So I got interested in the Monty Hall problem - I understand what it's about, but somehow I can't wrap my head around the idea of the final choice not being 50/50. More precisely: we all know (or maybe most of us do) the roulette progression systems which were popular a while ago - they told you that you should wait for a streak of some three-or-more consecutive reds or blacks and then bet on the contrary, always staying with this colour and eventually it has to be drawn as with every other spin, the chances become higher for the streak to be broken.
Of course the system is dumb and was shortly afterwards popularly neglected as a fallacy (though surprisingly many people still believe it works) as every spin is independent and even though you had a million reds in a row, in the next spin the odds for red, black and green are still the same as they had been these million spins ago.
And here I see an analogy to Monty Hall - sure, if we were proposed "Do you choose doors k and l (both at the same time!) or m?", it would be a straightforward 2/3 to 1/3. But why don't we cast aside the fact of some door having a goat and treat the two remaining doors as a simple 50/50 just like we do in roulette? Why aren't we interested in the past in roulette while it does matter in Monty Hall? Isn't the two remaining doors - one with a car - just "another spin"?