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Roger W. Johnson South Dakota School of Mines & Technology.

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Presentation on theme: "Roger W. Johnson South Dakota School of Mines & Technology."— Presentation transcript:

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2 Roger W. Johnson South Dakota School of Mines & Technology

3 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) 2

4 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. 3

5 Pathological Cases: Running out of cards during a War Draws Infinite length games Simulation: Running out of cards during a War considered a loss Cards won placed in random order at bottom of deck 4

6 Card ranks: 2,3,..., 10, J, Q, K, A assigned ranks 2,3,..., 10, 11, 12, 13, 14 One measure: Average Initial Rank Notes: Average rank over entire deck = 8 Players initial average rank between about 4.8 &

7 where is the rank of the ith card in As deck, is the rank of the jth card in Bs deck and 6

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10 Winning Proportion for Player A 9

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