Suited connector odds

[MattHH]

I was trying to figure out what the odds are of middle suited connectors making a flush draw and/or 8-out straight draw and having a little trouble.

I know that it is about 8:1 for making a flush draw and it is about 12:1 for making the 8-out straight draw.

How can I figure out what the odds are for making either/or?

[Danastasio1]

This thread may have what your looking for: http://forumserver.twoplustwo.com/showfl...part=1&vc=1

[MattHH]

That's a great thread, thank you. I started reading through it but need to read all the responses to see if anyone contests his math. One thing that raised an eyebrow for me is this:

[ QUOTE ]
REGULAR DRAWS

Odds of flopping...
9 outer (flush draw): 5.2%
8 outer (straight draw): 8.0%
-----------------
Total: 13.2% (1 in 7.5 times, 6.5:1)
These are your standard draws; when you flop a hand with which you can continue

[/ QUOTE ]

What I noticed about this is that he is adding the straight draw probability to the flush draw probability whereas some flush draws are also straight draws and vice versa, so he is adding extra probability it would seem... [img]/images/graemlins/confused.gif[/img]

[AaronBrown]

In this case it makes some sense to double count the flops that give you both straight and flush draws, because you benefit from both draws. But you're correct that you should figure those separately.

[BruceZ]

[ QUOTE ]
This thread may have what your looking for: http://forumserver.twoplustwo.com/showfl...part=1&vc=1

[/ QUOTE ]

I found a few errors in this post.

1. Under "Regular Draws" for OESD (8 outs), your calculation 8/50 * 4/49 * 34/48 * 3 double counts the cases where the board pairs. This is a very common error, and it makes a difference of about 0.7%. We could also view this calculation as correctly excluding the cases where the board pairs but including cases which pair the hand, but then the cases where the board pairs must be computed separately.

2. Under "Regular Draws" for flush draws (9 outs), the calculation 11/50 * 10/49 * 33/48 includes made straights, and this makes a difference of about 0.2%.

3. Under "Combo Draws", for OESD + flush draw (15 outs), this also double counts the cases where the board pairs. The final value should be about 1.2% rather than 1.4%.

I didn't check all of the calculations in this post, only enough to compare them to my numbers. The probability of a suited-connector flopping a flush draw or 8-out straight draw is 19.1%. This includes flops which make both draws, or in addition to either of these draws also make a pair or a gutshot, but does not include made straights or flushes. Note that 8-out straight draws also include the double gutshots. This calculation is known to be absolutely accurate as it has been confirmed by several different people using different methods, both analytical and by computer simulation.

The tricky part of this calculation is avoiding double counting the flops that make both types of draws. This is done either by adding flush draws which can include straight draws to straight draws that do NOT include flush draws, or visa versa. The calculation linked above contains both of these methods.

[MattHH]

AWESOME! Thanks!!