If you want to get really serious about the nuts and bolts of game design, a knowledge of game theory will help, whether you want to develop shoot-em-up, stealth, or table top strategy games. The book embedded below is the English translation of a textbook published in 1980 in the Soviet Union. It's a deep dive into the math of competition. The intro states:
The book is intended to disseminate the ideas of game theory which have practical economic or military applications.
Needless to say it's math-heavy, but is packed with information for anyone who wants to tackle game theory in depth.