If there are only two players, what is the probability they both draw the same letter or both draw a blank?

The letters (and counts) are E (12); A, I (9); O (8); N, R, T (6); D, L, S, U (4); G (3); B, C, F, H, M, P, V, W, Y (2); J, K, Q, X, Z (1); and 2 blanks. -- 100 tiles in all.

Bonus: What if there are more than two players: what is the probability of a tie for who plays first? (subsequent play is to the left so 2nd, etc. player are not determined by the draw).