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Congrats! This means that you are a Mensa-certified very one-in-a-thousand-billion-special snowflake! If you believe in the doomsday argument then this ensures either the continued survival of bio-humans for another thousand years or widespread colonization of the solar system!
On the other hand, this puts quite the upper limit on the (institutional) numeracy of Mensa... wide guessing suggests that at least one in 10^3 people have sufficient numeracy to be incapable of testifying an IQ of 176 with a straight face, which would give us an upper bound on the NQ (numeracy quotient) of Mensa at 135.
(sorry for the snark; it is not directed at you but at the clowns at Mensa, and I am not judging anyone for having taken these guys seriously at a younger age)
Regarding your serious points: Obviously you are right, and equally obviously luck (living at the right time and encountering the right problem that you can solve) also plays a pretty important role. It is just that we do not have sensible definitions for "intelligence".
IQ is by design incapable of describing outliers, and IMHO mostly nonsense even in the bulk of the distribution (but reasonable people may disagree here). Also, even if you somehow construct a meaningful linear scale for "intelligence", then I very strongly suppose that the distribution will be very far from Gaussian at the tails (trivially so at the lower end, nontrivially so at the upper end). Also, applying the inverse error-function to ordinal scales... why?
On the other hand, any regular reader of LW will (1) be aware that LW folks as a population are extremely smart and (2) notice that Viliam is demonstrably one of the smartest here, so the Mensa test got something right.
Of course any serious claim to be identifying people five standard deviations above average in a truly normally-distributed property is bullshit, but if you take the implicit claim behind that figure of 176 to be only "there's a number that kinda-sorta measures brainpower, the average is about 100, about 2% are above 130, higher numbers are dramatically rarer, and Viliam scored 176 which means he's very unusually bright" then I don't think it particularly needs laughing at.