Are your mages pretty common or are they pretty rare troops, like one in 1000 soldiers is a mage?

@AlexandervonWernherr depends on the country. If the country is rich, there are many mages. If it is not probably there are no mages at all. The richest country has a mage-only army, while the others have probably a 500 to 1 ratio of soldiers to mages.

You mention that the fuel is expensive. But how much fuel can a mage carry with him?

I'm unclear on the limits and abilities of this magic. can a mage control the flight of a pebble far from themselves? What's their maximum range or limits? could a mage sit half a mile back hitting the enemy commanders with magically guided thrown daggers coated in poison? Can they create magical traps? What kind of fine control do they have? could mage lift and maneuver a drop of poison into the meal of a general hundreds of yards away?

@Murphy Will update my question, thanks.

@Secespitus each "fuel piece" is the size of a iron ring. They would carry just enough to not slow them down.

@resch Can we also assume it is as heavy as an iron ring, 25-30 grams? 40 Rings would be ~1.2 Kilograms resulting in 400 fireballs or 4000 windblasts.

@AlexandervonWernherr exactly

I hope when they hold hands they also sway back and forth. Like that Coke ad.

What is the tech level? You describe the magic level, but what is the non-magical army fighting with?

Your rules for augmenting power by holding hands suggest to me that the power they have is not additive, but rather multiplicative. Can you clarify to make sure we get that right? If its multiplicative, 100 mages holding hands could rule the world!

@CortAmmon they could... as long as they keep holding hands forever. Remember, there is no permanent magic. A world ruling entity consisting of people that cannot stop touching each other is rather impractical to me. The rule is simple: I can carry a limited quantity of fuel and have limited concentration. Me and my buddy have double fuel and double concentration if we focus on the same spell. One person trying to lift a castle would probably die of stress, while 50 people have consistent chances of making it work out.

How do the powers increase then? If I have N mages of equal skill and equal power, how much can the group do together, as a function of N?

@CortAmmon haven't really thought on that... Guess if the power grows exponentially hundreds of mages would be able to literally crack the planet in two, right? Guess I'll have to rethink that and properly write the question. Thanks for the observation.

I have fun with hard magic systems =) One thing you might consider playing with: permit mages linking hands to have exponentially greater power but they have to be in sync with eachother. If they have different goals or cast the spell at different rates, the spell may go out of control. That makes for a nice check to the awesome power of holding hands! It's really hard to get people to all agree on a topping of pizza, much less spells to cast.

You might want to check out "Mistborn" - the magic fuel is metals, and there are a variety of different metals that produce different effects.

Another thing to play with would be having different ways of spending fuel which are more or less efficient. You fix the exchange rate at 1unit=10fireballs, but what if that was more flexible? Perhaps some disciplines are less wasteful and can make more fireballs, but may not be able to scale as well. This opens the door for a lot of martial arts analogies ("If you want to kill someone, use a gun. Martial arts is about efficiency of energy.")

You should read the fury saga by Jim Butcher. each person can control one element and they vary a lot by strength the main character wins some stunning victories by using weak mages in creative ways.

This question needs to define the criteria that determines the fuel cost for a particular effect. There is no way for us to know what kinds of spells would be cast without that information, other than a guess or throwing out a possibility and hoping that the fuel cost is low. Is the fuel cost related to the actual energy which would be used to create the effect wrt. real-world physics? It does not appear so. A gust of wind powerful enough to destabilize someone either has to happen when they are in a precarious position or be quite powerful (lots of energy) vs a very small amount of fire.

Eragon series of books spends some time focusing on this. For instance to kill an opponent it focuses on minor attacks on their biology (destroy major arteries, break vertebrae, etc)

@Makyen what about compressing air? Wouldn't an air explosion be powerful without using much energy? Didn't really gave a deep thought on that, thanks for pointing out. The cost is based on effort, basically. Lifting a car sized rock from the ground is hard. Lifting an orange sized ball of oil, not really.

Read and is possible enjoy playing Ars Magica RPG and you will got a good idea

War is expensive. Surely the cost of the mages is dwarfed by the cost of feeding a lot of men, their horses, arming same, etc etc. But once on the battlefield, a mage will spend any amount to stay alive.

All concussive explosions take the same amount of energy for the same power. Compressing the air would be just as expensive as a similarly powerful coal explosive - which of course makes coal preferrable, since you can carry it with you to provide bulk of the energy, while requiring much less mage-fuel.

@TonyEnnis That's a crucial point almost every answer that addresses the duels is ignoring. You save fuel in the battlefield because your commander ordered so, but while fighting for your life things are a little different...

Can't you use "wind" to create a vacuum around the opposing mages head, asphyxiating then fairly quickly? Probably cost the same or less than a wind blast, lethal, long distance, and fast. If casting requires speech, the opponent can't even fight back...

@IsaacKotlicky if your opponent is a non-mage or novice mage yeah... Or you could also crush him in is own clothes, which is even faster. What if your opponent is an expert mage? He has the same amount of air, and probably killed various people using that method. He would know how to defend.