around 1 in 3.

Originally Posted by DaNutsInYoEye

Where did you get these? I only glanced at a few and they were wrong...

All of these numbers were confirmed from external sources save the numbers of flopping 8 out straight draws. If you feel a number is incorrect, I invite you to point it out and we can walk through the math and the references. Errors are always possible. But, save for the 8 out straight draws, it would mean that lots of sources are making the same error or I mistyped an entry.

Originally Posted by dwarfman

They look wrong to me.

Odds of flopping one pair on unpaired hole cards is 41%, I am sure.

I'm certain that it is over 27%.

The 41% number is a common misconception. It is true that if your hole cards are unpaired then you have a 40.408% chance of having a pair after the flop. But that percentage includes pairs from the board that completely miss your hole cards. This is why I tried to be explicit and describe that you have a 26.939% chance of hitting a pair by pairing one of your hole cards. Again, while the numbers are easy to compute and available from multiple sources, I will quote Ken Warren from his guide:

Originally Posted by Winner's Guide to Texas Hold'em Poker, Ken Warren

When your hand is not a pair, you will flop one pair 40.408% of the time. However, 1/3 of these pairs will be on the board and not pair one of your hole cards. That means you will flop one of your hole cards 26.939% of the time.

To see where the numbers come from, you can compute them fairly quickly. You are looking for 6 possible cards (the 3 of each of your hole cards), then you are looking for a card that is not one of your hole cards (44 remaining), then you are looking for a card that is not one of your hole cards AND is not a match to the card that just flopped which would give you two pair using the board. Then there are three ways for that to fall (think of it as your pair falling on the first, second, or third card of the flop). All divided by the number of possible cards in each case, 50 * 49 * 48. The comes to ((6 * 44 * 40) / ( 50 * 49 * 48 )) * 3 which equals 26.939%.

Most of these numbers I computed myself and then confirmed from various sources. The primary source was Winner's Guide To Texas Hold'em Poker, Ken Warren. Though the numbers were available in multiple locations and are fairly easy to compute. The 8 out straight draws are tricky due to double barrelled gut shots. I think I found all the possible ways of making them for the various connectors but I may have missed some. I invite discussion.

As some have questioned the odds I posted, I will walk through the computations. As I stated above, save for the 8 out straight draw numbers, these numbers can all be found in reference manuals. But there is no magic to them so I will demonstrate how to compute them.

There are scads of ways to compute these numbers. Each correct method will arrive at EXACTLY the same number. I will choose certain methods that I think best describe what is going on. You can CERTAINLY arrive at EXACTLY these same numbers using different representations of the problem.

Holding unpaired cards and flopping EXACTLY one pair by matching a hole card.

I walked through that one above. You are looking for one of the 3 cards that match hole card 1 or the 3 cards that match hole card 2. So you are looking for one of 6 cards. Then you are looking for any card that DOES NOT match either of your hole cards (52 cards minus the 2 in your hand minus the 1 card that matched the first time minus the 5 cards that remain that match you hole cards = 44 cards). Then you are looking any card that DOES NOT match your hole cards AND does not match the card that just fell, because that would give you two pair (52 cards minus 2 in your hand minus the 1 card that matched the first time minus the 1 card that fell on the board minus the 8 cards that would match either your hole cards of the card that fell on the board = 40 cards.) Then divide by the total number of combinations, 50 cards * 49 cards * 48 cards. This comes to:

(6 * 44 * 40) / (50 * 49 * 48) = 8.97959%.

This is the chance of flopping one card to your hole cards ON THE FIRST CARD OF THE FLOP, as in:

Hole Cards: :Qc:
Flop: :Qh:

There is also that same chance to flop the pairing card on the second card, as in:

Flop: :Qh:

And the same chance to flop the pairing card on the third card, as in:

Flop: :Qh:

So you have 3 * 8.95959% or 26.939%

Holding unpaired cards and flopping EXACTLY two pair by pairing a hole card AND pairing on the board.

You are looking for one of the 6 cards that pair either of your hole cards, then you are looking for any card that DOES NOT match your hole card (there are 44 remaining), then you are looking for 1 of the 3 cards that will pair that second card. Then divide by the number of combinations. This comes to:

(6 * 44 * 3) / (50 * 49 * 48) = 0.673469%

As with the above example, this is the chance of flopping your hole pair on the first card. There is an equal chance of flopping it on the second card and an equal chance of flopping it on the third card.

