Presentation on theme: "Victory in the Card Game ‘War’ and Initial Hand Strength"— Presentation transcript:
1Victory in the Card Game ‘War’ and Initial Hand Strength Roger W. JohnsonSouth Dakota School ofMines & Technology
2Rules of ‘War’ Deck, face down, divided evenly among the two players In unison, each player reveals top card of their stack – this is a "battle" – player with higher card takes both cards (placed at bottom of their stack)
3Rules of ‘War’If equal battle cards, then “War". A face-down card followed by new battle card.If battle cards equal again then repeat until one player's battle card is higher.Game ends when one player, the winner, has all of the cards.
4Rules of ‘War’ Pathological Cases: Running out of cards during a War DrawsInfinite length gamesSimulation:Running out of cards during a War considered a lossCards won placed in random order at bottom of deck
5An Initial Measure Average Initial Rank Notes: Card ranks: 2,3,. . ., 10, J, Q, K, A assigned ranks 2,3,. . ., 10, 11, 12, 13, 14One measure:Average Initial RankNotes:Average rank over entire deck = 8Player’s initial average rank between about4.8 & 11.24.77 ~ 124/26 <= rank <= 292/26 ~ 11.23
6A Second Measurewhere is the rank of the ith card in A’s deck, is the rank of the jth card in B’s deck and