## Tuesday, February 2, 2016

### war variations

Most of you have probably seen how the standard card game "War" can be modified to make an arithmetic drill game. Denise Gaskins probably has the best description here: Game worth 1000 worksheets.

We have used three variations of this game a couple of times: straight War (J3 and J2 playing with greater than, equal to, less than), addition war (grade 1), and multiplication war (grades 2 and 3). Frankly, I am often surprised how enthusiastic the kids are to play, since there aren't any choices for them to make when they play. For those who are ready to move on from the basic game mechanic, here are some extensions and related explorations.

# Extension games

Currently, Vanguard, a deck building game, is very popular amongst the Js. One possiblility for War is to let the players arrange their deck in advance. In a sense, this is like a more granular version of rock-paper-scissors. I particularly like this variation for the 2 (or more) card versions where the kids need to think about how to mix high and low value cards. Also, the number of cards burned on each War battle can upset the organization for the rest of the deck, so that adds a layer of complexity for them to consider.

My favorite variation is to deal a hand (between 3 and 6 cards, replenished after each "trick") to each player and then let them choose which ones to play. You can either require simultaneous play or, as we prefer, have each person play one card at a time going around clockwise, like in Bridge.

# Explorations

Some exploration questions:

1. In basic War (high card wins): will there always be a tie at some point during the first pass through the deck?
2. In basic War: can there be a complete game (one player loses all their cards) without a tie ever occuring?
3. Does basic War always end with one player losing all their cards or can there be cycles?
4. How many times do we expect a tie on the first pass through the deck?
All of these questions can be explored for the different variations. For elementary kids, these are very challenging questions and I don't expect many answers. Two recommended ways to explore:

• Play many games, record data and observations. Make conjectures and see if there are any counterexamples that disprove your ideas.
• Play a simpler version of the game by reducing the number of cards in the deck. For example, play a demonstration game with only 6 cards: A, 2, 3 for two suits.