So you have 0.673469 * 3 = 2.020%

Holding unpaired cards and flopping EXACTLY two pair by pairing EACH of your hole cards.

You are looking for one of the 3 cards that pair your first hole card, then you are looking for one of the 3 cards that pair your second hole card, then you are looking for any card that DOES NOT pair either of your hole cards (there are 44 remaining). Then divide by the number of combinations. This comes to:

(3 * 3 * 44) / (50 * 49 * 48) = 0.336734%

This is the chance of flopping a match to your first hole card, then a match to your second hole card, then a rag card. Considering that you hold XY, this is the chance of flopping X Y r. There are 5 other ways of flopping what you want, that each have the same chance. They are:

X r Y
Y X r
Y r X
r Y X
r X Y

So you have 0.336734 * 6 = 2.020%

Holding unpaired cards and flopping EXACTLY trips by flopping two cards to one hole card.

You are looking any of the 6 cards that will pair one of your hold cards, then you are looking any of the 2 remaining cards that will trip that hole card, then you are looking for any card that DOES NOT quad up your hole card (that would give you 4 of a kind) and DOES NOT pair up your other hole card (that would give you a full house). Then divide by the number of combinations. That gives you:

(6 * 2 * 44 ) / (50 * 49 * 48) = 0.4489796%

That is the chance of flopping trips on the first two cards of the flop and a rag on the third. There are two other ways to flop trips that have an equal chance: (1) matching the first and third cards, (2) matching the second and third cards.

So, you have 3 * 0.4489796 = 1.347%.

Holding unpaired cards and flopping EXACTLY a full house, trips of one hole card and pairing the other.

You are looking any of the 6 cards that will pair one of your hold cards, then you are looking any of the 2 remaining cards that will trip that hole card, then you card looking for any of the 3 cards that will pair your other hole card. Then divide by the number of combinations. That gives you:

(6 * 2 * 3 ) / (50 * 49 * 48) = 0.03061224%

That is the chance of flopping trips on the first two cards of the flop and pairing on the third. There are two other ways to flop this type of full house that have an equal chance: (1) tripping the first and third cards while pairing the second, (2) tripping the second and third cards while pairing the first.

So, you have 3 * 0.03061224 = 0.0918%.

Holding unpaired cards and flopping EXACTLY four of a kind, three cards to one of your hole cards.

You are looking for any of the 6 cards that will pair one of your hold cards, then you are looking any of the 2 remaining cards that will trip that hole card, then you card looking for the 1 card that will quad that hole card. Then divide by the number of combinations. That gives you:

(6 * 2 * 1 ) / (50 * 49 * 48) = 0.0102%

Holding paired cards and flopping EXACTLY two pair by pairing the board.

You are looking for any of the 48 cards that DOES NOT match your hole card. Then you are looking one of the 3 cards that match that card. Then you are looking for a card that DOES NOT match your hole pair and DOES NOT trip up the first two cards of the flop, there are 44 such cards. Then divide by the number of combinations. That gives you:

(48 * 3 * 44 ) / (50 * 49 * 48) = 5.387755%

That is the chance of flopping the board pair on the first two cards. There are two other ways to flop a board pair that have an equal chance: (1) pairing the first and third cards, (2) pairing the second and third cards.

So, you have 3 * 5.387755% = 16.163%

Holding paired cards and flopping EXACTLY trips by flopping a set for your pocket pair.

You are looking for any of the 2 cards that pair your hole cards. Then you are looking for any card that DOES NOT quad up your hole card, there are 48. Then you are looking for a card that DOES NOT quad up your hole card AND DOES NOT match the other flop card (that would give you a full house), there are 44 such cards. Then divide by the number of combinations. That gives you:

(48 * 3 * 44 ) / (50 * 49 * 48) = 3.59184%

That is the chance of flopping the set on the first card. There are two other ways to flop a set that have an equal chance: (1) tripping on the second card, (2) tripping on the third card.

So, you have 3 * 3.59184% = 10.775%

Holding paired cards and flopping EXACTLY a full house, a set to your hole pair and pairing the board.

You are looking for any of the 2 cards that pair your hole cards. Then you are looking for any card that DOES NOT quad up your hole card, there are 48. Then you are looking for a card that pairs up that board card, of which there are 3. Then divide by the number of combinations. That gives you:

(2 * 48 * 3 ) / (50 * 49 * 48) = 0.2448979%

That is the chance of flopping the set on the first card and pairing the second and third. There are two other ways to flop this type of full house that have an equal chance: (1) tripping on the second card, (2) tripping on the third card.

