You're right. There are also game rules that can act as multipliers (e.g. who has the blind affects the game state in poker - so that means that there are actua

You're right. There are also game rules that can act as multipliers (e.g. who has the blind affects the game state in poker - so that means that there are actually multiple "games" for each given shuffle). Something you may find interesting is formal methods - what we're talking about here are "equivalence classes". In formal methods you want to analyze the totality of a system and understand every outcome based on every possible state within the rules of the system. Clearly this is a combinatoric nightmare in anything interesting (even a simple system like a card game and 52 cards, as we can see). Equivalence classes are a way of knowing distinct, but not actually different, states, and grouping them together so that they can all be considered just once.