Hi!
  OK, here is the scenario, see if you can break my resolution mechanics please.

  You are playing Guillermo Perez, his stats are as follows:
Super Stretching (Super, Power, Physical)
Super Toughness (Super, Power, Physical)
Martial Arts Training (Ability)
Computer Science Degree (Ability)
Intuitive (Ability)
Self-Reliant (Ability)
Driven
Loyal
Idealist
Mark of Gullibility
Mark of One-Track Mind
Rigid Thinker (Weakness, Mental)
Brutally Honest (Weakness, Social)
Grit: 3

  You have been battling against Terminull in a Physical Challenge (he tried to take over the world's economy using the internet and you could not let that stand) and finally won! His stats are:
Terminull
Wired (Super, Power, Mental)
Hard Body (Power, Social)
Fighter (Ability)
Friendly (Ability)
Iron Will (Ability)
Manipulative
Curious
Hyper
Mark of Agitation
No Tolerance for Pain (Weakness, Physical)

  During the battle, you used
Super Stretching
Grit - Double Super Stretching
Super Toughness
Grit - Double Super Toughness
Martial Arts Training
Intuitive
Grit - cancel play of Rigid Thinker

They played:
Grit - To play Wired
Grit - To play Hard Body
Fighter
Friendly
Iron Will
Grit - Play Rigid Thinker against Guillermo (You need Grit, because its Mental)

So, now the World has been saved, the Die can be rolled and the EPs can be totaled up
You got 501 EP
They got 133 EP

Here are the Effect Costs:
Effects
Add Standard Trait: 1
Add Ability: 10
Add Mark: 5
Add Power: 100
Add Weakness: 50
Add Super Power: 200
Add Super Weakness: 100
Remove Standard Trait: 2
Remove Ability: 5
Remove Mark: 10
Remove Power: 50
Remove Weakness: 100
Remove Super Power: 100
Remove Super Weakness: 200
Hospitalize: (100 x Super Power Arena Tags) + (10 x Power Arena Tags) + Abilities - Marks - (10 x Weakness Arena Tags) - (100 x Super Weakness Arena Tags) - Target is wounded and is laid up in the hospital and unable to act Physically for the Duration
Terminull has a Hospitalization cost of 102
Incapacitate: (100 x Super Power Arena Tags) + (10 x Power Arena Tags) + Abilities - Target is unable to act physically, mentally and socially for the Duration
Terminull has a Incapacitation cost of 113


Duration
One Scene: 0 (This is 3 days or one scene, whichever occurs first)
One Day: 1 (Any number of scenes, at least one)
One Week: 10 (Any number of scenes, at least one)
One Month: 100 (Any number of scenes, at least one)
One Year: 300 (Any number of scenes, at least one)
Permanent: 200 (Another Effect can still negate this though)

Target
One person: 0 (Besides self)
Self: 5 (Add this to another Target if you are affected along with others)
2 to 20: 1 (Group)
21 to 1,000: 3 (Village/Town)
1,001 to 10,000: 5 (City)
10,001 to 1,000,000: 10 (Big city)
1,000,001 to 10,000,000: 20 (Region/Small Nation)
10,000,001+: 100 (Large Nation/World)

You only have to buy Target and Duration once, but can buy multiple Traits

Also, you can spend EPs to cancel EPs of Terminull on a 1-for-1 bases (but not reduce him below 0)

How would you spend them?
I would like two types of responses please:
1) Ideal (in the spirit of the game)
2) Broken (Meaning you would like the results as a player, but not as a GM)
  Let me know what you would do, thanks!

Am I right in thinking you could cancel all his EPs and also hospitalise him?

AoF
  Yes, you could spend something like this:
133 Cancel Terminull's EPs
0 Target Terminull
102 Buy Hospitalization Effect for Terminull
50 Remove Hard Body
5 Remove Fighter (Ability)
5 Remove Friendly (Ability)
5 Remove Iron Will (Ability)
1 Add Afraid of Guillermo (Standard Trait)
200 To make it permanent (Poor Terminull, at least he can still do Mental and Social Challenges...)

Or possibly try something else if you wanted to...

  Basically, I am trying to get a good benchmark on what a single player can do if they game the system (and get a lucky die roll)...

My main feedback is that it seems like a lot of work to translate a 'plot' effect ("I want to fight him") to a 'game' effect.