So, you have 3 * 0.2448979% = 0.735% (reviewing my initial post, I transcribed this number incorrectly from my notes. I have fixed the initial post.)

Holding paired cards and flopping EXACTLY a full house, by the board tripping up.

You are looking for any card that does not match your hole pair, there are 48. Then you are looking for any of the 3 cards that will pair up the board. Then you are looking for any of the 2 cards that will trip up the board. Then divide by the number of combinations. That gives you:

(48 * 3 * 2) / (50 * 49 * 48) = 0.2448979%

Holding paired cards and flopping EXACTLY four of a kind, two cards to your hole pair.

You are looking for any of the 2 cards that will trip your hole pair. Then you are looking for the remaining card that will quad your hole pair. Then you are looking for any of the remaining 48 cards. Then divide by the number of combinations. That gives you:

(2 * 1 * 48) / (50 * 49 * 48) = 0.0816327%

That is the chance of flopping the quads on the first and second flop cards. There are two other ways to flop quads that have an equal chance: (1) tripping on the first card and quading on the third, (2) tripping on the second card and quading on the third.

So, you have 3 * 0.0816327% = 0.245%

Holding two unsuited cards and flopping a four flush.

You are looking for any of the 24 cards that are the same suit as either of the two cards that you hold. Then you are looking for any of the 11 cards that are the same suit as the first flop card. Then you are looking for any of the 10 cards that are the same suit as the first two flop cards. Then divide by the number of combinations. That gives you:

(24 * 11 * 10) / (50 * 49 * 48) = 2.245%

Holding two suited cards and flopping a flush.

You are looking for any of the 11 cards that are the same suit as the two cards that you hold. Then you are looking for any of the 10 cards that are the same suit as the first flop card. Then you are looking for any of the 9 cards that are the same suit as the first two flop cards. Then divide by the number of combinations. That gives you:

(11 * 10 * 9) / (50 * 49 * 48) = 0.842%

Holding two suited cards and flopping a four flush.

You are looking for any of the 11 cards that are the same suit as the two cards that you hold. Then you are looking for any of the 10 cards that are the same suit as the first flop card. Then you are looking for any card that DOES NOT match the suit of the first two cards, there are 39. Then divide by the number of combinations. That gives you:

(11 * 10 * 39) / (50 * 49 * 48) = 3.648%

That is the chance of flopping the four flush on the first two cards of the flop. There are two other ways to flop a four flush that have an equal chance: (1) matching the suit of the first and third cards, (2) matching the suit of the second and third cards.

So, you have 3 * 3.648% = 10.944%

The straights are tricky. I prefer to think of them in a certain way and I acknowledge that not everyone may think about them the same as I. A mental model that works well for me and simplifies the math is computing the chance of EXACTLY 1 of EACH of 3 ranks falling on the flop when you do not hold any of those ranks in the hole. There are a lot of ways to compute that number. I am going to stick with the method I have used throughout the other explanations.

If you want the flop to contain ranks X, Y, Z when your hole cards do not contain X, Y, or Z then:

You are looking for 1 of the 4 X. Then you are looking for 1 of the 4 Y. Then you are looking for 1 of the 4 Z. Then divide by the number of combinations. That gives you:

(4 * 4 * 4) / (50 * 49 * 48) = 0.054422%

That is the chance of EXACTLY flopping X, then Y, then Z. There are 5 other ways of flopping X, Y, Z that all have an equal chance:

X Z Y
Y X Z
Y Z X
Z X Y
Z Y X

So, the odds of flopping EXACTLY one each of ranks X, Y, and Z when you do not hold either X, Y, or Z on the hole are:

6 * 0.054422 = 0.3265%

We are going to call that number S, and we are going to be using it a lot.

Holding connectors 54 through JT and flopping a straight.

These connectors have room on both sides to form a number of straights. Graphically, if you are holding cards AB, then you could flop the following straights:

X Y Z A B - - -
- X Y A B Z - -
- - X A B Y Z -
- - - A B X Y Z

So there are 4 sets of X, Y, Z that will give you a straight. So you have a 4 times S chance of flopping a straight.

4 * 0.3265 = 1.306%

Holding one gapped connectors 53 through QT and flopping a straight.

