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1.
A smug or mischievous grin usually used after someone says or does something mischievous or sarcastic.
I knew he had done something just because of that shitty grin on his face
by brownbob August 31, 2010
 
2.
an overly large, or irritatingly smug smile, showing an excessive pride in oneself or one's achievements
her husband was wearing a shitty grin, thinking he had won
by DTinLA April 20, 2011