What is Jack Sparrow's best escape?

The opening of Curse of the Black Pearl: he arrives at Port Royal on a sinking ship, uses a chain of improvised interactions to free himself from prison, steal a faster ship, and escape with Will Turner — all without a plan that was visible until it worked. The sequence establishes everything about how he operates in 20 minutes.

What is his best scheme?

The parley gambit in the first film. When captured by the Black Pearl crew, he invokes the pirate code's right of parley — forcing them to take him to Barbossa alive. He then negotiates his position into a deal, which he partially keeps. He converts capture into leverage using a rule his captors have to respect because they wrote it.

What is his most creative escape?

The jar of dirt in Dead Man's Chest. He carries Davy Jones's heart in a jar of dirt (the dirt negating Jones's connection to the heart). When Jones comes for him, Jack simply refuses to engage directly, using the same logic he applies to everything: the direct conflict is the wrong game. Find the leverage point instead.

What is his least successful plan?

Essentially everything in At World's End involving his alliance-building with multiple parties simultaneously, which collapses repeatedly. He spends most of the film trying to maintain a position that his own nature — constantly shifting alliances, constantly negotiating for personal advantage — makes impossible to maintain.

What is the consistent logic across all his plans?

He never fights when he can negotiate; he never negotiates when he can misdirect; he never misdirects when he can disappear. The hierarchy: lowest energy solution first. Direct confrontation is always the last resort, not the first, because direct confrontation eliminates the flexibility he depends on.