Preflop - Final Hand Probabilities

[Slowplay]

Here's a curve ball question for the math guys (seeing as I have been crucified by a higher flush at least a dozen times in the past month):

What are the odds that another player has a suited pocket the same as yours (e.g. you hold 67d, they hold J9d)AND two hit on the flop?

Also, can anyone calculate a staggered set of odds that address a higher flush draw than 67s? (e.g. A2, T4, KJ, etc.)

Thanks if you can help at all.

SP

[asdf1234]

These are only approximations using random hands, which is not necessarily the case in real life.

If you have something like 7 [img]/forums/images/icons/spade.gif[/img] 6 [img]/forums/images/icons/spade.gif[/img] and the board is
K [img]/forums/images/icons/spade.gif[/img] J [img]/forums/images/icons/spade.gif[/img] 4 [img]/forums/images/icons/diamond.gif[/img]
then the chances of a single opponent holding a flush draw as well is 3.33%. If you extend this to 9 opponents, then it increases to 26.27%. It decreases 2-3% for each opponent you lose. Of course, the likelihood is probably less, because the king and jack are both out there, and people are less likely to play trashy suited cards, but we're not taking that into account anyway.

As far as the number of flush draws that will beat you, I'm sure you know, that if there is one out there, it's probably beating you. There are 36 other combinations of hands that can be drawing for a flush and 30 of them beat you. The chance that there is another flush draw out there and that it beats you is 2.77% for a single opponent up to about 23.4% for nine. Again, this decreases 2-3% for each opponent you lose.

These calculations are not exact because they don't take into account situations where multiple opponents hold flush draws, some players have one of the suit, but this is relatively close.

[Slowplay]

Hey ASD--Thanks a million for replying! I have been attempting to figure this one out for a while now, and it seems that most probability charts rarely list practical odds of this nature (I mean, sh**t, we're faced with this situation a helluva lot more often than flopping quads!).

So, basically, when your dealt suit-cons in a regular ring game and you flop a four-flush there's roughly a 30% chance that someone else has the same draw (assuming everyone calls). So it's 3-to-1 that you're the only one on the draw and these odds increase in your favor with less callers?

Great to know. Can I call upon your fountain of mathematics in the future? :O)

SP

[Festus22]

Just another angle on this and these are approximations:

3-Flush Board
Kx beat by Ax 6.2% of the time
Qx beat by Ax or Kx 11.5% of the time
Jx beat by Ax, Kx or Qx 15.9% of the time

Basically, the formula amounts to subtracting 0.9% from each previous result and adding that number to the total. So for 8x to lose = 6.2 + 5.3 + 4.4 + 3.5 + 2.6 = 22%.

Since there's already 5 of the suit out (your 2 + the board's 3), there's only 2 more possibilities to go meaning that 3-2s wins 74.5% of the time on a 3-flush board.