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Source: https://writers.stackexchange.com/a/27272
License name: CC BY-SA 3.0
License URL: https://creativecommons.org/licenses/by-sa/3.0/

Being opponents can take lots of forms, leading to a lot of different outcomes.

1. Direct Combat   
 This could be a physical fight with bare hands or weapons. This surely is the least complex form for a writer but also the one which leaves least room for ideas on how to form the outcome. Either you make it realistic based on your setup (then the villain should win in your scenario) or you introduce surprises (e. g. any kind of _deus-ex-machina_ or unbelievable incidents like the villain stumbling while charging or similar).

2. Indirect Combat   
 This could mean to choose a different battleground than expected, e. g. charging Al Capone with tax fraud. This opens way more options for ideas. Of course, all these can seem constructed (which of course they are); one trick to lower the appearance of being constructed is to place hints on these options in the beginning of the story when the reader does not yet think about these aspects. Good hints come disguised as something else which fits neatly into the story without raising too many red flags.

3. Seizing Attacks   
 This is like grabbing the fist which is going to punch you and doing something with it, like biting it, hurling yourself up on it, pulling yourself towards the opponent along it. It can mean to take a punch to get in a better position (like a gambit). In a way this could mean to let the opponent strike first to change the situation. Lure him into a trap, e. g. make him appear cruel or unjust or dangerous to the rest of the world, which can help raise supporters against him.

4. Evading Combat   
 This could mean to let the opponent run into empty space again and again until his resources are diminished and another form of combat seems more promising. A policy of scorched earth is such a strategy in which an opponent is lured into coming deeper and deeper into one's own territory but where no resources are to be found. Another form could be setting up meetings and not appearing again and again (while giving excuses or even better: while staging independent reasons like problems with the meeting place). Such situations can exhaust the one who always has to prepare for the fight.

5. Changing the Perspective   
 This is closely connected to plot-points. Introduce new information which lets things appear in a different light so that the complete enmity is questionable. The information can be fraudulent, and the created confusion can shift the power. E. g. make someone tell your opponent in the box ring that you are about to be shot in round two by a mobster. Combined with a sudden loud bang in the hall in round two this makes it believable enough for lots of things to happen.

6. Staying the Underdog   
 Several other answers deal with this option. To be the apparent underdog opens options which derive from the arrogance of the villain. Typical ways of exploiting such a situation can be to surprise the villain with an action which does not fit an underdog, e. g. being beaten down and kicked around for some time, but in the last second thrusting a poisoned dagger into the villain's foot.

7. Forming and Shattering Alliances   
 The basic difference between protagonists and antagonists is that between good and evil. Being one of the good ones often means to (be able to) form alliances while being one of the bad ones often means to have trouble keeping them (more betrayal, less confidence, more jealousy, more general hatred). Forming alliances based on being one of the good ones can shift the power, especially if the alliance is a surprise to the villain. That's what happened on Endor when Luke befriended the Ewoks. It turned the "pitiful little band" of rebels into a force which could beat a whole Imperial Legion.   
 The other option is to let alliances of the villains shatter at the right moment; this could happen repeatedly in a chain reaction when started, causing significantly more effect.

8. Strengths and Weaknesses   
 Being strong or weak, being smart or stupid, and being good or evil—all these can have multiple dimensions. Achilles was very strong but had a weak heel (similar stories for Smaug and Siegfried). A hobbit is a weak creature but can resist the One Ring longer than other beings. Sauron is not depicted as stupid but is outright stupid when it comes to considering whether others would want to destroy the One Ring (it would have been ridiculously easy to guard Mount Doom). The shrewdness of stupid characters like Stan Laurel's or Forrest Gump leads to believable successes. So if you say that your "villain is stronger than the protagonist" you maybe just lack multidimensionality in strength.

9. Avoiding Combat   
 Your protagonist could avoid any combat, go into hiding, support an underground movement, a rebellion, a resistance, leave the country. This can lead to many people changing their positions, shifting powers, etc.

10. Losing Combat   
 Losing any kind of combat also is an option which should be considered. Sometimes a loss can be turned into a victory later, given time situations can change, powers may shift, maybe the story is taken up by descendants, by colleagues, by friends, by allies.

Original score: 10