As far as 'a random player' goes, it's fairly obvious that getting a show means a whole lot more accomplishment-wise to a player who is struggling badly than to the dominant player who eats 7's for breakfast. So you've got that factor going for you.
But why include the loser numbers 12/3/45 and leave out the best ones, 12/3/128?
Otherwise, that seems like a great play, since:
A - 3 'naturally' comes in 2nd more often than 1st
B - when 3 is strong, 13 and 23 are almost 50% more likely than the best of the remaining 3-whatever exactas - even when the guys in 1 and 2 are just average.