One last time... TWO doors... ONE choice. 50/50. If you don't believe me, flip a coin ten thousand times and report back your results.

One last time: that's not equivalent. It doesn't matter that it looks as if it is. Try that link above. Being a bit obsessive I went as far as 100 trials and got 64% wins by swapping. Lewis Carroll claimed 'what I say three times is true', but outside literature just asserting it is 50:50 doesn't beat the experimental evidence