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
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