By spending $$2($or$,$ equivalently, by exerting effort that costs her $$2$ worth of psychic pain$),$ Sally can reduce the risk that a pickpocket steals $$100$ from her by $5\%.$ By spending a total of $$4,$ she can reduce the risk by a total of $8\%.$ By spending a total of $$6,$ she can reduce the risk by a total of $9\%.$ She cannot reduce the risk any further.

By how much will Sally choose to reduce the risk?