odds of flopping.. (need a math solution)
 

Hi,

I'm trying to figure out what the odds of flopping any of the following are, given that we are holding 67s (or any suited connector like 89s, JTs)

- two pair(using both hole cards, not a pair on board), trips, full house, quads

- OE straight draw or double belly buster

- flush draw

- made straight or made flush


It's been a while since I've done anything like this, so I'm afraid I wouldn't trust whatever results I did get. Anyone able to do this calculation?

Re: odds of flopping.. (need a math solution)
 

I will try this but hopefully someone will check my flush draw and open ended straight draws to insure I didn't double count anything. I will use 67 suited.

Straight Flush

There are four different combinations of three cards that give you a straight flush. They are 10,9,8 and 9,8,5 and 8,5,4 and 5,4,3.

So straight flush flops are 4*1*1*1 = 4 flops or .0204%

Four of a kind

= 2*(3c3) = 2 flops or .0102%

Full house with 6 and 7

= 2*(3c1)*(3c1) = 18 flops or .0918%

Flush

= (11c3) = 165 - 4 = 161 flops or .8214% (note you must subtrat out the straight flushes)

Straight

As mentioned before a straight will come with four different combinations of three cards.

= 4*4*4*4 = 256 - 4 = 251 flops or 1.2806%

Three of a Kind

= 2*(3c1)*44 = 264 flops or 1.3469%

Two pair with 6 and 7

= (3c1)*(3c1)*44 = 396 flops or 2.0204%

Flush and an eight out straight draw

The combinations that allow an eight out straight are as follows: 89x, 85x, 54x, 4810, 953. The easiest way to count these combo's is to insure the x doesn't create a straight and it is not the same as one of the other cards. For example:

89x were x is not a 10,5,8 or 9. Now in this combination we need to have two and exactly two of a specific suit. It can be 89 s, x not or 8x s, 9 not or 9x s, 8 not.

89/x = 1*1*27 = 27
8x/9 = 1*7*3 = 21
9x/8 = 1*7*3 = 21
89/9 = 1*1*3 = 3
89/9 = 1*1*3 = 3

Total for 89x is 75 * 3 total combo's = 225

Now for the 10,8,4 and 9,5,3

95/3 = 1*1*3
93/5 = 1*1*3
53/9 = 1*1*3

For a total of 9 flop * 2 combo's = 18

Total of 15 out hands = 225 + 18 = 243 flops or 1.2398%

Flush draw ( 9 outs)

Note some of these have 12 outs to a gutshot straight

= (11c2)*39 = 2145 - 243 = 1902 flops or 9.7041%

Eight out straight draw

We use the same combinations as discussed above but we then subtract out the flops that have a flush already and the flops that have two of our suit. These are already counted.

For 89x

= 4*4*34 = 544 + 2*(4c2)*4 = 544 + 48 = 592

There are three combo's = 1776 flops

for 9,5,3,

= 4*4*4 = 64 * 2 combo's = 128 for a total of 1904 flops

Now there is a total of 26 flops above that give a flush and 243 that have 2 of your suit. Therefor there is
1904-26-243 = 1635 clean flops or 8.3418%

Summary

Straight Flush.......4.......4

Four of a kind.......2.......6.....1 in 3266

Full house..........18......24.....1 in 817

Flush..............161.....185.....1 in 106

Straight...........251.....436.....1 in 45

Three of a Kind....264.....700.....1 in 28

Two Pair w (6,7)...396....1096.....1 in 17.9

15 outs............243....1339.....1 in 14.6

9 outs............1902....3241.....1 in 6.0

8 outs............1635....4876.....1 in 4.0

Cobra

Re: odds of flopping.. (need a math solution)
 

Excellent post, thank you!

Re: odds of flopping.. (need a math solution)
 

In the eight-out straight problem, where did

2*(4c2)*4

come from for 89X? I have only the 544 number as necessary.