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Only tame games can be played using the same strategy as misère nim. Nim is a special case of a poset game where the poset consists of disjoint chains (the heaps). The evolution graph of the game of nim with three heaps is the same as three branches of the evolution graph of the Ulam–Warburton automaton. [9]
Nim has a well-known optimal strategy in which the goal at each move is to reach a set of piles whose nim-sum is zero, and this strategy is central to the Sprague–Grundy theorem of optimal play in impartial games. However, when playing only with a single pile of tokens, optimal play is trivial (simply remove all the tokens in a single move).
Fibonacci nim is played with a pile of coins. The number of coins in this pile, 21, is a Fibonacci number, so a game starting with this pile and played optimally will be won by the second player. Fibonacci nim is a mathematical subtraction game, a variant of the game of nim. Players alternate removing coins from a pile, on each move taking at ...
The Grundy value or nim-value of any impartial game is the unique nimber that the game is equivalent to. In the case of a game whose positions are indexed by the natural numbers (like nim itself, which is indexed by its heap sizes), the sequence of nimbers for successive positions of the game is called the nim-sequence of the game.
With perfect play, if neither side can force a win, the game is a draw. Some games with relatively small game trees have been proven to be first or second-player wins. For example, the game of nim with the classic 3–4–5 starting position is a first-player-win game. However, Nim with the 1-3-5-7 starting position is a second-player-win.
In turn, risk-adjusted NIM compressed by 60 basis points in the quarter driven by the 70-basis-point decline in NIM explained by Lago earlier, partially offset by a 10-basis-point improvement in ...
Dr. Nim was based on a mathematical game called NIM, which similarly consisted of twelve marbles. A simple strategy will always win as long as the opponent goes first. This is the strategy for single-pile NIM: If the opponent takes 3 marbles, the first player should take 1. If the opponent takes 2 marbles, the first player should take 2.
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