After being arrested aboard Deep Space 9 in mid-2370 by Odo for swindling a couple on the station. Martus was locked in a holding cell and met a sickly alien named Cos, who showed him a gambling device that always brought him bad luck. Cos died and Martus took the device. Martus, after being released, convinced a widow, Roana, to let him turn her shop into a gaming establishment on the station's Promenade called "Club Martus". Club Martus used large-scale replicas of the alien gambling device. At first the club was a success, and seriously damaged Quark's profits. Even Rom left Quark and became a limited partner of Martus. But soon the device began letting everyone win, cutting deep into Martus' profits. His patron Roana wanted to close him down also.
Meanwhile, an abnormal amount of unusual coincidences and minor accidents started to occur and Jadzia Dax found that the laws of probability were seriously being altered when she discovered neutrinos were not spinning as they should. The gambling devices were the cause of this and they were destroyed by phaser fire. Once again broke and under arrest, Martus was bailed out by Quark with the provision that he leave the station; one con man was enough. (DS9: "Rivals")
The script for "Rivals" describes Martus as "A tall, elegantly dressed and mannered man in his forties..." 
Martus was the first El-Aurian identified as such in dialog. Fellow El-Aurian Guinan was not revealed to be this species until Star Trek Generations. The writers intended for Martus to be Guinan's son, but the connection was dropped when they found out Whoopi Goldberg was unavailable. He was also intended to be a recurring resident on the station, a rival for Quark. However "Rivals" was not a particularly popular episode with fans and producers so the idea was dropped. (Star Trek: Deep Space Nine Companion, p. 109)
Michael Piller originally envisioned the character of Martus becoming a recurring one but later decided against it, "When we did 'Rivals' I thought that the character of Martus had a chance of being a recurring one. It was like Harry Mudd or something like that. But I don't think it will. I thought it was an average episode, albeit with some great character stuff in it." (Captains' Logs Supplemental - The Unauthorized Guide to the New Trek Voyages, p.67)
Armin Shimerman had previously worked with Chris Sarandon on Broadway fifteen years earlier but he didn't feel their two characters worked well together; "Chris and I got along fine, but the one-upmanship that should have been there, these two swindlers trying to outswindle each other, didn't really work." (Star Trek: Deep Space Nine Companion, p. 109)
Mazur and the events of "Rivals" are briefly referenced in the SCe eBook Sargasso Sector, in which Fabian Stevens places a bet on Julian Bashir to win the racquetball game and subsequently loses a large amount of money.