What's a boy to do?

"Jonathan Cook" wrote in message
...

You posed the problem _singularly_. One try. Probability is about
expected outcomes over lots of attempts. It breaks down in a singular
event. As a _singular_ event, you either have the right board or not,
there is no "law of averages" to consider. And singularly, I'm not
convinced that it is worth switching boards (though I absolutely agree
that over lots of tries it is).

Probability is not the right analysis for a singular event.

No, that's not true. I think you're confusing that with a different
concept. There's something called "expected value" which averages out the
long run. For example, you win a dollar if you call a coin flip right, and
lose a dollar if you call it wrong. Your expected value is winning (or
losing) $0 (you're going to break even in the long run.) However, if you
only flip one time, that's impossible. You can't break even if you flip one
time (or 3 times, for that matter.) This doesn't change the obvious fact
that the probability is 50% for calling it right even if you flip just once.