GAME THEORY
BASH GAME
Definition
- Two numbers: \(N, K \ (1 \leq K \leq N)\)
- A pile of \(N\) stones
- \(2\) players (Player A and Player B)
- Rules:
- Two players take turns taking away stones, Player A starts first.
- \(1 \leq x \leq K\) stones can be taken each time.
- If no stone remains, the game ends.
- The last player who took stones wins.
With the value of \(N\) and \(K\) given, who will win?
Example
If \(N = 4, K = 2\):
Red numbers represent the number of stones Player A chose each turn.
Blue numbers represent the number of stones Player B chose each turn.
\[\begin{aligned}
&\quad \text{Steps} \quad \text{Winner}\ &①\ \color{#EA6C6D}{1} \ \color{#3199E1}{1} \ \color{#EA6C6D}{2} \qquad \ \ \color{default}{A}\ &②\ \color{#EA6C6D}{1} \ \color{#3199E1}{2} \ \color{#EA6C6D}{1} \qquad \ \ \color{default}{A}\ &③\ \color{#EA6C6D}{2} \ \color{#3199E1}{2} \quad\ \qquad \color{default}{B}
\end{aligned}
\]
As we can see, if and if only Player A chose \(1\) stone the first step, Player A wins.
GAME THEORY
原文：https://www.cnblogs.com/zhangtianli/p/14691158.html
