Blackbeard is lucky Shilliew saved him.
Shilliew was impressed by how cunning and manipulative Blackbeard was by deceiving Sengoku and the world government and joining the warlords in an elaborate and convoluted fashion for the sole reason of gaining access to Impel Down in order to find new crew mates. he's not only a long term planner but he also has the charisma to subdue many powerful followers.
Remember that Magellan only let Shilliew out when he knew Blackbeard was in the Impel Down. which further proves that Blackbeard's plan would succeed anyway since he already knew Luffy is making chaos and a huge breakout. when raiding Impel Down, Blackbeard knew about the chaos inside and said he's willing to take these surprises in stride.
he is lucky WB died the moment he died
It was smart from Blackbeard to strike the moment Whiteberad lost half of his head and was nearly a dead corpse. with the strongest criminals on his aid, it was the best time to attack and take the strongest paramecia devil fruit before the marine take his corpse away to celebrate victory.
He manipulated both the navy and whitebeard to go into war with each other. both suffered heavy casualties, but the one who took the advantage was Blackbeard.
he is lucky Luffy distracted Magellan
Whether he distracted him or not it's irrelevant. since Blackbeard already knew about the huge breakout in prison. sooner or later Magellan would be crushed.
he is lucky Thatch found Yami df
It was the beginning of the end to a Yonko. Blackbeard is a very patient and careful pirate, as stated by Shanks. unlike other powerful pirates, he never gained renown and remained concealed, up to the point that he only makes his moves when he sees an opportunity for power. when that
opportunity came, he went from a nobody to someone who threats Imu and the world in general with no alliances or people to help except his own crew.
He is too lucky to be considered a genius.
Something no one said at all. being smart at a certain field doesn't make you a "genius".
Ben Beckman was stated to have a lot of experience even among other Yonko Commanders. and has great
thinking capabilities. Blackbeard on the other hand is someone who doesn't waste a good opportunity but still is careful when it comes to planning and he execute them well. he was interested in researching history like Rocks. both had plans, schemes and charisma to hire powerful crew mates. plausibly the reason why the celestial dragons started to target both. you don't have to be a genius to have great planning insight. Orochi is prime example.
Smartness, in this context, is about calculations, manipulating and planning/scheming way ahead of time.