#Results
##One million games
###Probability Distribution
Here is the probability distribution calculated by the simulation with 1 million games.
After every turn, the winning cards are shuffled before being added to the bottom of the winners hand. Shuffling the winning cards speeds up the gameplay and keeps the game from devolving into an infinate loop.
Number of games played: 1,000,000
Shuffle the winning cards every turn
Player 1 wins: 499,958
Player 2 wins: 500,042
Number of infinite loops: 0
Max throws in a game: 2,966
Min throws in a game: 4
Avg throws in a game: 270.621807
Total throws in all games: 270,621,807
Max total wars in a game: 189
Min total wars in a game: 0
Avg total wars in a game: 16.925803
Total total wars in all games: 16,925,803
Max single wars in a game: 174
Min single wars in a game: 0
Avg single wars in a game: 15.053125
Total single wars in all games: 15,053,125
Max double wars in a game: 15
Avg double wars in a game: 0.860591
Total double wars in all games: 860,591
Max triple wars in a game: 3
Avg triple wars in a game: 0.047073
Total triple wars in all games: 47,073
Max quad wars in a game: 2
Avg quad wars in a game: 0.00245
Total quad wars in all games: 2,450
Max quintuple wars in a game: 1
Avg quintuple wars in a game: 8.7E-05
Total quintuple wars in all games: 87
Max sextuple wars in a game: 1
Avg sextuple wars in a game: 7E-06
Total sextuple wars in all games: 7
Max septuble wars in a game: 0
Avg septuble wars in a game: 0
Total septuble wars in all games: 0
##One hundred thousand games This time we ran the simulation on 100,000 games, but we didn't shuffle the winning cards after each turn. You can see that the average game takes much longer (about 594 turns), and about a tenth of the games are unending.
Number of games played: 100,000
Perfect play, no shuffling of cards between turns, infinate loops possible!
Player 1 wins: 45,044
Player 2 wins: 45,438
Number of infinate loops: 9,518
Max throws in a game: 6,516
Min throws in a game: 5
Avg throws in a game: 593.731847218231
Total throws in all games: 53,722,045
Max total wars in a game: 204
Min total wars in a game: 0
Avg total wars in a game: 21.9288
Total total wars in all games: 2,192,880
Max single wars in a game: 193
Min single wars in a game: 0
Avg single wars in a game: 20.20837
Total single wars in all games: 2,020,837
Max double wars in a game: 12
Avg double wars in a game: 0.8112
Total double wars in all games: 81,120
Max triple wars in a game: 3
Avg triple wars in a game: 0.0312
Total triple wars in all games: 3,120
Max quad wars in a game: 1
Avg quad wars in a game: 0.00107
Total quad wars in all games: 107
Max quintuple wars in a game: 1
Avg quintuple wars in a game: 3E-05
Total quintuple wars in all games: 3
Max sextuple wars in a game: 0
Avg sextuple wars in a game: 0
Total sextuple wars in all games: 0
Max septuble wars in a game: 0
Avg septuble wars in a game: 0
Total septuble wars in all games: 0