Ed,
All the idler is doing is transferring drive from one wheel to another, and reversing the rotation. It can be any size, because it transfers exactly the same "number of teeth of rotation" from the drive wheel to the driven wheel.
Consider:
Imagine your drive wheel has 100 teeth, and your driven wheel 50. So the driven wheel goes around twice for every rotation of the driver.
Now put an idler gear in, with 100 teeth. Every single rotation fo the driving wheel will turn the idler once. As the idler has 100 teeth, it will turn the driven wheel twice for every rotation - i.e. the same as if it were being driven directly.
Now put a 50 tooth idler in; the driver will turn the idler around twice for every single rotation; but the idler will only turn the driven wheel once for each of it's rotations: i.e. your 1:2 ratio is preserved.
Now put a 500 tooth idler in. The driver must turn 5 full rotations to make the 500 tooth idler turn once. And every single rotation of the idler will turn the driven wheel 10 times (500:50). So 5 turns of the driver = 10 turns of the driven, 2:1.
It doesn't matter how many idlers you put between driver & driven, or what size they are, they ratio of drive to driven will always remain the same; what WILL change is the direction of drive.
e.g. with no idlers, the driver turns clockwise (CW), the driven turns counter-clockwise (CCW)
With one idler, the driver turns CW, the idler turns CCW, so the driven turns CW.
2 idlers it goes CW, CCW, CW, CCW
3 idilers you get CW, CCW, CW, CCW, CW
and so on.