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Sure, it's worth it in many cases.

For instance, if your car is stranded in the middle of the wilderness due to a tire puncture, using magic to try and mend it would be reasonable. In this situation, the car having two punctured tires isn't any worst than if it only has one. You'll still have to make your way to civilisation on foot either way. On the other hand, in the best case scenario (50% chance, so it's not even unlikely) it'll be repaired and you can complete your journey within the comfort of your automobile.

Many similar examples can be thought of in the case of an injured person. Let's say one of your battle compatriots has been injured and you're about the be surrounded by the enemy who you know will show you no mercy. Well, then it makes perfect sense for you to attempt to cure him. Either he will recover and perhaps help your group stand a better chance against your foes, or he will die by magic instead of by the hacking and piercing of steel.

There are all sorts of times where a partly broken object or person is no more useful than a very broken object or person. It's times like these that magic comes in handy.

If repeated castings are possible, then the odds just got a lot better.

As AngelPray points out:

There are all sorts of times where a partly broken object or person is no more useful than a very broken object or person. It's times like these that magic comes in handy.

The corollary to this is that if you can keep trying repeatedly, and you're not significantly worse off with a failure, you'll eventually succeed. You went from one puncture to two? Cast it again. You have four punctured tires? Cast a spell to repair them all. Your car now has a giant hole in the middle? Cast it again. Eventually, you'll get your car back in perfect condition.

Obviously, this won't work if the "bad" outcome is worse than magic can handle (such as killing your friend, if resurrection is beyond magical means), but in that case, you're back to where we started with AngelPray's quote.

It depends on how unreliable your magic really is. If sometimes your magic does what you want, and sometimes does the opposite, then you can make it do what you want 100% of the time (for certain spells)!

1. Either way it goes, it still gets the job done. There are a lot of ways of hurting people. You could conjure an enormous fireball, adding an incredible amount of energy to a localized area... or you could conjure a blast of ice, removing the same amount of energy. But burned or frozen, the enemy is still just as dead.




2. Ignore the bad results. Sometimes when you try to make a pebble glow brightly, it instead creates darkness. No worries; if you cast the same spell a bunch of times, you can throw away the "darkness stones," and hang on to the glow stones you made. Or, in the case of a punctured tire, don't fix just one - try to fix a whole pile, and sell the ones you fixed. And when you need to inflate it, a spell that removes all the air from the tire is easy to revert until you get the spell that fills it up.




3. Make magical items. Sure, sometimes your spell makes a potion of healing and sometimes it makes a potion of harming, but you can test the result, and people will buy both.




4. Use spells that either work or fizzle. Trying to make something do something it's not doing - a person fly, a dog speak English, a cat obey - will either work, or do the opposite... which is nothing at all. Sure, you're going to have to cast spells more than once, but you'll eventually get the job done.

If you want to cause damage, that's easy; if you want to be constructive, that's a little harder, but carefully choosing what your spell does will ensure that after enough attempts, your spell will eventually work as intended.

Such a magic would be useful for those situations where you are not too concerned with the immediate outcome but rather the consequences of those actions.

Rough example. There is a war. You don't particulary care who wins but you want the ceaseless fighting and killing to end. So you cast your magic on one side to win. Either they win or they lose...but the war is over! (And if the magic did nothing...try again)

You have to trick the magic into giving you the real end result you want.

I suppose this depends if your 'opposite effect' is predictable. In combat you may, for example, try to fireball an enemy, or maybe throw them into the air; you may not necessarily be concerned if they end up frozen or pinned to the ground instead. But you may not want to risk casting the spells if other unpredictable outcomes are possible.

Statistically if you run the spell enough times you would eventually get what you want.

1. So you cast a spell to heal someone, but they die.


2. Then you cast a spell to bring them back to life but their body denigrates.


3. Then you cast a spell to turn their dust into the original person.


4. And so on.

Of course the down side is that each time you fail you may need a better and better spell (and possibly more energy) to fix the accumulated effects of the failed spells. So in the long run those who can cast better spells and who have more stamina have a better chance of getting what they want.

There is also the case of casting a spell that enables you to do something that was already very improbable.

So I cast a spell to print out the lotto numbers on a piece of paper...
There is a 50% chance that It doesn't work out and the paper disintegrates.
Well that's way better than the one in a billion chance I had before.

When it comes to effects whose opposites are also useful, it strongly depends on what "opposite" means when it comes to an effect. Hopefully it's not some kind of pseudo-intelligent monkey paw type of opposite.

For example, if I cast a spell to induce current in a wire, is the opposite effect to induce an opposite current from what I want? If so, we just add a rectifier to the circuit, so the output current is always the same.

