Here’s the scenario you describe: you have a 4 day trip, and you wish to drop it to attempt to get premium pay instead.
First to drop said trip, there must be above minimum reserve coverage for each day of the trip (green). There is a grid which shows you if this is possible and what that minimum coverage is.
You then can place yourself on one or both of two lists to make yourself available for premium assignments. Y list for short call trips within 3 hours of callout, or X list for trips 3:01 and beyond.
Who gets called is a bit complicated, but basically based on credit, legality, conflict, etc. The idea being to spread the love around, but this can vary depending on the day’s circumstances. It’s impossible to predict who will volunteer, for how many days, and what conditions they will stipulate (base, trip type, report time, etc)
The other important thing to remember is the rolling 48 hour window inside which scheduling owns the flying. So you cannot drop a trip Tuesday hoping they call you for premium Monday, and if they don’t try to pick your original trip back up again.
Clear as mud?