Hi all,
This is more funny than it is embarassing . . .
On thinking about it again, I realize that my previous analysis was quite wrong (convincing as it may have been).
On balance, it is worth switching ones guess.
The odds of the first guess being correct are 1 in 3, and of bing wrong, 2 in 3.
Thus, if we switch our guess, we lose out 1 in 3 times, but hit the jackpot 2 out of 3 times.
If we don't change out guess, the odds are worse.
As I said before, in the argument I witnessed previously, the issue was only really resolved when someone ran a simulation to test the odds empirically.
This brings me on to a joke about an experimentalist and a theorist:
Experimentalist: Why does treatment A always yield a higher value than B.
Theorist: Give me a week and I'll work on it.
1 week later . . .
Theorist: It was a tough one, but here is the answer (he take out a ten page proof)
Experimentalist: This is a bit embarassing, but I just found out that I have been misinterpreting my technician's annotations - treatment B always yields a higher value than treatment A. I had it reversed.
Theorist (smacking his head): I wish you had told me that a week ago. That's much easier to prove!
Jonathan
P.S. to Lawrence - the one about the coffee and milk is simple algebra. The dilutions cancel out and you end up with exactly inverse ratios of coffee to milk in the two cups (1 to x+1, where x is the total volume in spoonfuls)
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