A simple script to find the percentage chance of rolling a pair on N dice.

dice.ijs

NB. Preliminary research
die =. 1 + i. 6

solution_1 =. ,(2 = #@~.)"1 (,"0 1/ ,"0/~)~ die  NB. this solution assembles a matrix
solution_2 =. _3 (2 = #@~.)\ ; { 3 $ < die       NB. this solution uses the catalogue function to create a table of boxes
solution_3 =. (2 = #@~.)"1 (#: i.@(*/)) 3 $ 6    NB. this solution was provided by elcaro

calc_pct =. 100 * # %~ +/                        NB. chained forks are one hell of a drug

NB. Implemented solution

find_pairs =. verb define
  6 find_pairs y
:
  range =. 1 + i. x  NB. the dice values... to be fair staring at 1 isn't strictly necessary.
  window =. -y       NB. go through the range y items at a time. Negation is just there to make the window chunky rather than sliding
  counter =. y - 1   NB. when there are 3 dice, a pair will mean 2 unique dice, when there are 4, a pair will mean 3 unique dice.
  window (counter = #@~.)\ ; { y $ < range
)

calc_pct find_pairs 3
calc_pct 8 find_pairs 3