Every few weeks there's a post here asking how to get 'unique' alignments from bowtie2 output - there's a question from me in the archive, too.
Today I found this 'experiment' in which John Urban from (I think) Brown University went through the trouble of simulating reads and genome to finally find out:
(Remember that AS is the alignment score of the best alignment, XS is the alignment score of the second best alignment)
Bowtie2 does not use the number of times a read mapped in the calculation for MAPQ. Instead, it just uses the AS and the XS, which is either >= the minimum score or below it. If AS == XS, the read is considered a true multiread and can only get a score of 0 or 1. If XS is below the minimum score, the read is considered a true uniread under the given scoring scheme. True unireads can get scores of 0, 3, 8, 23, 24, 40 and 42. A score of 0 is reserved for the true unireads with an AS in the bottom 30% of allowable scores. The scores 3, 8, 23, 24, 40, and 42 are unique to true unireads. Therefore, if someone is hell bent on taking only "unireads" with decent alignment scores, the way to do it would be to take only reads with those scores.
P.S.: The follow-up post on multireads is worth reading too: http://biofinysics.blogspot.com.au/2014/05/where-does-bowtie2-assign-true.html