Game-Theory

Problem You are playing the following Nim Game with your friend: Initially, there is a heap of stones on the table. You and your friend will alternate taking turns, and you go first. On each turn, the person whose turn it is will remove 1 to 3 stones from the heap. The one who removes the last stone is the winner. Given n, the number of stones in the heap, return true if you can win the game assuming both you and your friend play optimally, otherwise return false. ...

Problem Alice and Bob continue their games with piles of stones. There are a number of piles arranged in a row, and each pile has a positive integer number of stones piles[i]. The objective of the game is to end with the most stones. Alice and Bob take turns, with Alice starting first. Initially, M = 1. On each player’s turn, that player can take all the stones in the first X remaining piles, where 1 <= X <= 2M. Then, we set M = max(M, X). ...