These connectors have room on both sides to form a number of straights. Graphically, if you are holding cards AB, then you could flop the following straights:

X Y A Z B - -
- X A Y B Z -
- - A X B Y Z

So there are 3 sets of X, Y, Z that will give you a straight. So you have a 3 times S chance of flopping a straight.

3 * 0.3265 = 0.980%

Holding two gapped connectors 52 through KT and flopping a straight.

These connectors have room on both sides to form two straights. Graphically, if you are holding cards AB, then you could flop the following straights:

X A Y Z B -
- A X Y B Z

So there are 2 sets of X, Y, Z that will give you a straight. So you have a 2 times S chance of flopping a straight.

2 * 0.3265 = 0.653%

Holding three gapped connectors A5 through AT and flopping a straight.

These connectors can only flop one straight. Graphically, if you are holding cards AB, then you could flop the following straight:

A X Y Z B

So there are 1 set of X, Y, Z that will give you a straight. So you have a 1 times S chance of flopping a straight.

1 * 0.3265 = 0.327%

Lastly, the 8 out straight draws. For all the other odds, I have confirmed my results against reference material and they match. I have not found any references for these 8 out straight draws. I may have errors and I invite discussion.

The 5 card, 8 out straight draws fall into two categories. First, there is flopping 4 consecutive cards such as:

- A B C D -

So there are 4 outs to the left of A and 4 outs to the right of D.

We will call this a TYPE-1 8 out draw.

Secondly, there are double barreled gut shots (double bellied gut shots) such as:

A - C D E - G

So there are 4 outs to the left of C that will give you an A - E straight and there are 4 outs to the right of E that will give you a C - G straight.

We will call this a TYPE-2 8 out draw.

Holding connectors 54 through JT and flopping an 8 out draw.

First, we will compute the TYPE-1 draws. Given that our hole cards are F and G and they are connected, graphically here are the three TYPE-1 8 out draws:

D E F G - -
- E F G H -
- - F G H I

For each of these we are looking 1 of the 4 left most flop cards, then 1 of the 4 right most flop cards, then any card that DOES NOT give us a straight (there are 40). Then divide by the number of combinations. That gives you:

(4 * 4 * 40) / (50 * 49 *48) = 0.54422%

That is the chance of flopping the cards in exactly the order: L R x. There are 5 other combinations that have an equal chance:

L x R
R L x
R x L
x R L
x L R

So, the odds of flopping any one of those TYPE-1 draws would be:

6 * 0.54422% = 3.265%

In turn, there are 3 of those TYPE-1 draws, so the odds of flopping any of the TYPE-1 draws would be:

3 * 3.265% = 9.796%

Second, we will compute the TYPE-2 draws. Given that our hole cards are F and G and they are connected, graphically here are the two TYPE-2 8 out draws:

C - E F G - I -
- D - F G H - J

This turns out to be a problem where we are looking for a flop containing EXACTLY an X, Y and Z rank. We already computed that chance, it was S. There are two sets of X, Y and Z that would give us two TYPE-2 draws so the chance is 2 * S or:

2 * 0.3265% = 0.653%

Lastly, the chance of any 8 out draw would be the sum of the chance of the TYPE-1 draws and the TYPE-2 draws. So,

9.796% + 0.653% = 10.449%

Holding one gapped connectors 53 through QT and flopping an 8 out draw.

First, we will compute the TYPE-1 draws. Given that our hole cards are F and H and they are one gapped, graphically here are the two TYPE-1 draws:

- - E F G H - - -
- - - F G H I - -
C D E F - H - - -
- - - F - H I J K

The first two require two cards to form up the 4 sequence. The second two require 3 cards to form up the sequence.

Using the numbers we figured out for the step above that give us:

2 * 3.265% + 2 * 0.3265 = 7.18%

Second, we will compute the TYPE-2 draws. Given that our hole cards are F and H and they are one gapped, graphically here are the three TYPE-2 draws:

B - D E F - H - - - -
- - D - F G H - J - - -
- - - - F - H I J - L

That would give us three TYPE-2 draws so the chance is 3 * S or:

3 * 0.3265% = 0.980%

Lastly, the chance of any 8 out draw would be the sum of the chance of the TYPE-1 draws and the TYPE-2 draws. So,

7.18% + 0.980% = 8.08% (I forgot to include two of the TYPE-1 draws in my initial posting. I have corrected the numbers.)

