radical addition
Add HBr to an alkene the normal (polar) way and the bromine lands on the more substituted carbon, following Markovnikov's rule. But add HBr in the presence of a peroxide and, surprisingly, the bromine lands on the LESS substituted carbon, the opposite of what you expected. This reversal, the so-called peroxide effect, is the signature of radical addition: HBr adding across a double bond through a radical chain rather than through ions.
The mechanism explains the flip. A peroxide initiates radicals; a bromine radical adds to the double bond first, and it adds to whichever carbon leaves the more stable carbon radical, which is the more substituted carbon. That puts the bromine on the less substituted carbon and the radical on the more substituted one. The carbon radical then abstracts a hydrogen from HBr, completing the addition and regenerating a bromine radical to carry the chain. So the regiochemistry is set by radical stability, not carbocation stability, and because the bromine atom adds first (not the proton), the product is anti-Markovnikov. A crucial limit: this trick works only for HBr. HCl's H-Cl bond is too strong for one propagation step, and HI's addition step is unfavorable, so HF, HCl, and HI do not give the peroxide effect.
Radical addition is the textbook way to get anti-Markovnikov hydrohalogenation, and conceptually it is the same chemistry that underlies thiol-ene 'click' reactions and the start of radical polymerization, where a radical adds to a C=C double bond over and over. The take-home idea: change the mechanism (ionic to radical) and you can flip the regiochemistry of the very same overall reaction.
Propene + HBr with no peroxide gives 2-bromopropane (Markovnikov), but propene + HBr WITH a peroxide gives 1-bromopropane (anti-Markovnikov) because the bromine radical adds first to the terminal carbon, leaving the more stable secondary radical.
Add a peroxide and HBr's regiochemistry flips from Markovnikov to anti-Markovnikov.
The peroxide (anti-Markovnikov) effect is specific to HBr; do not write it for HCl, HI, or HF. And it does not change which atoms add overall, only which carbon each one ends up on.