Legend drop rate is 25%
Master is 30-32%
With bad luck it can take 30 or 50 runs to not get anything. My record is 37 runs with no drop.
Then again, you can have 11 runs and every run drops exotic (has happened to me).
Excavation site takes 2-3 minutes (if you are not way underlevel) to run and even the worst lost sectors (moon ones) take under 10 minutes, so it is very generous way to farm exotics in comparison to what we used to have.
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I don't like this post because it doesn't affirm my feelings that bungie has an employee for every player personally altering their rng