I am obsessed with math. Not in the way that you think, however... It's more about discovering patterns and exploiting weakness.
It started with Sim City - well, perhaps Sim City 2000, or all of the early Maxis Sim-games. These games were all representations of systems, whether it was a city, or the world, or animals, or ants, or farms. Each system had variables and, since the games were at the infancy of PC gaming, the variables were fairly easy to take advantage of.
The games need the player to succeed. If the player fails miserably too quickly, then the player will quit in a fit of anger (see my little brothers). So the player succeeds early and often. As the simulation continues, the player's success is normally guarded by the idea of scale - the larger the farm, etc, becomes, the more that is at stake - the more challenging the system becomes. As noted, however, these early games were very easy to exploit. Strawberries sold well at market and had a relatively quick turnover rate - therefore you could easily create a farm that was profitable and scaled well. Cities needed a certain amount of diversity when it came to zoning - once the player figured out the optimum layout, the city will thrive.
The first step in those games was discovering the successful variables - the second step was to exploit them. Leaving Sim City 2000 on overnight would yield immense amounts of cash for a player. There was no penalty for such an action and, as long as the city was getting a profit, the coffers would be overflowing come sunrise. This, of course, only works if you turn off "disasters," which is the only random variable that really could mess up an everlasting game. The other Sim titles offered the same comfort, and math games were fun, but totally beatable.
Does this break the game? No. Once a player cracks the math, the real fun begins! That's when success changes from "make or break" to total perfection. How can I create the largest city? What is the most money I can raise? How fast can I conquer the world?
Tower defense games, such as Field Runners, are a perfect example of this. The player learns a formula and optimizes, experiments, and optimizes again. Eventually, the player can stay around forever, creating absolute chaos for the system - that is, of course, until the numbers take over. At some point, the computer will dominate, whether it's through time or firepower, but only because the computer has access to the math (and computers will always win when math is involved).
Simulations, in general, have gotten way too complex to be called formulaic. The new Sim City looks amazing, and I'm positive that it will be very difficult for players to simply "figure it out." Mobile games, however, have the same issues that the early PC games did - mainly that with limited resources, creating vastly complex systems is challenging, if not impossible. That's why tower defense games are mainly predictable (and that's why they're fun!) and why I happen to love the Kairosoft games.
Kairosoft is a developer that makes mobile games for Android and iOS that has been working in the mobile space for almost two decades. They have a line of games that are essentially math problems, all with a different theme and different set of spectacle for the player to work out. Game Dev Story was one of my favorites, although the game was quite easy. The formula for success was apparent after the second play-through and by the third time I played, I was able to unlock everything and have the ultimate gaming company.
The trick with all Kairosoft games is to find a way to balance the two (or more) economies that are present in the game. One economy is almost always based on money, or buying power. These allow the player to gain more abilities throughout the game. Also, this particular economy normally marks failure - you go bankrupt for a certain amount of time, you're dead. The second economy is the economy of skill. In this simulation, there are several computer characters that the player controls with a set of attributes. The greater the set of attributes, the better that character will be at performing a task. The last common characteristic is time, which is the most crucial piece of all Kairosoft games. Good timing and attention are how a player can go from simply winning to dominating.
These factors all line up differently in different games. In Game Dev Story, the player is managing a software company, hiring different members of the staff and creating new titles. It takes time to create the titles and sell them, and of course it costs money to hire a staff, buy licensing, and upgrade the office. The more skilled the employees, the better the end product, and the more money that piece of software earns.
In Grand Prix Story, the player is managing a team of technicians and race car drivers. The technicians install new parts and help create new cars, and everything costs money. Doing well at a race earns cash and sometimes a bonus "aura" which helps the computer character perform better.
Pocket League Story is about a soccer team, Mega Mall Story is about building a mall. Epic Astro Story is about exploring a new planet and building a civilization. Dungeon Village is about caring for and growing a village just outside of an RPG village. Pocket Academy is about managing a school. Cafe Nipponica is about creating a series of successful restaurants. Each has these various number elements in play, all demanding special attention to figure out how to best earn the most money and skill points in the least amount of time.
Pocket Academy and Cafe Nipponica have been the most difficult games from the Kairosoft library (at least, from what I've played). I lost interest in Hot Springs Story very quickly and I think there are two or three others that I have yet to purchase. The difference between the two that I had trouble with and the rest is that they demand more patience and more attention to detail. Players have to react more closely to the needs of the community and memorize the effects of different dishes or add-ons, neither of which terribly interested me.
Many games are math games - from Oregon Trail to Civilization. And there's nothing wrong with that - recognizing patterns and exploiting them for success is a very satisfying game element. Perhaps we should design an iD Tech math game...?