Suppose I can distinguish between the two blank tiles (say one has a small diagonal scratch, the other a horizontal / vertical one).
After arjay has taken his tiles, the first blank is either among his seven or the 83 with other players / in the pool. Probability of arjay holding is 7/90. Given that arjay holds the first, the second blank is either with arjay's remaining six or with other players / pool. Probability of arjay holding is 6/89. Probability that arjay holds both blanks is 7/90 x 6/89 = .00524.
So any one player could expect to be issued both blanks about 5 times in a thousand games.
(I give the probability as a fraction - I don't find odds so meaningful).