Joined: 10 Sep 2004 Posts: 4756 Location: Alpharetta, GA
Posted: Sat Mar 22, 2008 8:33 pm Post subject:
The odds of your opponent flopping the straight flush are the tricky part, since it depends on the specific suited cards he has as to how many possible SFs he can flop, and it depends on the actual question you're answering.
If we're to start from the very beginning, you'll need to know the odds of each opponent being dealt a suited connector with you at the same time being dealt the A of that suit (though I suppose we also have to consider the possibility that the opponent is dealt 54s and you get the K on an A23 flop). If we start from the assumption you've been dealt the A and your opponent has been dealt the suited connector, it's easier to figure (then, it's really just the odds he'll flop the SF, which is in the ballpark of 5000-1 against, depending on the specific cards involved).
Let's see, the odds you're dealt the A and a non-suited side card are:
4/52*39/51 +48/52*3/51 = 11.3%
Odds a given opponent is dealt a suited connector ~2.1%, but that needs to be the same suit as your ace (ignoring that you can actually hold AA some small portion of the time), so there's about a .53% his suited connector will match your ace, and about a .06% chance of that outcome occurring. He'll flop a SF with his suited connector about 1/5000, yielding about an 8.3M-1 shot that you flop the nut draw and he flops the SF.
Now, that's really only the case for HU versus one opponent holding specifically a no-gap suited connector. There are going to be cases where your opponent will have a one/two/three gapper and flops the SF to add, and the K-high nut draw that I mentioned before, and none of this takes into account the odds that the specific combos of hands will actually see a flop (you're going throw away As2h, and he's going to throw away 6s2s and the like). As a rough guess, I'd bet that you're going to have a combo of you being dealt a hand that would flop the nut draw and your opponent would at the same time have flushed the SF probably something more like 80K-1, meaning that it would be quite common if everyone always saw the flop.
Someone with better math skills may come along and give you a more exact answer.
Joined: 07 Apr 2004 Posts: 7626 Location: Drinking Carrot juice
Posted: Sun Mar 23, 2008 1:56 pm Post subject:
Suffice it to say the odds are very small. Too small to worry about. It happens. You can flop a straight flush of 89TJQ holding 89 and, somewhere down the road, you will lose to a royal. Often, no - but if it can happen it will (eventually, to somebody).
Don't sweat the small stuff. And this qualifies as small stuff. Improbable <> impossible.
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