[EricH]

Originally Posted by implosionprez

Gearing 1:3 from the motor to the wheel does, indeed increase the torque, doesn't it? Or is my thinking wrong alltogether?

It depends on direction and counting method.
For the following, the direction is assumed to be motor to wheel.

1:3, counted in revolutions/time: the wheel spins 3x faster than the motor. (Or: for every revolution of the motor's gear, the wheel's gear has 3 revolutions.) More speed, less torque.
1:3, counted in gear teeth: the motor spins 3x faster than the wheel. (Or: the wheel's gear has 3x as many teeth as the motor's gear.) More torque, less speed.
3:1, counted in revolutions: motor 3x faster than wheel.
3:1, counted in gear teeth: wheel 3x faster than motor.

3:1 in gear teeth is roughly equivalent to 1:3 in revolutions; 1:3 in gear teeth is roughly equivalent to 3:1 in revolutions.

I think it's a counting method miscommunication--they're counting the gear teeth (lightning fast wheel), and you're thinking revolutions.

Better get together and figure out your counting method...