By doing self-alignment, we can see exactly what percentage of the genome is uniquely mappable with different size reads. I've got these results laying around:

To be clear these are calculated by taking each possible read of a given length, mapping it back with BWA, and then determining whether it is mapped uniquely to the correct position. You can calculate these yourself in a pretty straightforward manner, or look at the "Mapability" track in UCSC to grab some pre-computed ones.

No genome resembles a random distribution of bases thus your formula does not apply directly.

The first high-throughput instruments had read lengths of 35. I would take that as guidance for the necessary length to produce acceptable rates for mapping.

I had to do a similar calculation for a recent paper. To break past the asymptotic line, the lengths of reads have to get much longer: http://www.biomedcentral.com/content/pdf/1471-2105-13-238.pdf (figure 6)