More or less skid patches for winter tires? Update: this question is NOT about how to calculate the # of skid patches. I've always used http://www.bikecalc.com/skid_patch_calculator for that and the math is sound.

So, I'm already thinking ahead to next winter to see what I could do better with my fixed gear winter commuter. I'm running a pretty conservative gearing with a deliberately odd-numbered cog (21T I believe) to spread the skid patches all over my rear tire (update: I'm running 44x21 so 21 skid patches, which is a lot). This winter I tried the Schwalbe Marathons and was pleased generally, but after only two months of daily riding, the rear tire looks like the tonsure on a monk's head: completely bald in the middle and treads on both sides.

Why? Because I have SO MANY skid patches that it's a pretty uniform wear. And I hear that the Schwalbes use a pretty soft compound so they wear fast.

So, I'm wondering, what if I switched to an even gearing with **LESS* skid patches? Like a 45x20 for 8 skid patches. Obviously, some parts of the tire would wear more... but others would keep their tread... Has anyone tried this and is it a horrible idea? Or is there some merit? Again, I'm focusing on WINTER riding where I might want to preserve a little tread for grip.

And yes I run a front brake.
To spread skid patches around the tire, you need to have chainring and cog that have mutually prime tooth counts, i.e. no common divisors. With a common 42 tooth chain ring, 21 is the worst possible choice because it produces a straight 2:1 ratio. If this did no seem to make sense, search for "skid patch calculator" to find interactive visualizations.

If you really want to avoid excessive tire wear at the cost of some style points, a front brake is great. Also, the current version of Schwalbe Marathons doesn't seem to wear that well.

Edit: After writing the answer, the question has changed. Having less skid patches is a good idea, if your aim is to wear the tire to cords faster. It will not help with braking because the tire has skid patch facing ground when you brake. It will also not help much with lateral grip, because the smooth patches will be even smoother.