There are two issues here:
1. We don't really understand which genes are responsible for human intelligence. Likely, the answer involve many different genes working together and some of the evolution has not been in changing the genes themselves, but the non-coding DNA sequences that regulate their expression.
2. In general, evolutionary biologists debate the extent to which evolution is reproducible and predictable. Stephen J Gould proposed the thought experiment considering what the Earth would look like if we were to rewind time a few hundred million years to an identical starting state and let evolution proceed to present day. He thought it would be likely that we would end up with a very different set of species populating the Earth were we to "replay the tape of life" in this way. Indeed, evolution has been shaped by many chance events (e.g. a mass extinction caused by a meteorite strike). Furthermore, many of the underlying processes of evolution, such as the appearance and propagation of new mutations in a population, are stochastic and rely on chance.
In recent years, there have been efforts to simulate evolution in the library to address questions about the predictability and reproducibility of evolution. For example, Richard Lenski seeded 12 identical populations of E. coli in the 1980s and has been tracking their evolution for the past three decades, providing insights into how new traits evolve in bacteria (e.g. see
http://www.pnas.org/content/105/23/7899). Researchers are also combining computational and experimental approaches to look at the evolution of proteins and understand the reproducibility of evolution at the molecular level (e.g. see this recent paper from Joe Thornton's lab at the University of Chicago:
http://www.nature.com/nature/journal/v549/n7672/abs/nature23902.html). For a general review of the reproducibility and predictability of evolution, see this review article:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4633862/
Of course, these experimental approaches are on simple systems (fast-reproducing bacteria) and simple traits (often encoded by a single gene). Studying a complex trait like intelligence in a slowly reproducing organism like humans would be very difficult.