12 runs of Honey B later...

[Reinha]

A tip for rolling in normal raids to win the item you want:

First, roll "Pass" on all the items you don't want, and wait until those items start being distributed. Only then roll "Need" on the items you actually want.

The people who have already received an item will lose their chance to roll on the item you actually want. That way you have less competition. In this case you want a chest piece, so roll "Pass" on accessories, hand, head, legs and feet. Party members will win some of those tokens and leave the instance. Now you're only rolling against a couple of people for the chest.

This is based on the fact that many players will roll on multiple tokens because they don't really care what they win. So let them win the item you don't want.