Re: 3 card Monty, and the incorrect poker math
The Monty's 3rd card (2/3 of being an ace) is clear to me, though it doesn't necessarily drop the odds of the first card to 1/3 as that's what it already was originally. Though if the upcard is an ace (random) it drops everything. If the upcard is or isn't random, there's again something to think about.
My poker example lacked cards; both down cards could be blank cards. The point however was that if I TAKE a "blank" card from the deck after the down cards (preflop) are dealt and place it up it gives us about no more information than what we had before it (the down cards will not include that specific card, that's all). The only difference is the non-randomness in that case, and the fun part is to understand (without formulas) why it makes a difference in this case if the card comes out randomly vs. when it doesn't come out randomly.
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