The Statistics of Coin Tosses for Theater Geeks | Hacker News Reader

The Statistics of Coin Tosses for Theater Geeks

daily.jstor.org

18 pointsaet5 comments

The article shies away from the fascinating question it hints: given the improbability of 92 consecutive tosses landing on heads, what are the odds that something else is at work here? (un-, sub- or super-natural forces, as they put it in the play). That is, at what point is the improbability so absurd that something else is more likely to be true? That the coin is biased. That Rosencrantz is lying. That laws of probability are actually not in effect. As it happens, this last is true. They're not. R&G are in a play, and the spin of the coin is controlled by Tom Stoppard, the playwright, and not probability. So how improbable does something have to become before you suspect that you're in, e.g., a simulated universe?

when the extremely unlikely happens, always keep in mind that somebody may be fucking with you.

Now there's an interesting question - what's the prior probability that you're actually in a play? Is it even answerable, when all knowledge you're allowed to have is fully controlled? Is it even worth bothering to think about, when (under this hypothesis) all of your thoughts are controlled by an author? All of which dodges the principle issue - do you really think Rosencrantz and Guildenstern are actually sentient, in any sense?

Some may be interested in Von Neumann's algorithm for getting fair results even from a biased coin: Toss it twice. If the results are the same, ignore. If they are different, use the first coin's result.

The coin tosser can make that unfair. http://statweb.stanford.edu/~susan/papers/headswithJ.pdf:

"We prove that vigorously-flipped coins are biased to come up the same way they started. [...] For natural flips, the chance of coming up as started is about .51."

So, start your first throw with the desired side up, and the second with the one you don't want.

I haven't calculated it, but I guesstimate that gives you about 52% probability to get the outcome you want (it certainly is more than the 51% of that paper)

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