How much thrust is gained from placing a propeller in a duct?
Relative to MAV, as opposed to large scale rotors:

Compared to the baseline open rotor, the shrouded rotors showed increases in thrust by up to 94%, at the same power consumption, or reductions in power by up to 62% at the same thrust.
At rotor collectives above 10°, all shrouded-rotor models showed improvements in performance over the isolated (‘open’) rotor — that is, higher thrusts and lower power requirements. At the same power consumption, increases in thrust over the open rotor by up to 94% were observed, or, conversely, up to 49% reductions in power at the same thrust, for the condition where the open and shrouded rotors are required to have the same tip speed. If, instead, the rotor disk areas are required to be the same, then up to 90% increases in thrust at the same power.
The effects of changing any one of the four parameters (tip, rlip, d, Ld) on the shrouded-rotors’ performance became more pronounced as the other three
parameters were changed to degrade the performance. It is therefore not possible to categorically state that any one particular parameter has a greater
effect on performance than any other, since the amount of influence of any
parameter depends on the values of the other parameters. The exception to
this seems to be the lip radius, changes in which had almost same effect no
258 matter what the values of the other parameters are.
Thus, in general, it would seem that changing the value of any shroud parameter so as to improve performance results in less sensitivity of the performance to changes in any of the other parameters; similarly, improving the efficiency of the rotor itself would seem to result in less of a performance benefit from the presence of a shroud.

Extracted from:
HOVER AND WIND-TUNNEL TESTING
OF SHROUDED ROTORS FOR IMPROVED
MICRO AIR VEHICLE DESIGN
Jason L. Pereira
Doctor of Philosophy, 2008
Dissertation directed by: Professor Inderjit Chopra
Department of Aerospace Engineering University of Maryland College Park
Rotor parameters including tip gaps, tilt and relative wind, collective, and motor characteristics will influence rotor RPM, and are indirectly addressed in Pereira's dissertation.  Again, there are very broad assumptions in the OP question, but Pereira substantiates generalized efficiency improvements for specific configurations.