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?
In: 312
I can’t prove this yet without some more thinking, but I think the expected value nature of the game will lead to a derandomizing. By this I mean:
13 values possible (2-10, J, Q, K, A). Imagine dividing the deck in thirds.
2,3,4,5 are very likely to ‘move’ on any given turn.
J, Q, K, A are very unlikely to move, and will act as magnets round after round.
6,7,8,9 are basically wildcards.
To me, I think what I’m getting at is that in each subsequent round a magnet card has a low *or* neutral card next to it. If it wins again, and the neutral card survives, it now has two low/neutrals next to it. Sure, it may lose the low card the next flip, but over the long run the power of the magnets should pretty well disperse them through the deck, surrounded by their neutral but not terrible colleagues, with the low cards that are traded back and forth endlessly sorting to the end.
So decks should show some mild movement from a random arrangement to stacks of thirds (or quartiles, if you want to put them in sets of 3 values each instead of 4 as I did above) roughly ordered high to low. How roughly depends entirely on the original random arrangement.
Edit: this assumes the cards are collected consistently as someone else called out. I tend to collect consistently, others may not.
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