So I'm confused. In my college classes, sometimes we'd get problems involving "construct a markov chain to model this process". Doing the naive, obvious soluti

So I'm confused. In my college classes, sometimes we'd get problems involving "construct a markov chain to model this process". Doing the naive, obvious solution wouldn't make the probabilities work because we'd "forget" crucial information, so we'd just add on extra bits to the state (e.g. "flag1 flag2 flag3 ...") that would make the number of nodes exponentially larger. But the infinite information part of markov chains is really helpful sometimes too, e.g. the position of your random walk wouldn't be encoded in your "state" (which could be infinite), it'd just be returned as a value (if you were trying to compute the distance from the origin or something). Are you guys just arguing over "at what point does this shoving a billion bits into my state make it not really a 'markov' chain like you'd traditionally think about it"? Basically the formal definition vs what we intuitively think about as the 'point' of markov processes and why the markov observation is important?