You've been told that innocent is more common then guilty and so you shouldn't flip a coin but instead roll a dice for results of guilty on a 5 or 6 or even just 6 or to flips two coins and pick guilty only if it came up tails twice.

You aren't supposed to randomize your selection of target, because one of the easiest ways for the scum to pick out fake cops is when they investigate non-suspicious people. You select your hypocop by picking the three or four most guilty seeming people at Twilight of the previous night, pick one, and then randomly determine guilt. The easiest method really is to take a coin and pick the four people you find most suspect at twilight and assign them each a result.

Bob - 1H/2H

Susan - 1H/2D

Mike - 1D/2H

Jen - 1D/2D

Then flip again twice and if it's tails both times list them as guilty. This makes a pretty solid screen against the scum picking out our cop because when half the players pick guilty odds are the scum instantly know almost all of them are not the cop. Keeping it random this way minimizes the number of people the scum can eliminate.