They could also have something like an unlucky 8 ball similar to that dog in fallout 2. It could be a quest item and you have to find the right person to give it to, to get rid of it.
Ah...http://www.uesp.net/wiki/Oblivion:Staff_of_the_Everscamp in Obl. Only you had a bunch of Mole Rats follow you around. The Unlucky 8 Ball of the Rat Pack. Which would be fitting, as the Rat Pack were of Vegas around the 50's.
EDIT : I stand corrected, they were in the 60's.