Probability that king of hearts remains when drawing until only face cards are left

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Ed_Collins said:
Quote by Ed_Collins
"...we know this depleted deck contains at LEAST one card..."

Reply by haruspex
"No, it may be empty."

Thank you for responding. But this is where I disagree.

The stipulation is to remove cards from a deck until only face cards remain. If NO face cards remain, well then, you didn't adhere to the stipulation, did you. So you try again/toss out trial. It's irrelevant and shouldn't be considered. It's not a part of the "equation."

When you DO remove cards from a deck until "only face cards remain," you will have between 1 and 12 cards left in your deck. Zero isn't possible.

Just for fun, I'm asking the question in another forum, where many of the members are very math-oriented. It will be interesting to see their responses and how they interpret the question. (I'm not pointing them to this forum.)

Thanks again.

I'd be most interested to see what "very math-oriented" people say. If they agree with you, ask them please what they would expect if you take the set of integers and remove as many as possible until "only numbers that are both even and odd remain". The wording is the same as with the card example, so if these people accept the empty set as a mathematical concept, they shouldn't agree with your saying "zero isn't possible".

In everyday life, we might say "the guests left the party, until only the hosts remained", and we mean that there actually were some hosts (more than one, as well). Mathematically, this can be understood as "until no one remained who wasn't a host", and that could be just one host, or even nobody (the hosts might have beren called away from their own party earlier).
 
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Ed_Collins said:
The stipulation is to remove cards from a deck until only face cards remain. If NO face cards remain, well then, you didn't adhere to the stipulation, did you.
As Michael Redei says, it is normal in mathematics to accept the empty set as a valid subset of any set. The property "only face cards are in the deck" is the same as "every card that is in the deck is a face card". If the deck is empty that becomes vacuously true.