Alice and Bo play the following game. They start with four piles of gambling chips, containing respectively c1, c2, c3 and c4 chips. Then, they alternate turns. In each move, a player can take out either i or i-1 chips out of the ith pile (i = 2, 3, 4) or a single chip out of the first pile, but never more chips that in the pile. For example, if the piles contain 1, 1, 3, 3 chips, Alice can make any one of the following moves: The first player that runs out of moves loses, and the other player wins. For example, if Bob finds no chips in piles 1 and 2 and only one chip in piles 3 and 4, he has no move, and lose Describe an efficient algorithm to find out if either player has a winning strategy. Suppose now that after each turn, a single six-face die is tossed. If it comes out to one, a single chip is removed from the fourth pile; otherwise, the board is left as is. Describe an efficient algorithm that maximizes Alice's chance of winning the game