3 card draw

[The_shootist]

Any of you math guys know the odds of catching runners for a straight with a three card draw after the flop? Also with the 3 card flush draw? or both? For instance, hero draws (9 /images/graemlins/heart.gifq /images/graemlins/heart.gif) pre flop (let's say late position for argument sake) followed by (3/images/graemlins/spade.gif 5/images/graemlins/diamond.gif 8/images/graemlins/heart.gif) on the flop. I understand position and bets have everything to do with this type hand, but Sklansky, Jones and others never discuss actual probabilities of catching running straights and flushes with 3 card draws after the flop. Is this because you should never play a three draw post flop? It seems like this is a gap in explaining the methodologies of the texts I have read thus far. I would love to hear some input on these situations because I come across them all the time and have never read anything on how to handle these situations.

[Phat Mack]

Well, there are 47 unknown cards on the flop, so there are 47*46/2=1081 turn-river combinations. There are 10 hearts or 10*9/2=45 2-heart turn-river combos, so the odds are 45/1081 of catching a flush.

Any 67 or TJ makes a straight. 32 of these. So 32/1081 for making a runner-runner straight. 32+45-2=75 total combos of runner-runner straights and/or flushes = 75/1081 or about 14:1 dog.

I did all this math in my head so it's probably wrong but it may be close. You'll notice that the odds are bad, and that most of the draws are not to the nuts. It's hard to make these plays.

[The_shootist]

I have 24:1 dog on flush draw and about 15:1 dog on either flush or straight draw based on your math; wonder why this is not explained in texts; could be significant in low limit games.