War — the Card Game, Simulated
Play War and see the simulation behind it: one house rule for returning won cards makes a tenth of all deals run forever.
A game with no choices in it can still fail to end
War has no decisions. Turn a card, higher one wins, ties start a war. There is nothing to think about — which makes it the purest possible test of a rule set, because the rules are the game. And one rule nobody bothers to state decides whether the game finishes at all: what order the won cards go back into your pile.
| Rule for the won pile | Games that ended | Games that cycled forever |
|---|---|---|
| Shuffle it — the usual house rule | 20,000 of 20,000 | 0 |
| Fixed order — fully deterministic | 17,957 of 20,000 | 2,043 (10.2%) |
| Winner’s cards first — also deterministic | 20,000 of 20,000 | 0 |
Not “ran long” — cycled. Under a deterministic rule the entire game state is the two piles in order, so an exact repeat of that state means the game must now repeat for ever. The simulation detects the repeat rather than giving up after a limit, and one flagged deal was replayed to 400,000 tricks without ending.
Two deterministic rules, differing only in the order two cards go back, and one deadlocks a tenth of the time while the other never did once in 20,000 deals. If a game of War at your table never seems to finish, it is not bad luck.
How long is it? Longer than you think, and skewed
Over 20,000 shuffled games the mean is 272 tricks but the median is only 206. The mean is dragged up by a long tail: one game in ten passes 560, and the worst ran 2,582. Quoting the average badly overstates a typical game.
| Cards buried per war | Mean game length |
|---|---|
| none | 587 tricks |
| 1 | 457 tricks |
| 2 | 355 tricks |
| 3 — the common rule | 268 tricks |
Burying more cards is the strongest lever there is, because each war then moves a bigger block of cards at once. Playing wars with no buried cards more than doubles the length of the game — which is the opposite of what most people assume when they simplify the rules for a child.
And the deal really does decide it
Since there are no decisions anywhere in War, nothing but the deal can predict the winner. It predicts it strongly. Win rate by how many aces you were dealt:
| Aces dealt | Win rate | |
|---|---|---|
| 0 | 21.2% | |
| 1 | 35.6% | |
| 2 | 49.1% | |
| 3 | 64.6% | |
| 4 | 77.2% |
Four aces makes you nearly a four-to-one favourite before a card is turned, and no aces leaves you a four-to-one underdog — a 56-point spread in a game where neither player ever makes a choice. Overall the first player won 49.5%, so there is no seat advantage; it is all in the cards. Which is worth telling a child who is losing badly: it was over at the deal.
How to use
- Turn a card, or play the whole game out at once.
- Change how won cards go back into the pile and watch the game length move.
- Try the fixed-order rule — some deals will never finish.
- Change how many cards are buried in a war, the strongest lever on length.
Frequently asked questions
How long does a game of War take?
Over 20,000 simulated games the mean is 272 tricks and the median only 206. The mean is dragged up by a long tail — one game in ten passes 560 tricks, and the longest ran 2,582. Quoting the average badly overstates a typical game.
Can a game of War go on forever?
Yes, and it is not rare. If won cards go back in a fixed order the whole game is deterministic, so an exact repeat of the two piles means it must repeat for ever. That happened in 10.2% of 20,000 deals, proven by the repeated state rather than by giving up after a limit.
How do you stop War from never ending?
Shuffle the pot before putting it at the bottom of your pile. Every one of 20,000 shuffled games ended. Curiously, one other deterministic rule — the winner’s own cards first, then the loser’s — also never cycled once, so the order matters as much as the randomness.
How can you make War shorter?
Bury more cards in each war. Going from none to three face-down cards more than halves the game, because each war then moves a bigger block at once. Simplifying the rules by burying nothing, which people often do for young children, makes the game far longer.
Is War decided by the deal?
Entirely — there are no decisions in it. Win rate by aces dealt runs 21.2% with none, up through 49.1% with two, to 77.2% with all four. That is a 56-point spread in a game where neither player ever makes a choice.
Does the first player have an advantage in War?
No. Across 20,000 games the first player won 49.5%, which is a fair split. There is no seat advantage because there are no decisions to take advantage of.
What happens if both players run out at the same time?
If the flip resolved, whoever won it takes the pot and wins, even though the flip emptied both hands. If the cards tied and neither player has anything left to fight the war with, it is a genuine draw.
Does this send anything anywhere?
No. Both the game and the simulations run in your browser.
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