For most scenes in a film, on average, how many cameras do you have at hand
being used simultaneously?

Mostly one for a normal dialogue scene in a room: 2 for daylight scenes involving some complication ie children, animals, weather etc.
Then 3 upwards for action scenes or any scene where doing it again is a problem - like blowing up a house etc. The main problem with using more than one camera is that it is hard to make the lighting look good from more than one angle, although if the 2nd camera is used carefully then it can provide very useful additional footage.

When shooting a multi angle scene how do you not capture the other cameras from being seen while shooting all angles at the same time?

Well it's quite simple really.. you can't shoot the angle where you see another camera unless you are prepared to get rid of it in post. Sometimes you can hide a camera within the set, put a tree in front of it etc but most of the time you just shoot the wider shot from the front and the tighter shots from the sides (in a typical TV setup). More than 2 cameras is usually TV or action, so the 'precision' of the shot is less important. Getting 'coverage' is the all important watchword of today's 'new' directors. Getting good shots is more what I am interested in, and that is generally achieved by using one camera for all sorts of reasons: lighting being the most affected by multi cameras.

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