wrote in message
I don't see how it's (objectively) counter-intuitive,

There are two remaining choices, switch or don't switch. I think 50:50 is
an easy conclusion to draw from that.

About the only thing I can figure is that it is much like many threads
on ROFF in that most folks, myself included at times, don't always
_read_ what they are "reading," but rather, um, infer from what is
written by what they _think_ is being said.

No doubt many ROFFians are guilty of that; but that is also the intentional
nature of "brain teasers".

In this case, they are
simply ignoring that there are 3, not 2, boards and therefore, the
chances cannot be 1 in 2.

Not exactly, but similar IMO. There are, in fact, 2 choices remaining. The
failure is that of seeing the two choices as random for the original player.
Most folks, I expect, see the problem from the perspective of your "third
person" for whom they *are* random.

Joe F.