I'm not sure if we're saying the same thing but I think the reason they're equivalent is just that the cost of the first ticket is sunk so in both cases you're $10 poorer and are faced with the decision of whether to spend $10 on the show.

Yeah, I think we are saying the same thing. History is irrelevant when determining the worth of a movie ticket. I just mentally represent it as a state diagram instead of worrying about whether the ticket lost was a sunk cost in order to avoid a fallacy.

By the way, there are two ways to fall prey to the sunk cost fallacy. [...] In examples like in the original post, I will ask myself "would I go to see this show (or whatever) right now if it were free?".

Right, and I think your question is the valid point.

For what it is worth, the state diagram for the first example would shift the worth from the movie ticket to watching the movie itself:

• Initial state: A ticket costs $10 and allows admission to a movie. If you predict watching the movie will be worth $10, buy the ticket.
• Purchased state: The night of the movie, since you have a ticket, you can watch a movie without paying for a ticket. If it is worth watching the movie, use the ticket.

By the way, the reason I use state diagrams is because I arrive at the "purchased state" if someone else gives me a ticket. If someone gives me a ticket to a movie, am I obligated to use it? Ignoring any social concerns, the answer is no.