Three days ago I asked about the probability of drawing a straight flush when being dealt $26$ out of the $52$ cards of the deck, which Michael wisely solved.
Now I'd like to make things more complicated, I want to know the probability of drawing a Mega-straight flush! I define a Mega-straight flush simply as $7$ cards of the same suit that are consecutive. But that wouldn't change much of the calculus. So there comes the twist. In this game, after being dealt the $26$ cards, if you have a straight flush, you are dealt $6$ more cards.
So given that, what's the Expected Value of Mega-straight flushes? (I find it easier than calculating it's probability)
EDIT: I'm aware the first problem wasn't completely solved, but Michael offered a way to solve it in polynomial time using a computer (I actually did it and took less than a tenth of a second), while apparently would require going through all the possible deals. That's the kind of solution I have in mind: Some insight into the problem that reduces the complex combinatorics it have into something that can be easely treated.