any time you run a gear ratio that comes out to an even integer (1:1, 2:1, 3:1, 4:1, etc.) you will get exactly one skid patch. With a 1:1, when the pedals are in the position used to skid, the tire will always be in exactly the same position. With a 2:1, the same thing happens, but the tire went around an extra time in the mean time. #:1 gives you two extra rotations before it stops at the same spot again.

The most skid patches you can ever have is the same as the number of teeth on your cog. The best combinations are ones in which the cog tooth count and ring tooth count are relatively prime with regards to eachother. Using Yoshi's example, this would be any instance where you cannot reduce the fraction at all.