Just spot checked simplified chainring / sprocket ratios with a brute force skid patch calculator I wrote and Fraction is correct.

So for simplified ratios:

odd / odd -> doubles skid patch count w/ ambidextrous skidding
odd / even -> doubles skid patch count w/ ambidextrous skidding
even / odd -> does not double skid patch count w/ ambidextrous

maybe i'll write up a little applet with pics 'n all.

Rabbit has been updated to reflect the results of Fraction's skid patch theorem.