If you were to play the card game of war with only 4 cards total, and each player received two cards each to begin with, under which circumstances would the game go on forever?
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If you were to play the card game of war with only 4 cards total, and each player received two cards each to begin with, under which circumstances would the game go on forever?
All four cards being the same rank.
Also, if I recall the rules of war, you'd have a problem if you had two pair of different ranked cards and the initial distribution gave one to each rank to each player. The only way to capture the highest ranked cards to be captured is face down in a war when they're not used. A scenario that couldn't occur with 2 cards each, so the war would always guarantee that a war ends in another war between the other cards. I don't know what happens in a game of war when both players have no cards left to play, but if you assume the game doesn't end in a tie the only reasonable solution would be that each player takes their cards back and shuffles. (Anyway the result is no different than all four cards be the same rank in this case).
There is no way to capture the highest ranked card and since capturing the lower ranked card forces your higher ranked card to the bottom of the deck, it guarantees that the next round would leave you pitting your lower ranked card against their higher ranked card just offsetting the whole thing.
Of course I did just wake up, so I could be missing something... and you know I must be drowsy if I'm forgetting a permutation of four items! O_O