As a final note, the 53 and QT combinations cannot form one of the TYPE-2 draws as there is not enough room to the left and right respectively so their odds are slightly lower.

Holding two gapped connectors 52 through KT and flopping an 8 out draw.

First, we will compute the TYPE-1 draws. Given that our hole cards are F and I and they are two gapped, graphically there are five TYPE-1 draws:

- - - F G H I - - -
- D E F H - I - - -
C D E F - - I - - -
- - - F - H I J K -
- - - F - - I J K L

The first requires two cards to form up the 4 sequence. The remaining 4 require 3 cards to form up the sequence.

Using the numbers we figured out for the step above that give us:

1 * 3.265% + 4 * 0.3265 = 4.571%

Second, we will compute the TYPE-2 draws. Given that our hole cards are F and I and they are two gapped, graphically here are the two TYPE-2 draws:

- C - E F G - I - - -
- - - - F - H I J - K -

That would give us two TYPE-2 draws so the chance is 2 * S or:

2 * 0.3265% = 0.653%

Lastly, the chance of any 8 out draw would be the sum of the chance of the TYPE-1 draws and the TYPE-2 draws. So,

4.571% + 0.653% = 5.224% (I forgot to include four of the TYPE-1 draws in my initial posting. I have corrected the numbers.)

As a final note, the 52 and KT combinations cannot form one of the TYPE-2 draws as there is not enough room to the left and right respectively so their odds are slightly lower.

Holding three gapped connectors A5 through AT and flopping an 8 out draw.

First, we will compute the TYPE-1 draws. Given that our hole cards are F and J and they are three gapped, graphically here are TYPE-1 draw:

C D E F - - - J - - -
- D E F G - - J - - -
- - E F G H - J - - -
- - - F - H I J K - -
- - - F - - I J K L -
- - - F - - - J K L M

These all require 3 cards to form up the sequence.

Using the numbers we figured out for the step above that give us:

6 * 0.3265 = 1.959%

Second, we will compute the TYPE-2 draws. Given that our hole cards are F and J and they are three gapped, graphically here are the two TYPE-2 draws:

D - F G H - J - -
- - F - H I J - L

That would give us two TYPE-2 draws so the chance is 2 * S or:

2 * 0.3265% = 0.653%

Lastly, the chance of any 8 out draw would be the sum of the chance of the TYPE-1 draws and the TYPE-2 draws. So,

1.959% + 0.653% = 2.612% (I forgot to include scads of the TYPE-1 draws in my initial posting. I have corrected the numbers.)

As a final note, the actual numbers vary all over the place for three gappers. Only the 95 and T6 three gappers can form all of the combinations listed. As the three gappers get closer to the edge, fewer combinations are possible. In short, do not expect much from three gappers.

My Head hurts

Pyroxene, PM me; I'm working on sketches for bunch of elaborate odds charts/software, and seriously could use a partner

(I'm not joking)

{This post has been removed}

I love posts like this! Sticky?

Someone has apparently studied this subject "a bit"
Nice work mang!

My bad about the 41% bit, I was technically correct in a different sense though :P

Nice post.

Awesome post man, that helps me get the math right.

Have you considered expanding the straight action to five cards?

LeFou - I might also be interested in that odds calculator. I do C++ or VB (only if I have to).

Hey, thanks. I always thought the odds of getting a OESD on connectors was about 10%, but I was always too lazy to calculate it. Also, I like to do them in my head, and I CANNOT do the straight draws in my head (I also round fractions)

A few things to add on...

"edge" connectors like 23 and KQ make fewer straights (duh)

For flopping the straight, deduct one "S" (.3265%) for each step closer to the edge:
QJ = ~0.98% (~100:1)
KQ =~0.66% (~150:1)
AK = 0.3265% (~300:1)

Same for 34/23/A2.

For draws, the double bellybusters become just gutshots... and I am NOT going to calculate odds of getting a gutshot draw on the flop! And there are fewer OESDs, too

QJ - 2 possible OESDs, 6.5%
KQ - only one possible, 3.265%

AK, of course, cannot flop an OESD.

Pyroxene,

Thanks for writing this thread! I added it to the charts section on the http://www.flopturnriver.com/Common-Flop-Odds.html page.

