Pick 3 is not a tiny ball lottery.

Replacement changes everything

Each position is categorical with $P(d)=1/10$. For $m$ positions,

$P(R=r\text{ distinct digits})=\frac{(10)_rS(m,r)}{10^m}.$

The exact sum law is given by coefficients of $(1+x+\cdots+x^9)^m$, and a palindrome has probability $10^{\lceil m/2\rceil}/10^m$.

Repetition is ordinary here

Repeated digits look special in Pick 3 because our eyes import the no-duplicates rule from lotto. The machine never did. For three digits, only 72% of outcomes have three distinct values.