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During the game of war, if you could order the cards in your deck of 26, what strategy should you employ?

  1. Assume Player 2 has a random ordering of 26 cards and is not allowed to change the order in anyway.
  2. Let Player 1 have the advantage of looking at one's own deck of cards and reordering the cards.

Several theories may apply: game theory, combinatorics, simulation, etc. What are some of the ideas that would help one dissect this problem into something useful and begin to solve it? By solve, I mean describe the strategy Player 1 should employ and why he should employ it.

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closed as unclear what you're asking by Pedro Lauridsen Ribeiro, R W, paul garrett, Alexey Ustinov, Stefan Kohl Jan 16 '18 at 10:30

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ A plausibly interesting-enough question, but would be more appropriate for MathStackExchange. $\endgroup$ – paul garrett Jan 15 '18 at 22:02
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    $\begingroup$ mathoverflow.net/questions/11503/… may be relevant, as in the answers therein include an ordering of an infinitely long game. $\endgroup$ – Mark S Jan 15 '18 at 22:15
  • $\begingroup$ I had seen that question, @MarkS. It discusses the outcome under the basic rules, not a variant in which a player orders his deck. $\endgroup$ – Mark Jones Jr. Jan 15 '18 at 22:36
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    $\begingroup$ Upon reflection, if this question is construed as addressing the larger game-theoretic issue, then (so far as I know) it is worth keeping on this site. (I did not vote to close, in any case.) $\endgroup$ – paul garrett Jan 15 '18 at 23:22
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    $\begingroup$ @MarkJonesJr. any chance you can formalize the question better? $\endgroup$ – Robert Jan 15 '18 at 23:56

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