The gambling device was a purple, hand-held spherical gambling toy covered by angles and curves, as if fashioned from exotic seashells. The gambling device fundamentally altered the laws of probability so that those who won would experience good luck, and those who lost would experience bad luck.
A person plays the device by pressing a key located on the surface – winning was signified by glowing accompanied by a humming sound, losing by a whistling sound only. It was not known how to turn the device off, and its power source was assumed to be internal.
In 2370, Cos brought the gambling device to Deep Space 9 where it was acquired by Martus Mazur after Cos's death. After Quark offered to purchase the device for use in his casino, Martus realized that the device could bring him profit. He replicated several larger versions of the device and opened a competing casino, "Club Martus", across the Promenade from Quark's. Whereas the original device only affected the user, these large-scale devices affected seemingly the entire station, resulting in a plethora of bizarre coincidences and improbable accidents. It was only after Lieutenant Dax discovered an easily traceable side effect - high percentages of otherwise-equal neutrino rotations - that they were discovered to be the cause. Sisko and Dax then destroyed them all via phaser fire. (DS9: "Rivals")
Originally, there were three designs for the probability machine; the handheld device (which was initially designed larger than its appearance in the final episode), the larger device created by Martus, and a four-person gambling orb for the casino. Ultimately, only the first two designs (with some elements from the third) were incorporated into the final production. (The Making of Star Trek: Deep Space Nine, p. 47)
The script for "Rivals" describes the handheld version as "small, spherical, softball-sized, handheld GAMBLING DEVICE. It has a strange design, covered by curious angles and curves, as if fashioned from exotic seashells."