A simple game invented in my high school.
You start with an arbitrary number and can add or subtract one of its prime factors. Each prime factor can be used only once in the whole game. The score is computed as the final number divided by the original number.
Generally speaking, a score of 3 is decent. Starting with prime numbers seems to have an edge (not always).
For example, $\displaystyle{ 11 \to 22 \to 24 \to 21 \to 28 }$ The score is $28/11 = 2.54545...$