Learning how to abuse game mechanics was an essential part of my getting a good grasp on mathematics. Developers can't be bothered to model things like economies accurately. As a consequence, they are rife for abuse. If you understand math, you can see this, and abuse for fun and profit.
Take for instance, Fable II and Fable III.
Those games really strongly introduce a "Real-estate" mechanic. it's wholly optional. You can choose not to, but you would be stupid not to abuse the shit out of it. The problem is that this mechanic does not self limit like genuine real-estate does. Once you own 100% of the properties, prices dont suddenly shift-- or other forces related to supply vs demand. Instead, it is a guaranteed income generator. You can LITERALLY make 10 million gold every 10 minutes, doing NOTHING, if you aggressively go for the real-estate mechanic.
Another is Elderscrolls III: Morrowind. The game bases certain actions/outcomes on certain base values using a bland formula. This gives rise to things like the "Super potion" exploit. Basically, the game bases the strength/duration of a potion on your intelligence value, and your alchemy skill level, with no cap. So, if you brew a fortify intelligence potion, it makes your INT score go up-- now your potions will be slightly stronger. Buy up ingredients, make a potion, quaff a potion, rinse, repeat. After a few minutes of doing this, your fortify INT potions will be upping your int score by millions of points, the potions will last for literal days worth of time, and be worth millions of GC. Once you have done this, you can fortify other base stats while grooving on super potion, making any and all challenge to the game evaporate. (Try dying when your health regenerates at +10000000hp/sec, for instance.)
Understanding math is a very powerful tool for smashing video games. Seeing the opportunities gives you more deep insight into the math behind the game, and in particular, the failings behind those mechanics.