We could also generate power pneumatically by casting a spell to double the pressure inside an air tank. If this tank has one-way check valves (i.e. a rectifier), we can control the flow of air and use that to spin turbines.

It's even possible to build rotational rectifiers, so you could spin something with magic and have the output always be the same direction. Or magically kick a pendulum hooked up to an escapement.

If any of these work, congratulations, you have infinite free energy and with that you can develop technology that is distinguishable from magic by being actually reliable.

Sometimes a simple corollary is the most efficient way to answer a question:

People undergo surgery to fix something. Sometimes it kills them.

Surgery is a $21 billion dollar industry

Your magic is statistically useless on the individual level.

If I have a band of soldiers, all wounded badly, then I don't have a fighting unit. If I do nothing, then over time they will either heal or die. In fact, until the invention of antibiotics and other modern medicine, the chance to die from a serious wound was pretty much 50:50 anyway.

Your magic basically just accelerates this process. But that means I get a fighting unit back! It is now half the original size, but that half is healed and ready to fight. Very useful!

So on the level of groups or collections, your magic is far from useless.

Use it as a weapon. Your mages go into battle and heal the enemy. Fix their high blood pressure. Congenitive heart defect or heart murmur? Cure their gout. If it succeeds the enemy isn't really better off, you aren't reviving a fallen warrior. You may also be able to cast it again until you do cause catastrophic or deadly injuries. If it fails, one less enemy. With a fifty percent success rate your mages will be racking up kills fairly quickly.

I'll not add more of the "use chance calculations" answer but provide a surprisingly still unique view on this subject.

Your magic is what I think of as "aware magic". If you try to mend a hole in your Tire the magic (or the user of the magic) is aware of what a hole is, what a wheel is and how it needs to be to be "repaired", or how to punch a hole in another wheel instead of in the car door, the asphalt or the person casting the spell. So if you are aware of what the magic or the user thinks is the opposite you can use it.

Example: you fill two large canisters with gas or liquid and connect them, put a dynamo in the middle and a release valve. Make the gas/liquid something valuable.

Now you cast a spell on the contents of one canister to double its contents, increasing the pressure. If it succeeds then the pressure drives the dynamo as the pressure pushes the opposing piston. If it failes it will halve the contents and the opposing canister will now have its contents flow to the other side. No matter which outcome you get you get electricity, and probability says that because the gas creates an equilibrium, you are more likely to create more gas in the long run.

If you get more gas and the pressure gets too high the release valve can be used and now you have created both energy and a valuable material, which you can store, sell or use. Sometimes chance will make you halve the gas content so much that you have to refill it, but with the stored gas from the times you generated too much you should be able to do this virtually forever.

Another option: nuclear waste disposal. You cast a spell to rejuvinate the waste into useable nuclear fuel. If successful you need to buy less of the expensive nuclear fuel or get rid of it.

If unsuccessful it depends on the outcome:

• It disappears. Yey! No disposal and a lot of concerns put to rest.




• It doubles. Yey! Double the nuclear waste means double the chance to purify it (even better if your spell can target the heap and have 50% chance success each time). This means absolute infinite energy for everyone, assuming magic avoids the Newtons law pitfall (which it usually does).




• It becomes extremely radioactive. Well either you can use that for the nuclear reactor, or if he was alive Ghandi would know how to use that.

https://youtu.be/lQBV3-kwh5k

Unreliable Magic worth it as long as the risk, production and cost is under control within a sustainable amount.

The sustainability can be subjective. Putting those environmental drawback aside. Nuclear power having risk of leakage and it is costly compare to gas and oil, but the power produced is far greater in 10x.

Another example with unreliable magic in some other culture, Strait_Jacket treats Unreliable Magic as a kind of pollution.

Due to an invisible contaminant called the "malediction", or simply the "curse", people who use magic too often are at risk in transforming into "Demons," or horrific, malevolent abominations of nature that become immune to ordinary weapons.

This is sustainable as long as the damage comes under control with a special mess cleaning up organization. One of the scene, the surgeon having magic overdosed in the operation theatre while using magic like x-ray. Potentially the x-ray benefit produces a lot more than the risk of having the additional bit of pollution.

In the Coldfire trilogy, by Celia S. Friedman, magic is very wild. It can manifest just by a person untamed thoughts/fears, yet it can be controlled by very talented people.

https://en.wikipedia.org/wiki/Coldfire_Trilogy

One of these people is Gerald Tarrant, who is capable of controlling it beyond what anyone believes is possible. He can do it because of his very powerful mind, among other reasons.

This isn't an exact 1:1 relationship with your world, but there's a lot of similarities. With about 1000 pages to each book, you should run into a lot of the same problems as your world. Even if not, it's a very good series and might give you some ideas anyway.