interesting ... are we going to discuss the everlasting topic to
decide "what's lucky ?" ;)
My opinion was the opinion of a FMC cuber, so don't hesitate to
discard my 2 cents (actually 2 swiss cents = US$ 1.6 cents, so my
opinion should not count as much as the opinion of US or EU cubers ..
.)
More seriously, what I wanted to point out is the somewhat unclear
definition of a lucky solve. I totally agree with Chris' (although you
make nicely optimistic assumptions about FMCers ;) ), Per's and Mike's
posts, but depending on the method you use, the notion of "skipped
step" can hardly be defined, and my (too ?) scientist point of view is
that rules based on other criteria may be more consistent, like the
one proposed by J. R. Taylor (An Introduction to Error Analysis,
University Science Books, Mill Valley, 1982) to define outliers in a
series of data : it is a simple test based on the mean and standard
deviation of the series. You assume your times distribution is
gaussian (mean u, std dev s), and compute the probability of getting a
time t using erf function table. Typically, Taylor defines an outlier
when this probability multiplied by the number of trials N is lower
than 5% (usual threshold). In your cas Pedro, u = 20, t = 11.xx and s
is probably around 2.6 (just an assumption, it computed it for two
guys averaging around 20 on speedcubing.com website)
Now the fun part: assuming you get a time of u-3s =12.2 sec for
example, som maths (actually I hope I did them correctly) show that
the required number of solved cubes to consider it non-lucky (=non-
outlier) is ... exactly 10 ;) So if you were courageous enough to
follow my thinking I'll change my vote: if in your entire cuber life
you have already solved as much as TEN cubes, I consider your solve
wasn't lucky :) (of course, you should adapt the values for your real
u, s and t, but I don't expect the results to change in an
extraordinary way !)
sorry for the long post, actually I thought my conclusion would be
more spectacular (like you should have solved some billions of cubes),
but actually probability laws are not always intuitive. It makes me
think about a problem with 3 doors I saw on a forum some weeks ago ;)
Last word for Per: don't insinuate I'm jealous ;) How could I ? I'm
not even a speedcuber !
cyril
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