The best way to get better at being a systems designer is to design game systems for games. This doesn't have to be designing systems for video games - a lot of system designers I know are extremely proficient card, board, and tabletop game designers too. Remember, the purpose of system design is to create an elegant set of game rules that convey a game experience to the player. The rules of play will direct how the player feels, so we must take care in crafting them.
For beginners, try building a variant mode on a board, card, or tabletop game you already have. Maybe take your old Monopoly board and try some rules variants. What happens if you increase or decrease the number of houses you can build? How does the game experience change if you halve the price of every property? What happens if each player starts the game with a monopoly? How does it feel if you add new kinds of cards to the Community Chest and Chance decks? Then playtest your changes and see how things feel. Try to figure out how and why the changes you made affect the feelings the players feel.
Once you start getting a feel for how rule changes affect an existing game, take the next step - try building your own board or card game. Choose a theme or experience you want players to have, and then build a game to get them to feel it. Maybe you want to emulate the experience of surviving alone in a wilderness, climbing a mountain, opening a treasure chest, shooting at a bullseye, or getting your senpai to notice you. Whatever it is, try creating a set of rules to try to emulate that experience. Then gather some friends, playtest the game, and see if it feels good. Why or why not? How do you improve it?
By doing this over and over with different games, you will level up your system design skills. I know several designers who have crossed over between tabletop/board/card game and video game system design positions because design skill translates from platform to platform.
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