3 card Monty, and the incorrect poker math

[DrVanNostrin]

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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 no more information than what we had before it. 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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I'm missing the connection this has to poker. In poker the cards are random so what comes out does alter the density function that describes your opponents' hands. In your example, taking a blank card out randomly would give you information about what your opponent held.