3 to a flush and 3 to a straight

[jacki]

Example:
Holding J /images/graemlins/heart.gif T /images/graemlins/heart.gif
Flop is 9 /images/graemlins/spade.gif 4 /images/graemlins/heart.gif 2 /images/graemlins/club.gif

What are your odds of hitting the flush or straight, or are the odds of hitting your flush or straight even worth figuring?

[bigpooch]

A useful number to remember is 1081, the number of card
combinations after the flop. Of these, you will make a
flush C(10,2)= 45 times and a straight, 3x(16-1)=45 times
or altogether 90 times or about 8.3256% of the time. In
this specific case, you could also hit an overcard which
might be good.

[trillig]

In most cases that is an auto-fold to any bet, unless there was some insane betting preflop.

About 1 out ever 12 of those you would hit either flush or straight, trouble is with flush, not likely to be the nuts.

I wouldn't advise chasing that one.

-t

[RatTamago]

bigpooch,

Could you please clarify how you calculated the # of str draws? I dont understand the short hand 3*(16-1)...
though your method seems MUCH easier than how I would do it.

Thanks in advance

Paul

[bigpooch]

Suppose you have Th9h and the board is 8s3h2d. There are 3
combinations of straights than can show up: QJ, J7 and 76,
hence the first factor. The second factor is just the suit
combinations of these: 4 x 4 - 1 (can't be both hearts for
then a flush would be made and those were already accounted
for in the number of flush combinations). Clear enough?

[RatTamago]

Yes, crystal clear & like I said... much simpler than how I was thinking about it.
Reminds me of something a math prof said a few years back.. he called it problem solving's: "Conservation of Difficulty".
Often, there are innumerable ways to arrive at a solution for a particular problem, yet the problem is only as difficult as its simplest method to solve. Choosing more difficult means only results in inefficiency and unnecessary headaches.

So again, Thx Much!!