I’d typically assume that after most card games, the cards become at least semi-ordered in some way, necessitating shuffling. However, after a standard game of war, I can’t quite figure out how the arrangement would become less random, since the winning and losing card stay together. If they’re indeed mathematically “less random,” after the game, why?
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One point folks are missing is that, although the deck may still be random, and so alright to hand to someone else for their game of war without shuffling, it may still not be random from the perspective of the current players.
Although I don’t remember exactly how war plays out, I assume after a game you could theoretically memorize which cards went back on top or bottom. This could help you figure out who has better odds at winning and so help you place your bets and increase your chance of making money, or bragging rights if no money is at stake. You could even rig the deck by cleaning things up creatively. Even without trying to cheat, you might accidentally recognize a sequence of cards and thus accidentally spoil the game. I think I’ve seen this happen before.
Basically, randomness can be subjective.
A deck can go from random to non-random without ever adjusting the order, if you just decide to scan and memorize it.
A very real change occurs. The top card goes from a 1/52 chance of being an ace of spades to either a 0% or 100% chance, as one example.
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