Balance is generally desirable, as it means each option is viable, giving the player real choice. It also means the game is probably fairer, and there are no parts of the game that no one ever uses.
People drastically overestimate the importance of balance. It's nice that things are balanced, but plenty of other things are more important.
Balance is also very easy to achieve. Almost anything can be balanced, which means that you can really do whatever you like, and just balance it all later.
Balance is not the same thing as fun. Do not excuse un-funness for balance reasons.
Chess is still a great game, even though white wins more than black. It's even less important that rooks are better than knights.
I've talked about the Depth:Complexity ratio. Balance is like a third component in this equation, but I consider it to be far less important than the other two factors.
I know some cards I make are imbalanced (too strong, or too weak.) That's fine. It just happened that the simple, clean version of the card was imbalanced. Choose elegance over balance. As long as the card has some value, and isn't "feelbad" for anyone, I'm happy with it.
The other thing about cards is that a player has many of them. Some will be imbalanced individually, but a hand is likely to be balanced overall.
I do like to make all options balanced, but each option need only be balanced enough to be worthy of consideration by the player. If there are two options, and one is chosen only 25% of the time, that's still fine.
Try to convert everything in the game into your game's "lowest common denominator" resource, so you can roughly compare things. That's about the extent of what you can and should do, however.
Don't try to do mathematical calculations beyond that. I've been guilty of trying to balance things with a spreadsheet. It might seem doable, but what's the value of something that's slow, or the value of something that's overkill? There cannot be an absolute system for balance.
I just guess the value of things in my game, and try to find similar things to compare them to. When I play, I see that some things are imbalanced. I strengthen the weak things, and weaken the strong things.
A good designer balances by changing numbers. A bad designer adds text, rules, and caveats.
It's handy to make sure your cards (or other components) have a number on them. It could be a cost. It could be a points value. This allows easy fine-tuning of balance.
In Radlands, each player starts with three camp cards. These are important. When I started designing these camps, I knew balancing them would be difficult, so I added a numerical component. Every camp card has a number in its corner, and each player draws a starting hand equal to the total of these numbers on their camps. This way, weaker camps can be balanced by having a higher number, and vice versa.
Just make the simplest and nicest version of each object, and then balance it by tweaking its numbers.
Sometimes, you want to imbalance things.
In deck-builder game Dominion, you start the game with a deck of ten bad cards. You add good cards to it, and try to remove the bad ones. The Chapel card can remove four cards from the deck in one turn. This card is amazingly good, but the designer knew that. The idea is that a game with Chapel in it will be distinctly different from other games.
I like to imbalance things that are necessary for the game to progress, or otherwise remain healthy. Every option should be worthy of consideration, but I make these options have a clear edge over the others.
In an earlier version of my gangster game, location cards would come and go throughout the game. I wanted the board to keep changing. I could've said "every turn, or round, draw a new location card." However, I didn't want any kind of turn structure, where players had to remember to draw a new location. I wrangled with this for a long time, before settling on a fantastic and easy answer. I created a clearly imbalanced Getaway Car space, that people wanted to go to, but which also drew a new location card.
Don't forget that options should be similar in fun, as well as in strength.
In my gangster game, players can take various actions. Some
will increase their health. Staying alive is necessary, but it's also boring.
Players greatly prefer the actions that give them money, because money is cool —
it can be spent on all kinds of stuff. To make health more interesting, I
created some new and exciting places for the player to go, but only if they have
enough health.
In an earlier version, you would sometimes draw cards.
These were interesting, so I paired them with those boring health locations.
In the old Fighting Fantasy "Sorcery" game books, you could be a wizard, and cast all kinds of cool spells, or you could be a warrior, who had... two extra Skill points.
In simpler, more fun-based games, imbalance can add excitement. It might not seem like a good idea for some things to be clearly better than others, but when you get them, it's exciting.
In Scrabble, some tiles are blatantly better than others. The blanks are the best tiles by a huge margin. That's imbalanced and a bit unfair, but there's excitement to be had every time you reach into the bag and draw your tiles.