Photo by Jack Hamilton on Unsplash.

A war in a three or four player game: If there is a 3 or 4 person tie for highest card, each player places a single card face-down followed by a single card face-up. The player who has the highest card wins. Full Playlist: more How to Play Card Games videos: http://www.howcast.com/vid.

During Thanksgiving Break I played the card game War with my girlfriend and remembered how wonderfully mindless it is. Because there's no strategy or decision-making, it was feasible to write a program to play the game. Once I could simulate one game, I could simulate several and collect some statistics.

Evidently the rules of War have some gaps, including what to do with the cards you win. Do you place them on the bottom of your deck, in order, or do you shuffle and reuse them once your deck is empty? Why not program both methods and compare? Here is a plot of both approaches after 100,000 trials of each. The x-axis is the number of turns required to complete the game, and the y-axis is the frequency of that outcome across 100,000 trials.

Card Game War Rules

The data proved more interesting than I expected.

• Shuffling the winnings led to much faster games — a mean of 262, a mode of 84, and a max of 2,702 turns.
• When the winnings aren't shuffled, the numbers are less clear. Many games were seemingly infinite so I added a cap of 5,000 turns per game. 11,837 (11.8%) of the games hit this limit (and do not appear on the graph). But plenty of games ended after 4,000+ turns, so we could expect many of these long games to be finite as well. If we ignore the capped games, the mode is 104 turns.
• Both plots show a binary distribution of the results, as you can see in the higher and lower groupings of dots. It turns out that games are more likely to finish after an even number of turns. Each player starts with 26 cards, so if there are no wars and one player wins every hand, the game will last 26 turns. For every turn that player loses, they must win an additional hand to cancel the loss, so the game still requires an even number of turns. Only a war will break this trend because 4 cards change possession instead of 1. A game with an odd number of wars will take an odd number of turns to complete (ignoring wars with fewer than 3 cards, when one player's deck is low).

As for the program, here it is in JavaScript. The highlighted lines show the changes made between the Shuffle and No-Shuffle versions.

To close, enjoy the amazing uniqueness of a well-shuffled deck.

War is a card game that due to its simplicity it is a most often played by children. It is played with two players. Variations using three or four players are not uncommon. The game can be played using a standard deck of cards.

Card Game War Ace

The Object
Be the player to capture all the cards.

Setting Up the Game
Shuffle the cards.
Deal the cards between the players.
Players place their cards in a stack face down.

Playing the Game
Players turn over the top card of their deck and present it for 'battle'.
Cards rank from 2 (lowest) to Ace (highest).
Whoever turned over the higher valued card 'captures' the opponents card and adds both cards face down to the bottom of their deck.
Both players turn over the next card and play continues.
If both players present cards of equal value they both lay down four cards. The first three cards are placed face down while the fourth is placed face up. The player whose fourth card is the highest captures all ten cards. If the fourth cards are equal the process is repeated until someone wins.

Card Game War With 3 Players

Winning the Game
The player that captures all the cards is the winner.

Card Game War Play

Variation
To shorten the length of play some people choose to end the game after three battles are won. This may be the option to use when playing with young players.

Card Game War With 4 People