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Does this mean that they have a certain number of FPs available for all rides each day? So, at 12am every night there's a chance you could score a FP to anything if you're one of the first 100 people to book (only an example).
Correct. Just like the original version of FP, there is a set amount of FP+ "slots" for any given time period. The exact number of slots per period is set for each attraction based on capacity and the ratio of FP vs Standby used at that attraction. Once they're gone, they're gone, unless someone cancels.
That 'unless someone cancels' part is one of the good things about the new system. Since you have the ability to change up your FPs after they've been selected, FPs can come available even though they were previously 'sold out'. Theoretically, TPTB could also tweak FP allotment in real time causing more to come available.