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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I would think high cards would tend towards having sequential descending cards following them in the deck over time, assuming that the winner adds the hand back to their deck with the winning card in a position to be played first.
This is because higher cards are less likely to change hands, and can only be captured by high cards themselves.
So say you play a Queen and are lucky enough to capture a Jack. On future rounds, that Queen might capture a 4 and a 6, but when that 4 and 6 trot out into the field of battle they’re more likely to leave your deck than the Jack. So the Jack would tend to move closer to the Queen over time.
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