After a seemingly un-ending game of the card game War with my daughter, we asked the important questions:
- Can a game of War theoretically go on forever?
- How long is the average game of War?
Some smart folks already answered that - it is finite. But I like to code so I thought I'd try to get some stats about an average game of War with a simple Python simulator.
The rules of the game are simple enough it can be fully automated.
After running about a million rounds of War in the simulator the stats were pretty well converged to the values in the table below. The shortest and longest games there are not theoretical values - just observations from the samples I did run.
It is theoretically possible to win in 2 rounds if there is an epic series of ties, and it is possible for a game to go on for much longer than 5000 rounds if you are very unlucky.
| Stat | Value |
|---|---|
| Average length | 440-445 rounds |
| Median length | 330-335 rounds |
| Longest game | ~5000 rounds |
| Shortest game | 18 rounds |
| 95% game length | 1160 rounds |
| 99% game length | 1750 rounds |
| 99.9% game length | 2600 rounds |