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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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
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 🙂
> 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.
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.
I believe there was a Vsauce where Michael discusses the process of shuffling a deck of cards. Effectively, anytime it is shuffled, it is a completely new, never before ordered deck. This is because if a deck was shuffled once a second, 52! is more seconds than the universe has existed.
If my logic is correct then a shuffled deck WILL result in a new order but an unshuffled deck will not (assuming you’re playing standard war with 2 players and must play top card).
Because if so assume the deck is arranged A-K spade-club-heart-diamond: player 1 gets A-K in spades and hearts player 2 gets A-K in order in clubs and diamonds. And they deadlock every turn
How many ways can a deck of cards be arranged so they don’t repeat? There is nothing random about it.
The relevant property you have to look for here is the game being a _bijection_: does every potential ordering of the cards actually result from _some_ game of War, and do two different starting setups result in the exact same order?
If the answer is yes, and the initial shuffling is truly random, with all draws having equal chance, then the same will again hold for the state after a game of War. Otherwise, the chances are uneven for sure; for example, that one (or more) impossible ordering can never come to be.
By things being fine, one can also note that the two halves of the above each imply the other: if every ordering happens at least once, then each comes from exactly one initial arrangement; and if no arrangement happens twice, then none are missing.
**So the question left to check is if absolutely every potential ordering can result as the end state of a game of War.** I would doubt it, and it definitely depends on how you play; in particular, if the winning card ends up on top, or the same player’s card always will be on top, those forbid some arrangements already. If the winner of the previous “fight” has their card out first and thus on bottom, things get a bit more complicated and it is too early here to think this through, but I doubt it works either.
If the winner of the previous “fight” has their card out first and thus on bottom, things get a bit more complicated and it is too early here to think this through, but I doubt it works either.
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