Definition:Fibonacci Nim/Examples

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Examples of Games of Fibonacci Nim

$11$ starting counters

Let a game of Fibonacci nim between player $\text A$ and player $\text B$ have a starting pile of $11$ counters.

$\text A$ removes $3$ counters, leaving $8$.

$\text B$ may remove up to $6$ counters, and takes $1$, leaving $7$.

$\text A$ may remove $1$ or $2$ counters, and takes $2$, leaving $5$.

$\text B$ may remove up to $4$ counters, and takes $1$, leaving $4$.

$\text A$ may remove $1$ or $2$ counters, and takes $1$, leaving $3$.

$\text B$ must remove either $1$ or $2$ counters, leaving $\text A$ in a position to take all the counters next turn.

$\text A$ wins.


$1000$ starting counters

Let a game of Fibonacci nim between player $\text A$ and player $\text B$ have a starting pile of $1000$ counters.

The optimal strategy for player $\text A$ is to take $13$ counters.