如果玩家最多可以获得4个硬币,那么赢得比赛的策略

两个玩家正在玩游戏,其中每个玩家必须在每个回合中选择1,2,3或4个硬币.总共有n个硬币.拿起最后一枚硬币的玩家,他赢了.设计一个赢得比赛的策略.

什么是解决问题的算法策略,以便我可以赢得比赛,假设我是其中一个球员？

为前10场比赛制作一张桌子; 会有一个明确的模式.如果有...

1 coin: take 1, you win
2 coins: take 2, you win
3 coins: take 3, you win
4 coins: take 4, you win
5 coins: you lose (whatever you choose, the opponent wins by rule 1-4)
6 coins: take 1, opponent loses by rule 5
7 coins: take 2, opponent loses by rule 5
...
10 coins: you lose (whatever you choose, the opponent wins by rule 6-9)
11 coins: take 1, opponent loses by rule 10
...

所以,你总是拿n % 5硬币,除非它是0(如果是的话0,你输掉了对手的完美游戏,无论你做什么,所以拿1来最大化他犯错误的机会).