Dr. Monadnock’s Socks

Dr. Monadnock, the myopic but lovable precalculus teacher, got up so early each morning that he had to dress in the dark. Each day he would grab two socks at random from his sock drawer. His exceptionally perceptive math students saw him on various days in matching pairs of black, gray, or blue socks, and also in mismatched pairs of these same three colors. After taking careful sock-color statistics, they concluded (quite correctly, as it turns out) that their teacher had exactly a 50% chance of wearing matching socks on any given day.

Assuming he owned more black socks than gray, and more gray than blue, what is the smallest number of each color sock that Dr. Monadnock must own?