Luck has nothing to do with it. Zurg has advantage on saving throws for non-magical effects.

Spellcasting. Zurg is a 2nd-level spellcaster. Its spellcasting ability is Intelligence (spell save DC 14, +5 to hit with spell attacks). Zurg has following wizard spells prepared:
Cantrips (at will): mage hand, fire bolt
1st level (4 slots): magic missile, burning hands

Frightful Appearance. Any creature of good or neutral alignment that can see Zurg must make a DC 13 Charisma saving throw or be frightened. Said creature can repeat the saving throw, ending the effect on a success. A creature who has succeeded the save throw is immune to this ability for 24 hours.

Mage Hand Choke (requires concentration). Melee Weapon Attack: +5 to hit, reach 20 ft., 1 target. Hit: 7 (2d6 + 1) bludgeoning damage. The target must make a DC 14 Strength saving throw or be grappled and take an additional 2 (1d4) damage each round until either Zurg makes another attack, or a successful save throw is made. The grappled creature can repeat the saving throw, ending the attack on a success. Attacking Zurg breaks his concentration, ending the effect.

Zurg Blaster. Ranged Weapon Attack: +4 to hit, range 100/600 ft., 1 target. Hit: 8 (2d6 + 2) force damage.