Mixing fuel grades

Say (for the sake of argument) that my car needs higher octane than the 87 that comes out of the regular pump… but the local gas station markets 89 for +$.20 and 93 for +$.30 (this is true). Does it make sense to buy 1/2 of 87 and 1/2 a tank of 93? do i get the equivalent of 90 octane out of that? or do i just get an 87 knock every other stroke? or 1/2 a knock every stroke? or is there an 87 gas molecule that is fundamentally different than the 93 molecule and it knocks away and takes the 93 molecules along for the ride? (and mixing gas is just a complete waste with no benefit at all)