You need spaces around the splats, otherwise they are taken as formatting. I assume you mean 1/2 * 1/3 + 1/2 * 2/3 = 1/6+2/6 = 3/6 = 1/2. You can also reformat that as:
I wasn't explaining, I was just talking about the formatting which was originally wrong, and is now corrected.
And sure you can find it weird, lots of people do, but the reply by DoctorOetker was trying to point out reasoning which, when properly internalised, can make it feel less weird. Some people - possibly you included - never lose the sense of weirdness. I have.
But in truth, sometimes we never really understand things, we just get used to them. For me, maybe this is one of them.
I'm not annoyed at all and added the smiley to try and soften my post. I got the Monty puzzle straight away (brought to my attention by Cecil Adams when I followed the SDMB) but I find it interesting to understand why so many intelligent folk get it wrong.
As for understanding; the stack exchange question on whether it's coincidence that the value of G is approximately pi squared is one of these things I bear in mind whenever I think I understand something. :
)
Edit: and if I'm not mistaken, you once spent far more time than I would have the patience for explaining how this worked to a rather offensive young person. I admired your patience there. It was more than I had and had better results.
I think people get it wrong because they assume that with two options the odds are the same, and you can't know anything to make it otherwise. That's why it can help to explain about where the knowledge is.
One reason why g is close to pi^2 is related to the original idea to define the metre as being the pendulum length required to give a 1 second half-tick. If that's your definition of the metre then g is exactly pi^2. So in some sense it's not entirely coincidence. I should go and find the stack exchange discussion, but I don't have time just now.
And thank you for the compliment about my patience - I appreciate it.
I find it weird that that resets the odds back to 50:50