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.
[egin{aligned}
&quad ext{Steps} quad ext{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.