At least the way my family plays, turn order is determined by drawing tiles and seeing who has the letter closest to A (blanks taking precedence). If I recall correctly, there are 100 unevenly distributed letters.
Intuitively, it seems like it would be unfair, though I can't come up with a way to prove it. Obviously the distribution matters: my thoughts are if there are more tiles in the first half of the alphabet (including blanks), then the starting player holds an advantage since they're more likely to get a tile earlier in the alphabet than the next (and vice versa if there are fewer tiles in the first half). That doesn't seem too right, though. I'm probably just forgetting some basic prob stats.
I imagine this is likely a duplicate, but I couldn't find anything relating to it (maybe since I've been searching for Scrabble). My apologies if it is.
Please feel free to edit in appropriate tags.
Best Answer
Because of symmetry, no player has an advantage. That is, if $\mathscr A$ is the set of outcomes where player $A$ gets the letter closest to A and $\mathscr B$ is the set of outcomes where player $B$ gets the letter closest to A, there is a one-to-one correspondence between $\mathscr A$ and $\mathscr B$ obtained by interchanging the letters players A and B get. Since all outcomes are equally likely, they have the same probability of getting to go first.