Is Scrabble's method of determining turn order fair? 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.
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.
The drawing order matters because tiles are drawn without replacement. If drawn with replacement, the order wouldn't matter.

Drawing without replacement changes the tile frequency, relatively more if an unfrequent tile is drawn. Drawing without replacement also changes the pool size, with an impact on tile frequencies.

It appears to me that frequent tiles of high value favour at a small extent the last player to draw.