War is actually not a game but an Automata, as players don't have any options.
Wimpy Programmer already made this simulation, he found that when shuffling the winning cards, the mean number of turns is 262, the mode is 84, and the max (on a sample of 100,000 trials) is 2,702 turns. He also found that without shuffles of the winning cards, the game might be ...
The linked Wikipedia article has this to say:
Most descriptions of War are unclear about what happens if a player
runs out of cards during a war. In some variants, that player
immediately loses. In others, the player may play the last card in
their deck as their face-up card for the remainder of the war.
There is a variant of war, called "Strategy War" or "Armed War" (a joke on hands) where, instead of pulling the card from the top of your deck, you chose it from your hand. This works as follows:
You shuffle the deck and deal it out in equal parts. Each player takes the cards dealt to him/her and puts them in his/her hand.
All cards a player plays and all ...
As a math problem, this is a case of a random walk ("walking" N cards at a step from your opponent's deck to your deck, where N is usually one, but can be 4 or 7 or whatever depending on ties.) It is often framed as the "gamblers ruin" problem. Ignoring the issue of ties and treating each throw of cards as an independent trial, the average number of turns is ...
Well, from that same link you shared, on the summary table on the right reads:
Playing time 10–40 min.
Which directly says the average duration of a game.
Now, turns on this game, as per my experience, are quite fast. They can last a few seconds (reveal cards, someone wins, cards are taken, end of turn), or in case of a tie some extra few seconds.
My simplified version of War involves splitting the card deck into equal black and red piles. The two jokers can be added on to each pile as either the strongest or weakest cards as agreed upon by both players. I prefer the latter. Both players can choose any card from their respective piles and present it face down, then simultaneously turn them face up. ...