I just want to add something up real quick, postin' for you guys. Odds of breaking a higher pocket pair than your connexors:

Holding suited connectors from 54s to JTs, your odds of flopping uber are:

flopping a flush (including the slight chance of a straight flush in some cases) 0.842% - suckout chance that higher PP has card of your suit's outs (50% * 6 outs * .842 = .841% ) .841%
flopping a straight (including the slight chance of a straight flush in some cases) 1.306% (not counting Flop JQK when you hold T9 or similar, or flopped trips turning into 4-of-a-kind)

flopping EXACTLY two pair by pairing EACH of your hole cards 2.02% - 2 chances for trips on the turn and river, 3 of the unpaired card on the board on the turn and river, and 3 more from the turn card pairing on the river if the turn card does not give your opponent a set (2 cards), or pair that third card for a better 2pair already (3 cards, so 40/45 remaining cards we're counting the river outs). These odds exclude your chance to hit a full house, which gets too damn meticulous for me.

The math is as follows:

2.02% - 5 outs - (40/45 * 3 river outs)
2.02% * (1 - (20.3% + (8/9 * 6.5%)) =

1.493% that you will flop 2pair and it will crack aces, or any higher pocket pair.

flopping EXACTLY trips by flopping two cards to one hole card 1.347% - 2 outs for aces = 1.347 * .916 = 1.234% that your flopped trips will hold up against aces.

The odds of a full house or four of a kind flopping are about .101% after you account for runner runner aces.

So here we havvvvvvve:
00.841%
01.306%
01.493%
01.234%
00.101%
---------
~4.975% that you will cracka some aces with your crappy sootorz. Call it 4.95% because I missed some stuff there with the straights and 2pair.

SO! in the rare case that you are very certain your opponent has aces, and he lays out a raise of less than 20.2% of your stack and also 20.2% of his stack, you have odds to call, assuming you know he'll push at some point after you flop your 2pair or better. If someone would check this I would be appreciative. I used the pot odds charts on FTR, which I believe innaccurate in this case because we know of 7 cards, not 5, so this isn't exact, but 22 or 23:1 is fo sho.

Pyroxene,

Very nice work...all of that is going to improve my game.

Thanks a lot.

I know it is good to know your odds but I also know that the odds differ when it is a full table of players and who stays in and why! What are they looking for and are you going to get what you need and is better than what they needed. To me these complicates and puts more stress on a card player. You see some people and they are always calculating everything, and in the long run maybe this amkes them a better player in the mathmatical field than what you may be, but to posses natural and mental awareness skills of this great game is a feather in your cap, although you might not be able to count how many feathers you have in your cap because your math is not that good! I believe having confidence in yourself and knowing that the table you are getting ready to sit down at is going to be your table and you are going to be the captain is just as good as being the mathe professor at the table! He!He! LOL!

hello everybody. , i was wondering what are the odds of FLOPPING a straight flush draw, or flush draw , or just a straight draw combined when you are holding suited connectors like 45 suited? okay everbody, thanks in advance.

Originally Posted by unlucky#

hello everybody. , i was wondering what are the odds of FLOPPING a straight flush draw, or flush draw , or just a straight draw combined when you are holding suited connectors like 45 suited? okay everbody, thanks in advance.

You asked your question very nicely, but this is fucking ridiculous. THE ANSWERS ARE IN THE THREAD YOU POSTED IN!!!

sorry guys, i tried to read it, but i just can't find it. the only title that makes the most sense for what i am trying to look for is the part where it says holding connectors 54 through JT(there is no where that says SUITED connectors it just says CONNECTORS, and in this part i don't see anything that answers the question. i did find alexsandr posts in which he talks about suited connectors but he is talking about hitting the hand , i'm just talking about hitting the draw on the flop. i think there is a difference, unless i'm just not seeing something, i don't see anywhere with the exception of alexsandr's post where it says suited connectors. can anyone help me out plz? thanks

fair enough, sry I was rough. An estimate...

From above:
~10% of the time you flop a straight draw
~10% of the time you flop a flush draw

so 90% of the time you don't get a flush draw, 90% of the time you don't get a straight draw. .9*.9 = .81, so 81% of the time you get neither.

