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Markovnikov addition, also called Markovnikov's rule, states that a protic acid (HX) will add to an alkene such that the proton will bond to the less substituted carbon.
During this addition, the carbocation intermediate bares a positive charge on the most substituted carbon. The more substituted carbon, the more stable (tertiary > secondar > primary > methyl). If the reverse occurs, that is the more electronegative atom (X) ends up bonding to the least substituted carbon, it is termed anti-Markovnikov addition. The figure below shows a figure of both additions:
Fig. 1. Markovnikov and anti-Markovnikov additions of HBr to 1-methylcyclohexene.