Go here and put in the numbers, it will tell you how big the wire should be.
http://www.csgnetwork.com/voltagedropcalc.html
Current is carried on the surface of the wire, not in the center, so the more strands you have the more current it can carry. In other words, more surface area of copper.
Fine stranded wire is also more flexible and should allways be used in automotive and marine applications. Things are allways moving and vibrating. Copper work hardens and if it is bent enough times the strans will break, that introduces resistance into the circuit. That makes voltage drop at the appliance (headlight gets 10v instead of 13v) and the current draw goes up (that makes heat) and you burn wires and blow fuses.
You allways measure distance from the source (bat + to the appliance (headlight) and back to the source (bat -)
If a wire is corroded, like on the last inch of you battery cable, the corrosion on the surface (remember current uses the surface of the copper strand) of the strands resists carrying current (resistance) and thats why things get hot, starters dont work, etc etc.
Corrosion can be anywhere, on any wire or connector. Most folks dont understand how important this is. Just ask Don. He works in the marine industry. I can tell you, if a boat has a problem, its in the wireing. Am I right Don?
Electricity is mathmatical. It's a formula between Voltage, Amperage and Resistance. Change any one of these and the others will change to make the math work.
Finally, if you let all the smoke out of an electrical thing of any kind (motor, wire, etc) you have to get another one with more smoke in it.