War is a card game played by two players, each of which has half of a deck of cards. At the same time, the players take the top card from their deck, and place it face up in front of them. The player with the higher card takes both cards and puts them on the bottom of their deck. If the cards are equal, a "war" ensues. Each player places three cards face-down behind their first card, and then plays another card face-up. The player with the highest face-up card takes all the cards. If they are equal again, they repeat the process of a war until someone plays a card higher than the other. Aces are the highest card, followed by Kings, Queens, Jacks, and then $10$ all the way down to $2$. The first person to have all the cards wins.
Now I was wondering whether it would be possible to have an infinite game of War. That is, a game of War in which the players return to the exact position they were in earlier. War has no skill involved, but to make this possible we'd need to add a few ground rules, such as "place the winning card on the bottom of your deck before you place the losing card". Making these rules would make the game completely deterministic; that is, once the cards have been dealt, the outcome of the game is already decided.
So my questions are:
With a standard $52$-card deck, would it be possible to have a game run infinitely?
Does changing the ground rules change the answer to the previous question?
Do the answers to the previous questions change with smaller or larger decks?
Just an answer to one of these questions would be great. I've thought a little bit about this but I don't see any way to find answers.