A War Amongst Siblings… Part II

If we alter gameplay such that Player B’s card is returned in front of Player A’s in the first turn, the stable state pattern is broken and the game resolves immediately.The effect on full games is equally dramatic..Randomizing the order with which cards are returned the winner’s hand reduces the portion of unfinished games from 1/3 to a flat 0..Games finish much more quickly as well..75% of games with this random element finished within 500 turns compared to 14% of games without..Randomness makes the stable state untenable and never-ending games practically non-existent.This is great news for my side of the argument!.We no longer have evidence that the game of War (if it is simulated realistically) can go on forever.I’d love to call it a day and claim victory..But, against my own best interests, I’m going to try to be a good scientist (and a good brother)..As they say, absence of evidence is not evidence of absence..We need to take it a step further if we want to prove that a game cannot go on indefinitely.One Out of InfinityLet’s put on our scientist hats and start with a thought experiment.Take our four-card example..The first turn has only one possible winner, Player A, because ten is larger than two..However, it has two possible outcomes in terms of how the cards are returned to Player A’s hand..Let’s say that there is a 50% chance that Player A’s card gets returned to Player A’s hand first and a 50% chance Player B’s.. More details

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