FWIW I believe cigar ash is much finer than wood ash, the brand of cigar is of no consiquence. Cigerette ash will also work much the same, just there is less quantities in a cigerette.
Cigar ash and wood ash is about the finest gtrit abrasive you can find and has loooong been used as a polish on fine furniture. If you get a water ring ona good piece of furnatire a couple drops of wood alcohol (I think) and cigar ash will polish it out- depending on the finish. Usually shelac (which is alcohol soluable) and Laquer are on the furnature I am referring to.
Search in furnature restoration and refinishing sources for more info reguarding it's abrasive properties. It comes up as a 'handy home tip' on home shows and such regularly.
They also use powdered limestone as an abrasive in furnature refinishing.