As it is pointed out in a footnote in A. Zorich's survey "Flat surfaces", Anatole Katok promised (on behalf of the Center for Dynamics and Geometry of Penn State University) a prize of 10,000 euros for the solution of the problem of finding periodic orbits and describing the behavior of generic orbits of billiards in (all/almost all) triangular tables. See page 13 of the ArXiv version of the survey for more comments.
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