So your math was sound, but your grammar wasn't? Weak defence
Huh? What was wrong with the grammar?
Let's revisit Carson's quote:
Assuming organizer's do not throw out scrambles because they are too easy: someone will eventually get something like a R U R' or a U Perm as a solution. It could happen this weekend, or it could be 10 years from now
First of all: "someone will eventually" implies that we're talking about
the first occurence. Secondly, the examples of "this weekend" and "10 years from now" suggest that there's a reasonable chance that this happens in our lifetime. And that is simply very doubtful.
Of course it is much more likely that it will happen in the future than that it will happen exactly tomorrow
In this case, yes. But not always! Imagine you're flipping a coin. When is the first time you get heads? Is it more likely to happen in the first three attempts or in the next billion? That's right, more likely in just the first three! About seven times as likely! And the
expected number of attempts is just 2.
Back to the cubing case. There are 43*10^18 possible states. I'll be generous and extend Carson's lucky scrambles to all that can be solved in up to four moves (
about 47000) and all "alg scrambles" (let's say you know 100 algs and you can apply them from 24 angles). That's about 50000 such lucky scrambles. So about one in 10^15 scrambles. So you'd expect 10^15 scrambles until the first such lucky one. I'll be generous again and assume we have 50 competitions every weekend with 4 rounds and thus 20 scrambles each, so 1000 scrambles every weekend. So you'd expect it to take 10^12 weekends which is about 19 billion years. That's where my "few billion years" came from (you didn't think I pulled that number out of my ***, did you?). With "few billion" meaning something
"could be 4 billion, could be 30 billion, could be something in between".
Remember the coins where it's way more likely to happen in the first three attempts than in all future attempts? Even if I extend Carson's "this weekend" and "10 years" to mean something like "in our lifetime" or "in the next 1000 years", it's much more likely to happen much later, and the expected range is in the billions of years (well, assuming a slight increase from now, and not considering the sun exploding or people stopping cubing or us replacing ourselves with robots than can multiply faster and cube more often or whatever). Also, he said "someone
will eventually", and that's rather doubtful, given how long it should take and how much can happen to humans/cubing in the meantime, quite possibly stopping cubing completely so it
never happens.
Bottom line: I felt Carson's statement sounded like it's reasonable to expect this to happen in our lifetime, and I disagree and didn't want others to accept it uncritically. I could've estimated how unlikely it is, but I simply preferred to express it in his terms (saying when it might happen).
