Like many human endeavors game design is part art and part science, this implies that is actually quite difficult to completely predict if a game will be fun a priori and usually requires a quite a bit of trial and error. However the last decades have taught us a lot regarding Game Design as a science and also an interest from mathematicians have helped in defining some way to better understand how to make a game that is balanced and challenging without being frustrating.
Rock-paper-scissors, RPS for short, is a perfectly balanced game, for example (let’s forget for a bit the psychological factors). The concept of balance is a cornerstone of tactical gaming and applies strongly to the concept of spells in Wizards’ Duel. RPS can also be extended indefinitely while keeping it balanced by adding two “weapons” that wins against exactly half of the other ones (see figure): mathematics aids us in creating a perfectly balanced system of powers.
I would argue, however, that a completely balanced game is not actually challenging or fun. If we do not consider other factors, a perfectly balanced game is just about probability, there is no choice nor sense of agency. In particular the game needs to give the player choices by promoting uncertainty, the player must be offered a meaningful choice at every possibility! How can we have a balanced game but giving choice to the player? You can use symmetry and variations on the same premises, like in Chess.
In Chess the possible moves of the two player are symmetrical and every turn you can do just on thing: move a piece. Having just that many pieces and configurations on the board alone almost guarantees that a game will offer meaningful choices (as in Checkers). Why “almost”? Well, Checkers is a “solved game“, that is, it is possible to mathematically play a perfect game and predict the moves of a perfect player, thus ending every game in a draw.
In Chess having different pieces moving in different ways creates an unsolvable game, meaning that every turn will be meaningful and every move will represent a choice (actually it is demonstrable that chess can be solved, but as of today it seems impossible to calculate all the possible game choices within a finite time frame). This can be applied to our design pretty well, and in roguelikes in general. The combination of different enemies and generated maps creates uncertainty and thus force the player to make choices.
I have talked about balance, which is somewhat easy to design but boring, then moved to uncertainty, again nothing impossible to achieve. Can we then “mathematically” create a perfect game that always offer challenging choices to the player? Not really because videogames in general are complex. Games have more than one mechanics and these are usually asymmetric. I think that non trivial videogames, especially “simulationist” ones like roguelikes and tactical RPGs, can be modeled as chaotic systems. Each mechanic that we include adds a level of complexity that leads very soon to unpredictable behaviors because it impacts every other rule like in a feedback loop.
Finally we arrive to the “art” part of Game Design. Our approach to game design is to collect ideas and try to balance each of them in such a way that they can always present a choice and, within reason, try to imagine if the choice are still meaningful when confronted with the mechanics that were already included. Finally, we test internally the changes to understand if there are occasions where the element of choice is lost (for example presenting a strategy that is always preferable to the other ones). If the specific mechanic, be it a new gimmick, or a new terrain, or an enemy type, does not offer a choice or, worse, removes a choice then it is scraped.
Until, of course, the rule of cool dictates otherwise… but I will leave this discussion for another time.
Thanks for reading.