By Nielsen-Thurston Classification, every mapping class of a closed surface is one of three types: periodic, reducible or pseudo-Anosov. Pseudo-Anosov maps are precisely those with a representative preserving a pair of transverse measured foliations and they are shown to be generic in the mapping class group due to the work of Maher and Rivin. One of the main ways to construct explicit pseudo-Anosov mapping classes is via the Penner-Thurston construction, and fairly recently, it was shown by Shin—Strenner that not all pseudo-Anosov mapping classes arise from this construction. In this talk, I will discuss how dense/generic the Penner-Thurston pseudo-Anosovs are. This is joint with Justin Malestein and Joshua Pankau.