In a lot of games balance is a big concern. If a game offers a lot of options, it will be at its best when a player has interesting decisions to make between them. Should one option simply be better, every player will select that and large chunks of the game will not have the chance to shine. This is worse if the best option can only be selected by one player, for instance if a particular character is very powerful, so players and designers alike seek balance.
Sometimes a game can be balanced mathematically. It's plain to see that if two characters are identical except that one does extra damage and moves faster, they are not balanced. It can be possible to derive whether attacking more often or attacking for more damage is preferable, but if this has interactions with other game mechanics the calculation can become more complicated. If the designer is using incomparables then a simple determination of balance is not possible.
In this situation the answer is playtesting. I'm becoming swiftly aware that this is my answer to everything. At least I'm not alone in that "By now you know that you need to playtest, playtest, playtest, but it is worth mentioning again because it is that important." - Danny Devine via Cardboard Edison.
Let's talk about another option though, making a game in which components are unbalanced but have the capacity to balance themselves. In these instances one card, character, ability or general mcguffin might be strictly better than another, but the game does something to bring them back into line. There are a few ways to achieve this.
The crudest approach is to rely on players to gang up in order to take down a stronger opponent (Not pictured: 100,000 Persians have teamed up with this feeble elephant in the hopes of crushing a superior Spartan foe). If the unbalanced decision is taken early enough then there's plenty of opportunity for a group of players to negate the early advantage. My playgroup has debated at length whether the various races of Twilight Imperium are balanced but in a lot of ways it doesn't matter if they aren't. Alongside the positions of the starting planets and some other considerations a player's racial powers contribute to how much of a threat they are assessed as being, if a player is assessed as being too great a threat alliances are formed to curb their power (or just outright destroy them). If the game supports it, every overpowered option has the drawback "Will make the other players stomp you." until it is roughly balanced with the other options. This only works if such alliances are practical in the context of the game and where the unbalanced elements are introduced early enough for players to react to them, but it can work.
Another option is to make the act of choosing a game effect. If two players have a pool of options and both select one for themselves and one for their opponents, it is desirable for some of those options to be unbalanced. Each player should end up with one "good" option that they chose for themselves and one "bad" option chosen by their opponent. In this way the lack of balance between options doesn't cause a lack of balance between the players and victory can be determined by who most effectively makes the best of the bad option they've been lumbered with.
This can also be approached by making choice a reward for previous actions. For instance in Blood Bowl Team Manager earning a start player symbol entitles a coach to draw a star player. Earning several allows them to draw several and keep whichever one they like best. In this case the options need to be unbalanced or drawing several and choosing one is not a significant advantage. Personally I dislike this approach as some good luck can make one draw as good as six, but the extent to which luck should influence a game is a discussion for another day. This approach does work to allow the inclusion of unbalanced options while mitigating the extent to which this unbalances play.
The third option I'm going to talk about is having unattractive options explicitly improve until someone shows them some love. This is common in a lot of games, I think I first encountered it in Small World but I was late to the party. Every time an option isn't selected it gains a cumulative bonus. Eventually the option accumulates enough bonuses (whatever these bonuses may be) that it becomes the most powerful option and someone selects it. How well this will work will depend on the disparity between the options and the magnitude of the bonuses, but it's a very tried and tested approach.
None of these options replace the need for playtesting and tweaking, but they can all serve to create a balance between elements that would otherwise struggle to be included in the same game. That's a pretty neat thing, since it allows for the inclusion of a wider range of elements, which in turn can provide players with more interesting options and more tough decisions. Thanks for reading