My track record with 50/50 odds Has been 50/50. HOWEVER, My track record with unlikely things has been well above average. Won a 1-in-500 gift card. Won a 1-in-1000 quilt. Won a 1-in-5000 piece of art.
But the thing in terms of astronomical odds is that every time some one hands me their Pokemon game to fiddle with (I don't play, but I know enough to walk around and level grind), I've found a shiny Pokemon within fifteen minutes of playing, six times in row now. I have no idea what I'm doing.