Summarizing

r = r + r - 2r r
    = 0.2+0.2+2(0.2)(0.2)
    = 0.32

where

r = 0.16 + 0.04 = 0.2
r = 0.16 + 0.04 = 0.2
r = 0.32

If recombination fractions were additive, then r should
= r + r.

You can see from the above analysis that Haldane only considered 2-strand double crossovers. He did not consider 3-strand and 4-strand double crossover.

The physical distance between loci does not equal the observed recombination fraction due to double crossovers which result in unobservable recombination.

Haldane showed that when the coefficient of coincidence equals one, then the map distance = m = -1/2ln (1-2r) where r is the observed recombination fraction.