Mathematics Background

I find that I use averages and simple probabilities more than anything when I design games.

For example, I use averages to help me determine how many turns a typical game will have before the game ends or how much damage/life something should have over a period of time.

I use probabilites as a secondary support for a concept. For example, I might say, "this is something that should occur frequently in the game" so I will design the game to allow this thing to happen on 80-90% of the turns.

After many rounds of playtesting, I usually apply both of these mathematical concepts to the playtesting logs to see if the game is playing as expected.

I rarely use algebra after the basic game is designed, and during the design stages, I only use it for simple equations.

If you plan on having a card game where players are making choices based on values (like buying cards, using cards for one value over another at certain points, etc) then you'll want to read up on the economics field of "game theory." You can use this to measure the probability of player choice given the weight of their options towards the player's goals.

There are a number of introductory books to game theory. Here's a list of some.

And if you're going to read about what could now be called "classical game theory," you should also read about the "quantum mechanics" of the game theory world, too. Basically, why people don't tend to follow the most "optimal" choice in every situation. Basically, blending the math with psychology. It's cool stuff.

Here's a video from Duke University that defines it, without getting deep at all.

Then you can read some scholarly works