We forget today that years ago Taiwan's Kuomintang (KMT) party claimed (claims?) sovereignty over mainland China.
"Tricky Dick" Nixon figured out that if we say we agree China is one country, then we could seemingly recognize both claims, and we'd all get along fine, right?
But the US has been committed to Taiwan's defense since the time of President Truman and the Korean War.
All that "strategic ambiguity" means is that we don't say in advance exactly what forms our defense of Taiwan will take.
Publicly it's said that Pentagon war games show we can't win a fight over Taiwan.
My guess is, if that were really true, then it wouldn't be made public.
Interesting
From that map, obviously Taiwan will have to do most/all of the defending by itself - even if the US wanted to help, Okinawa is still too far away
that’s why the Russia-Ukraine War is so relevant ... a smaller force managing to thwart a larger one with lots of MANPADS, NLAWs, drones, high-tech electronics, etc., shows that it can be done
and Taiwan has a strong will to fight any invasion