How to find out what is the frequency of a given flop ?
e.g. A67 OR KJ2 OR 925

Thanks !

There are 4 of each rank.

You can make an A67 flop by combining any of 4 Aces with any of 4 '6's, and then adding any of 4 '7's

that's do-able in 4x4x4 = 64 ways.

There are 52C3 = 22100 ways of picking a 3 card flop.

So p(flop is A67) = 64/22100 = 0.2895%

Same calculation for a KJ2 flop and for a 925 flop

so p(flop is A67 or KJ2 or 925) = 3 x 0.2895% = 0.868%

EDIT: Can also use OddsOracle from ProPokerTools

ProPokerTools Odds Oracle Results (2.25 Professional)
Holdem, Generic syntax
PLAYER_1 *
PLAYER_2 *
600000 trials (randomized)


How often do(es)
the board matches range A67,KJ2,952
0.8613% (5168)


Note that that's using simulation so there's going to be a small difference compared to the answer got from first principles but close enough for sure.

That's giving two players random hands.
If you want to think about giving them blockers, OddsOracle is super-fast at giving you very useable answers.

Could you help me with the following too, please:
1. What is the probability of the flop to come A high ?
2. What is the probability that the flop will be just one face card and the others two cards NOT face cards ?
3. What about 2 face cards and just one low card ?
4. What about all 3 cards to be face cards ?
5. What about all flop cards to be low cards and not face cards ?

Thank you a lot !

PS: Sorry, I don't know, but how to use OddOracle to get these answers ?

Are you planning to use these answers to help with your preflop decision making?

The OddsOracle has a built in question feature which allows you to ask a number of questions, including how often the board matches your specified range.

If we give two players a random hand each (and assuming you count an Ace as a picture card):

ProPokerTools Odds Oracle Results (2.25 Professional)
Holdem, Generic syntax
PLAYER_1 **
PLAYER_2 **
600000 trials (randomized)

1. How often does the board match range A[K-2][K-2] ie. a single Ace
20.4850% (122910)


2. How often does the board match range [A-T][9-2][9-2] i.e. precisely 1 broadway card
44.9318% (269591)


3. How often does the board match range [A-T][A-T][9-2] i.e. precisely 2 broadway cards
27.5288% (165173)


4. How often does the board match range [A-T][A-T][A-T] i.e. 3 broadway cards
5.1368% (30821)


5. How often does the board match range [9-2][9-2][9-2] i.e. no broadway cards
22.4025% (134415)

But yeah, as I think ReidLockhart is implying, how useful is that really?

Yes. And also I want to study how a specified range will hit a given flop.

It is very useful for me. I'm gonna build my own strategy, step by step and very powerful.

Sorry, I forgot these questions, please:
1. What is the probability of flop to come just ONE broadway and the other cards will be the same. ex. A22 or K77 or J99 etc.

2. What is the probability of flop to come two broadways and one low card but the browadways to be the same: ex. AA3 or KK9 or QQ2 etc.

3. What is the probability of flop to come all three cards the same. 222 or AAA.

4. What is the probability of flop to come one broadway card and the other two cards to be connected ex. A89 or A67 etc. ?

5. What is the probability of flop to come one broadway card and the other cards to be same suit or both: same suite and connected at the same time ? ex. Ad3s9s or Ad6s7s or As6s7d or As9s3d ?


Thank you a lot !

on a random occurrence? you do realize variance will take care of any strategy you have planned, right?

If you want to study how hard any given range hits a flop, just get Flopzilla ffs.

Swear you just want to go on Mastermind with 'poker probabilities' as your specialist subject.

While ProPoker Tools and Flopzilla are great tools, I don't think they're free. What is free is calculating it yourself, possible here, but not particularly easy in many cases.

For example, for exactly 2 broadway cards, you can have two different broadway or a pair of broadway, each with a third card of rank 9 or lower, the latter occurring in 8*4 ways.

Combos of 2 different broadway & 1 non-B = C(5,2) * 4*4*(8*4) = 5120
Combos of pair of broadway & 1 non-B = 5*C(4,2)*(8*4) = 960
Success combos = 5120+960 = 6080
Total Combos = C(52,3) = 22100

Pr(Success) = 6080/22100 = 27.51%

In the interest of full disclosure, I have written a simplified version of Flopzilla and often use that instead of going through the math, so I'm somewhat of a hypocrite I suppose.

For the 1 broadway with a pair, e.g., A99, here is the calculation:

There are 20 broadway cards. To meet the required condition, for each of these 20, there are 8 non-broadway ranks, and C(4,2)=6 ways of getting a pair for a total of 48. Thus, there are 20*48=960 successful flops out of a total of 22,100 for a probability of 4.34%.

Questions 2, 3, and 4 are similar in methodology. I got 4.34%, 0.24% and 10.2%, respectively. Question 5 is more complicated and is one for which I would use a simulation or canned program rather than sweat the math.

hi everyone, which are the flops that come with more frequency?
e.g. the ten more frequent flops

Axx when you have KK

This question cannot be answered until a set of possible flops is defined. For example, do you want to include connectors, and if so, do you want to differentiate between 1 and 2 gap connectors.

Anyway, without much thought, you can think likely flops contain more non-Broadway cards, no pairs and no monotone flops. Considering only Broadway cards, pairs, and suitedness, running my simple simulation program showed that one of the more likely flops is 1 Broadway card, 2 of a suit and no pair. It had an occurrence frequency of 22.8%.

Ace high boards are the rarest, then king high, queen high etc, but the difference in frequency is only small. Interestingly, the most common river card is a 2. Barry G's 'ace on the river' is actually quite rare. http://www.spadebidder.com/flop-analysis/part2/

Kxx when you have AQ. Every, single, time.

Agreed. And I always have a BDFD with AQs in that spot, so I always float the flop, and then I turn a combo draw, so I call again. And then I brick the river. #SoRigged