You are not nearly geeky enough. This all assumes that you have a "fair" dial, that age and strength don't have a bearing on the outcome and that the behavior is uniform over time (wear and tear don't affect the results).
Now if you were to do this MythBuster's style:
- Calculate the average force by applied by yourself and then your child
- Set up a robot that could apply that force in alternating spins
- Set up a web cam to snap pictures at regular intervals
- Write software to intepret the picture to both determine which number is landed on and when to trigger the robot (dial is not spinning)
- Let it run over a prolonged period of time
- Provide us all with the results and tell us if we can expect the same with our games at home
This is way cool by the way!