That means 19% of the time you flop a straight draw or a flush draw, or both. This also implies 1% of the time you flop a straight flush draw.

sorry to be a pain. But when you have a piar isn't it 7:1 to flop a set or 12.5 %. or are you calculating something else. confused ? and as for two pair why is it so low 2.5% with un paired cards getting two pair surely it should be higher than trips with a a pair. the calculations seem strange un paired cards have 2 cards to hit so 6 out of 50 whereas the pair only has 2 out of 50. is two pair less likely than trips but in total trips is less likely cause you have to add the fact of having a pair in hand which is 20:1 or something, thanks

Been searching for this kind of thread... didn't find it on the other forums I'm reading... Weird though, any respectable poker forum should have an odds section... thank you, you spared me some serios head akes. Btw, these odds are correctly calculated

I was trying to calculate the odds of the flop containing a pair (but not three of a kind) assuming that your pocket cards are not paired.

My calculation was that there were:

C(4,2)*11*46 + C(3,2)*2*47 = 3318 combinations of flops containing a pair (but not three of a kind).

When this is divided by the number of flop combinations (19600) it gives a probability of 16.9286%.

My problem is that the only reference I could find to this probability was a link on wiki
http://en.wikipedia.org/wiki/Poker_probability_(Texas_hold_'em)
which gave the odds at 16.941%. This appears to indicate that the author of that link counted 3320 combinations.

Does anyone know which is correct?

lOL at the odds of flopping quads

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Good luck!

LOL at bumping a sticky.

Originally Posted by tipsaren

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Good luck!

Is this considered spam even though he never actually tells of a poker room?

I realize this is an old, stickied post (and I am a total noob here), but I don't think these figures are entirely correct.

Don't get me wrong, I think they are fine for hands where you are IN the hand, but any hand you folded preflop, the numbers are way off.

I mean, if you folded 2 suited cards preflop, the odds of ending up with a flush are like 99%!! A set is flopped at least 50% of the time you fold any 2 random cards. And, for sure, any time you fold a small pocket pair after seeing the flop, the turn card "hits" 100% of the time.

Don't believe me? Just listen to the person next to you!!

Hello! I am fairly new to Poker, playing for free on line and learning the game. I play at all sites, mostly Full Tilt. However, I can't seem to amass more than 20,000 free chips. Then I play the 2000 table and have to start again.
Any tips for a b-ginna? This is a Kool site! THanks

deposit a little $$ and play for real money.
Play money does not even compare to the .01/.02 cent real money games.

They look about right to me...

I find it tough to figure out the percentages but this should help!

Originally Posted by mrhappy333

deposit a little $$ and play for real money.
Play money does not even compare to the .01/.02 cent real money games.

Well there i must say you are wrong, i have played to much at the 0,02/0,04 and compare this to a playmoney table 200/400, its allmost the same.

Some plays like maniacs while some are playing pretty serious.

But i see your point.

Pyroxene, what are the odds for you to flop a pair (hole cards) while villain flops a higher pair (with his hole cards that both are above yours) in a heads up match?

So basically like:
You hold 78, villain holds QJ, What are the odds for you to flop a 7 or an 8 while villain flops a Q or a J?

And what are the odds if he's holding like Q-4?

Originally Posted by Levian

Pyroxene, what are the odds for you to flop a pair (hole cards) while villain flops a higher pair (with his hole cards that both are above yours) in a heads up match?

So basically like:
You hold 78, villain holds QJ, What are the odds for you to flop a 7 or an 8 while villain flops a Q or a J?

And what are the odds if he's holding like Q-4?

Levian,

I am also new, and am going to attempt to answer your question because I want to practice calculating odds myself. I would love for someone to check my math, as I'm sort of treating this like a GRE practice question, so:

For the purposes of this exercise, it's not relevant to take into account that villain has two hole cards higher than yours, only that he has two hole cards different from yours. So, you are looking for the probability of him hitting one of his hole cards, and you hitting one of your hole cards, and the third card coming up a blank for both of you:

(6 * 6 * 38)/(50 * 49 * 48) = .01163

Since this can happen one of three ways, multiply that by 3 and you get .034898, or 3.5%

That's your answer for the 78 v QT problem, since it doesn't matter which hole card he hits, or which hole card you hit, either way you'll be behind.

For the 78 v Q4 question, since villain only has one hole card that can beat you, you just chop that percentage in half. There'll still be a 3.5% chance of you both hitting hole card, but only the higher card will put villain ahead. In other words:

(6 * 3* 38)/(50 * 49 * 48) * 3

These percentages only represent the chances of you and villain both hitting EXACTLY one pair.

Now, having done the math, I would recommend that, regardless, if you're playing suited connectors or gappers, and you pair the board with no draws, and there are overcards, you're probably gonna want to play the hand with extreme caution.