Tychokinesis: As the Goddess of Luck, Fortune and Chance, Tyche has absolute control and divine authority over luck. If a person receives too much good luck, Nemesis will provide them with bad luck to balance it.
Her symbols include the Cornucopia, the wheel of fortune, four-leaf clover, mural crown, and the ship's rudder.
Tychokinesis, the ability to manipulate probability, is named after her.
Sometimes the Constellation Virgo is associated with her.
According to Rick Riordan's website, Tyche is the most difficult goddess to find. It is said that if you just keep on praying for good luck, she isn't as likely to give you some. If you just go ahead and do something, chances are she may lend you some. This explains the random behavior of her children.
On Rick Riordan's website, Nemesis is said to be sisters with Tyche's Roman counterpart, Fortuna. Whether this is true to the series or if Rick Riordan made a mistake is unknown.
In the books, Tyche is seen only to bring good luck, but in mythology, she can grant either good or bad luck.
In myths, Tyche was sometimes regarded as a fourth Fate, but not legitimately so. However, she is in a way intertwined with fate.