This is exactly right, given that you specify that the quad is dealt first,
then the dealt SF, and that they occur in two particular hands specified in
advance. If you just wait for a dealt quad, the chances of the NEXT hand being
a dealt SF is one in 72,193.
For a full time pro, who is dealt 2 million hands per year (and that's a LOT
of dealt hands, even for a pro!), this will happen once in about 150 years
of play. You beat the odds, Grump!
If you ask a similar question, like "What are the odds of being dealt a
quad, and on the very next hand, being dealt the SAME quad?" you get one chance
in 225,513,925. This happened to me a few months ago at the Palms, when I was
dealt (natural) quad 10s two hands in a row. Unfortunately, I was playing
NSUDs at the time. 
I always find this sort of thing fun and interesting, simply because these
occurrences are so unusual. Anyone else with a story?
Brian
···
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In a message dated 6/10/2007 4:09:38 PM Pacific Daylight Time,
jeff-cole@comcast.net writes:
Grumpy wrote:
I am speaking of the odds of getting any four of a kind followed by any
straight flush without any redraws.
There are 40 straight flushes (4 are royals), so the probability of
being dealt a straight flush is 36/2,598,960.
Any card can be paired with 4 of any denomination, so there are 48
ways to get four of a kind for any denomination, and there are 13
denominations, so the probability of being dealt a four of a kind is
(48*13)/2,598,960.
Multiply the two probabilities and take the reciprocal to get
300,685,233.3...so about 300 million to 1 seems right.
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