Algebra is the manipulation of symbols and patterns of them to a set of rules to convey information. You create expression (or do reductions!) of a new pattern of symbols to say what you need to say.
Fundamentally if you are doing arithmetic, you are doing an algebra. You are manipulating symbols, forming and reducing patterns and interpreting those patterns. The number symbols used are irrelevant, you could use Roman, Greek, Chinese etc. number systems and it would still be the same.
If you play cards, it’s an algebra!
Language is an algebra! Letters are its basic symbols, words higher order structures (patterns) as are sentence (even higher!) & paragrpahs (Higher still!) Spelling\grammar are it rules.
If you have to program something - your cell phone, your DVD player, any of your surveying instruments. You’re using symbols to convey information or perform a task.
It’s all an algebra!
This is plainly not true. I know people who play cards as a child plays cards. Just placing a random one in front of themself.
Playing cards well requires both algebra and statistics.