It is not a 100% chance that this will make a Phantom Roll behave as though the correct job is in the party. It is currently assumed to be around a 33% chance.
Also it seems that the +1 version of this does not increase the chances.
Still a very nice hat that increases Cor's buffing ability, even if it is just a chance.
Augments Phantom Roll by making roll effects work as though you had the proper job in your PT, without actually having one. For example, you'd get the effect of having a DRK in your PT when using Chaos Roll, without actually having a DRK. If you do have the job of a roll in your PT, it doesn't give any extra bonus, though.
There's almost no equipment available that enhances rolls in any way apart from this and Luzaf's Ring. What with rolls being a Corsair's primary job in a party, this is certainly one of the most useful items you can get as COR.
If you have any doubts, here's just one example: how often do you do Evoker's Roll on a party with a SMN in it? Guaranteed +1mp/tick (no matter what you rolled) on a SMN-less party anytime the effect kicks in.