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Trying to construct the full tree for a 9 game token of Nim and am slightly confused. I don't understand how two players, min and max, will make their pick. For example, max picks first and can only pick [9]. Min then picks from [8-1], [7-2], [6-3], and [5-4]. How does min calculate it's utility value here?

max                              [9]
min                 [8-1]   [7-2]   [6-3]   [5-4]
max        [7-1-1] [6-2-1] [5-3-1] [5-2-2] [4-3-2] [3-3-2] 
min    [6-1-1-1] [5-2-1-1] [4-3-1-1] [5-1-2-1] [4-2-2-1] [3-3-2-1] [4-1-2-2] [3-2-2-2] [3-1-3-2][2-2-3-2] [2-1-3-2] 
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    $\begingroup$ I removed the part of your question about checking your working: we don't accept that kind of question because they're not interesting to anybody except the person who did the working, and they don't help anyone understand anything. $\endgroup$ – David Richerby Feb 28 '16 at 22:16
  • $\begingroup$ This is not the most common ruleset for Nim. Please explain the source of this problem. (The game seems like it might be Grundy's Game instead of Nim.) The source of the problem (notes? a textbook?) may include the relevant convention for utility value for a combinatorial game like this. $\endgroup$ – Mark S. Feb 29 '16 at 15:14

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