In my world, magic is unavoidably unreliable, for example:
You have a puncture. You cast a spell to mend it and with equal probability either it is mended or another tire is punctured.
You are trying to save an injured person. You cast a spell. Either they are saved or you kill them.
It seems to me that such a magic is completely worthless. Can anyone prove me wrong by suggesting a case where both the intended result of a spell and its opposite would both be advantageous?
There is no way to make magic more reliable. It is just a fact.
I have been asked to clarify the extent of the unreliability. It does not happen with mathematical precision but there has to be some proportionality. For example if I try to light a fire I won't accidentally freeze the entire continent.
Examples of how things might go wrong:
I try to heat up my dinner. I end up with a frozen meal.
I try to repair a broken vase. Something else of a similar size falls off a shelf and breaks.
The supreme being has tasked sprites with keeping magic balanced. There must be an equal amount of desired results as undesired. The sprites however have limited intelligence and a short attention span. Therefore to make their job easy they apply this 'balance' to each spell as it happens. They do their best either to comply or to do what they perceive to be the opposite. They are not mathematicians, they just do their best to maintain balance. Sprites flit around in the spirit dimension so you are very unlikely to get the same one for two spells in a row.
Magic is fairly small scale. It relates to everyday life. You can't use it to make the Sun disappear or even make a person disappear. The spell has to be 'plausible' and within the capabilities of a sprite.
Some are trying to get me to redefine 'unreliable' as 'predictably wrong'. However those are quite distinct concepts. Sprites have autonomy and can use a certain amount of discretion to suit the circumstances. Sprite A might think "opposite" of "cast fireball at enemy" is "cast ice ball at enemy" but Sprite B might think the opposite is "cast fireball at spellcaster."
Most sprites would treat a simple coin-toss as resulting in heads or tails. In probabilistic terms your spell won't make a difference. However life in general isn't that simple so they have to use discretion in the limited time they have. Sometimes they will make a snap decision that is roughly opposite in their estimation.
As a guide, imagine that you are a sprite. You have no vested interest in or sympathy about the result - what do you choose in a given situation to be the desired outcome or the opposite? Pick the most obvious and move on.