# Is a deck of cards arranged any less randomly after a game of War? Why?

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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

Entropy would have decreased as instead of the cards being in a less organized state, the cards are now in a pattern with winning and losing cards paired up.

Will this loss of randomness affect a future game, maybe, maybe not.

But it is definitely less random/less entropy.

Fun Fact: Every time you shuffle a deck of 52 cards, its the first time in history those cards have ever been in that order.

The number of potential combinations in a deck of cards, is more then the number of seconds since the universe began

> I can’t quite figure out how the arrangement would become less random, since the winning and losing card stay together.

At the start of the game each player’s cards are arranged randomly, in theory. However after you have cycled once through each player’s cards you can be sure they are arranged in a sequence of “high, low” or “low, high”, assuming of course they always keep the winning card in the same relative position.

Even if the cards are inserted in random order onto the bottom of each player’s deck, it is evident there is some sorting occurring. Someone with more high rank cards is going to be gradually inserting lower cards into their deck, and someone with low cards is going to be gradually losing them bringing the overall rank of their deck up.

Am I remembering War right? You split the deck, then both flip a card, whoever is higher keeps both?

As far as I can tell, it’s an input-less game. You can influence it by how you divide the deck at the start, whose card goes on top of the other in each battle, and maybe by shuffling between rounds, but there’s no way for you to make any decisions in the game or put any deliberate order into the cards.

So you’re essentially just looking at the cards as you shuffle them in a more complicated way. I suppose some genius could remember the order of the cards but that’s not likely 🙂

This would depend entirely on whether or not the played cards were collected in a consistent order (winner on top/loser on top), which has been the case in precisely zero of the games of War I’ve ever played.

The only condition that War guarantees upon a played deck is that each card will be worth either more or less than the card next to it. Which was already the case beforehand. The exception would be in the case of a draw, at which point two equal-value cards would probably be collected adjacently.