The Scoring System, Nimbers II

Beginning with two stacks, the properties of Nimbers start appearing.

Two stacks of equal height (with equal Nimber values) turns out to have a total value of 0 (the first person to move loses). If the first person takes an entire stack, the second person take the second stack and the first person is left without a move. On the other hand if the first person takes only part of a stack, the second person takes the same amount from the other stack and leaves the total value 0 as before.
Thus the first property of Nimbers is that two Nimbers of equal value total to 0 (n* + n* = 0). In other words, a Nimber is its own negative.

Two stacks of unequal value mean that the first person wins, of course. The best strategy is for the first person to equalize the stacks leaving a Game with the value of 0 for the second player.

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