Margaret Beaufort - Savvy political player or lucky opportunist?

What are they defining as her "long game"? Her son becoming king? Margaret was 12 when she married Edmund Tudor, I doubt very much she was strategizing becoming the mother of the king at that point. I would say she took full advantage of the opportunities that came along and made some smart, strategic decisions. But she could not have originally known that most of the claimants to the throne would get killed off in a civil war, leaving a clearer path for her son. At some point, she certainly saw how the cards were falling, saw her chance, and she took it. It is possible to be both a savvy political player and a lucky opportunist. Doesn't matter how lucky you are if you're throwing your opportunities away with bad political decisions.

Well, the entire concept of "Grand Strategy" has been debunked over and over again so I'd say that she was a savvy opportunist.

History, Sociology, Psychology, and Political Science all consider Grand Strategy to be nonsense.

Henry VIIs title claim was based on the death of the entire male side of the Lancastrian family even then how Salic law treats that situation is very grey. Henry taking the throne also required the deaths of most of the Princes in the Tower which made Elizabeth the rightful Yorkist heir and it required them to die because Richard III usurped the throne opposed to getting sick(while its possible Henry still marrys Elizabeth in that scenario Henry would just be the consort). Henry and thus Margarets importance came from decisions made by other people that Margaret Beaufort had no way of influencing or forseeing. Besides Henrys marriage to Elizabeth which was a logical play for both sides because of said events she did nothing to influence the events that ended with her son taking the throne. There was nothing predictable or plannable about said events that can be summed of as "everyone male dies and no woman has ever successfully taken power".

She likely was scheming for political favor within the court of Henry VI but it had nothing to do with the end result. An aristocrat currying favor wouldn't otherwise be given a second thought.

TV docs are always hyping up the conflict. Margaret being a random aristocrat being brought into the spotlight by chance doesn't play as well as "Margaret was playing a game of high stakes chess with her life at stake" with dramatic music playing in the background. Its one of the reasons TV documentaries are the least credible form of historical content. Theres nothing preventing the creation of quality TV historical content opposed to other platforms but for whatever reason that usually doesn't happen.