In Gin-Rummy, what are the chances to make Gin on the first turn?
I modified that program by Andrew Inwood to count them (including all the three-of-a-kinds, still), and it finds 5,379,372 11-card hands that contain a 10-card gin hand.
Out of C(52,11) hands, that makes the odds about 1 in 11,228 or 0.00891%