In Avengers: Infinity War, why didn't Dr. Strange use the time stone when Star-Lord woke up Thanos?
Did he forget?
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Previously in the movie, Dr. Strange used the time stone to view the possible outcomes in the future, discovering that there was only one way for the good guys to win. We can therefore interpret that every decision Strange makes afterwards is necessary to directly influence the future into the correct course for them to win.
Potential Future Spoilers:
But, they didn't win, and Thanos obtained all of the infinity stones and killed half of the universe. So how does this equal a win for the Avengers? Well, in the comics the Avengers eventually get the Gauntlet from Thanos and undo the snap, restoring everyone that was killed. According to Strange's actions, Tony being alive is important for this to happen and for the Avengers to win.
So, in conclusion, Dr. Strange allowed Starlord to wake up Thanos, Strange allowed Thanos to impale Tony, and Strange willingly gave up the stone, all in order to set up the end game.