It's not always possible to improve beyond what randomness would yield. Consider, for example, the coin toss predicting game. Or the face-the-firing-squad game.
@michael e sullivan
You are right, my mistake. I was assuming that running, say, 100 trials meant going all the way through a 100-card deck without shuffling. Going back over the description of the problem, I don't see where it explicitly says that the cards are replaced and reshuffled, but that's probably a more meaningful experiment to run, and I'm sure that's how they did it.
At least I'm not crazy (nor, hopefully, stupid, if only 30%). :)
@A Pickup Artist
No worries, I made a bad assumption.
@A Pickup Artist
I got the point of Eliezer's post, and I don't see why I'm wrong. Could you tell me more specifically than "for the reasons stated" why I'm wrong? And while you're at it, explain to me your optimal strategy in AnneC's variation of the game (you're shot if you get one wrong), assuming you can't effectively cheat.
(Incidentally, and somewhat off-topic, there's a beautiful puzzle with a similar setup — see "Names in Boxes" on the first page of http://math.dartmouth.edu/~pw/solutions.pdf. The solutions are included, but tr...
The assumption behind this post, as AnneC touched on, is that higher scores are linearly correlated to what is perceived as a good outcome. Guessing blue every time will guarantee a worst case and best case outcome of 70%; as such, guessing randomly becomes a much better strategy if the player puts a significant premium on scoring, say, 95% or higher. Whether this valuation is rationally justifiable is another question entirely (though an important one).
The same assumption lies behind A Pickup Artist's post. It all depends on your objective: if you want...
Robin:
I don't think that this is what Eliezer is saying (and correct me if I'm wrong). What Robin seems to be inferri... (read more)