AoF,
  Hm, that's been on my mind. I want to see if someone will hash these numbers with me a little before I subject my playtesters to it and find out if its an issue or not.
  My guess is it is probably the same amount of crunch/work as M&M or whatever, just distributed differently. I think the build up to the EPs will be slick and simple, then the spending of the EPs might be a little heavy. As opposed to doing a bunch of small calcs each turn of a fight, does that make sense?
  Does it affect your opinion one way or the other?

  I do have a Playtest group lined up, but I do need to write it in one doc and smooth out the setting a little. While I do that I am looking for someone to break my EP mechanic, any takers?

I think most games would do it action - roll - result, new action - roll etc, like

"I try to hit him"
(roll)
"You miss. He tries to hit you and..."
(roll)
"hits for 3 damage."

Whereas you seem to be have people make one set of rolls, then make a set of results that add up to the result you got.

So I can see why you say it's not necessarily more rolling.

However, it might seem to be. Partly because

i) people will start by getting the 'payoff', of knowing whether they won or not. In a normal game that'd be the end of that bit of decision-making, but in this game it's the beginning. And it might seem a bit like work ("you just told me I've won/lost, what does it matter exactly what happened?")

ii) you're asking players to 'do the GM's job' ("tell me whether he's killed, or captured or gets away" "What? How do I know - you tell me.")

Point ii) actually raises another question - beyond the initial scenario, if the players are interpreting all their results, and there's a set method for doing that, what role does the GM have?

AoF,
  I definitely do not want to make a GM-less game. Partly because Its less fun to me, but also because I would not know how to advise players to play one.
  I've only played a few sessions without GMs in other games and some were good and some were bad, but I don't know enough about GM-less play to figure out why the bad ones went bad or how to fix it...

  Also, I think the point is, during the fight, you are fighting for what you believe in or what your character believes in. When it all is said and done, your character can change the world with that belief.
  By letting the players buy that affect, I hope to skip that point where the players intentions are misinterpreted or twisted on purpose or by accident by the GM.
  Don't get me wrong, that twist can be great game play, but it should be the result of a NPC victory, not the natural flow of the GM subverting what you personally care about.
  A great example one player asked me was, The villain wants to destroy the town and I want to save my uncle, who wins? The answer of course is, roll em! If they get enough points, the Uncle is saved, even more and maybe the town too, right?

  I guess I imagine the play being more like a CCG, where you play your powers through turns and narration and in the end, the GM combines the effects you bought with the effects the other side bought into the actual effect on the game world.

  I have played in a couple of Supers campaigns where the PCs never actually changed the world, sometimes they saved it, but its not the same is it?

  Does that explain it better? Does it make you more or less interested?

So how do you prepare an adventure?

AoF,
  Good question.
  In my mind, game prep would be comparable to other games you play.
  The players will provide you with nemeses at chargen and you can make your own villains too. Then come up with who they will threaten, and how and narrate. If the players try and thwart his plans, you have a Challenge, right?
  My hope is this will be a low prep game, but I would never even try and market it as a no prep game. I feel that most games benefit from GM prep, as long as the GM doesn't not fall into bad patterns of railroading, etc.
  One fo the best pieces of advice and one I have followed for a looong time is, present the players with a problem, let them come up with the solution, right?

It seems like one roll in this game covers what would be a whole adventure in another.

AoF,
  I think it depends on the scale of the campaign.
  For instance, we can take a simple example, Dr BadGuy wants to dominate the world.
  You are right, in some games, this would be a whole adventure. But maybe in other games, this is just a stepping stone to a larger conflict (maybe Dr BadGuy is just a pawn of a more sinister villain, right?)
  And that's the point. The GM controls which actions are Challenges and how big they are. He can call that the entirety of Dr BadGuy's plot is one big challenge. And if he is just a pawn, that makes sense, right? Or he can break Dr BadGuy's plot into smaller steps each one is a separate Challenge.
  One thing that helps judge when this happens is that the stuff you buy with EPs and the EPs themselves can only be generated through a Challenge that incorporates at least one PC. So for instance, if Dr BadGuy needs to add the Hypnotized Trait to the President in order to take over the world, then that is a challenge all by itself, right?
  In other words, you can't change the world without a Challenge. Of course clever GMs and Villains can use that to their advantage and use the world's existing foibles to kick off their plans, but that is fun too (and more realistic), right?