AT: "xx" Luck is superstitious supposed influence on probability, whether a favorable outcome (good luck) or an unfavorable one (bad luck). Luck is a popular concept in gambling.
In 2258 of an alternate reality, Spock wished his younger counterpart "good luck" instead of his customary farewell, which he considered to be in this case "oddly self-serving". (Star Trek)
Before Spock embarked on a scientific mission into the space amoeba in 2268, Leonard McCoy expressed his lack of understanding of Vulcan dignity, so Spock asked him to employ a human superstition and wish him luck. (TOS: "The Immunity Syndrome")
William Riker once remarked that "Luck... protects fools, small children and ships named Enterprise." (TNG: "Contagion")
Data had Vanessa blow on his dice for good luck. (TNG: "The Royale")
Julian Bashir and Miles O'Brien wished Odo "good luck" before the constable departed to deal with Changeling infiltration on Earth. Odo appreciated the sentiment, though he said that he did not personally believe in luck. (DS9: "Homefront")
Senator Letant stated that Romulans did not believe in luck, and Garak stated that Cardassians don't either. (DS9: "Tears of the Prophets", "Distant Voices")
Michael Eddington owned an heirloom coin that he called his "lucky looney". (DS9: "Blaze of Glory")
When Seven of Nine discussed a precaution against Theta radiation with Tuvok, he stated that "With any luck, we won't be needing it." Seven replied that she thought that Vulcans didn't believe in luck, but Tuvok replied that serving with Kathryn Janeway had taught him otherwise. Seven agreed that she did seem to succeed more often than random chance would allow for, and stated that she would factor it into her calculations. (VOY: "Juggernaut")
"Beginner's luck" was a type of luck sometimes attributed to those who win a game on their first try, sometimes even against an experienced opponent. In 2378, when Icheb won a game of kal-toh against Tuvok, he attributed to beginner's luck, though Tuvok recognized his loss as being due to lowered neuropeptide levels caused by a Vulcan neurodegenerative disease. (VOY: "Endgame")
A bit later that year, Admiral Kathryn Janeway arrived from the future with a plan to return the USS Voyager to the Alpha Quadrant by utilizing a Borg transwarp hub. Her Captain counterpart was wary, stating that they shouldn't push their luck, but the admiral replied that luck wouldn't have anything to do with it, as she had developed weapons and technology to defeat the Borg. (VOY: "Endgame")