Fibonacci Nim/Examples
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.