In the disagreement between Howard and John, Howard seems to me to be correct, especially since he understood what I was getting at with the second player.

So two perceptive people who understand the calculations still disagree about various additional issues shows. That shows just how confusing the whole set-up really is.

I'm tempted to press some of my unanswered questions, but since they're expressed in words rather than numbers they may be too troublesome to fool with.

Yes, we have come a long way from the original problem, because to the naive observer (me) the solution raises additional questions about what kinds of situations resemble it.

As for the pigeons, it's silly to suggest that they're "smarter" than the students. The only thing that "smart" could mean in a sentence like that is "far more efficient in learning to respond rightly to stimuli, unconsciously and without preconceptions."

If the students were like most people, they were hampered by the years-long conscious conviction (rarely if ever challenged) that two doors must always give a 1 in 2 chance, regardless of additional factors. The pigeons, so far as we know, weren't. And unlike some people, they can't explain why they're right.

But it's conscious awareness and the ability even to have preconceptions (or any conceptions) that makes people generally smarter than pigeons.