Can you state and explain the chemistry behind Markovnikov's rule?

Markovnikov's rule states that, during electrophilic addition to alkenes/alkynes, the hydrogen atom in the electrophile will be added to the carbon atom in the alkene/alkyne that is bonded to he most hydrogen atoms already. This process by which an electrophile chooses to add to one carbon atom in preference to another is known as 'regioselectivity', and it occurs due to the movement of electrons during the reaction.
In the case of hydrogen bromide (HBr) adding to 1,1 dimethylethene, the electron density of the alkene's double bond (C=C) moves towards the hydrogen of the HBr electrophile, eventually reducing the C=C double to a C-C single bond and making a C-H single bond. Simultaneously, the H-Br bond starts to break, eventually releasing Br- into the solution. Overall we have broken one double bond (C=C), one single bond (H-Br) and made on single bond (C-H). Because the bromine carries a negative charge, and because charges must always balance, the alkene is now positively charged with the charge residing on the carbon atom that didn't bond to the hydrogen atom from the electrophile. This positive charge is most stable when surrounded by alkyl groups, as alkyl groups push negative electron density towards the 'thing' they are bonded to. In other words, the most-substituted carbon atom is the best place for the positive charge to be, and that the least-substituted carbon is the best place for the hydrogen to be. Now that the positive charge is stabilised, we have a stable reaction intermediate and the negative Br- ion can attack the positive carbon centre, completing the electrophilic addition reaction. Overall, the hydrogen atom has added to the least substituted carbon atom (i.e. the one bonded to the most hydrogen atoms already), and the bromine has added to the most substituted - as stated by Markovnikov's rule.