I think Im doing the same puzzle as you. I thought the answer would be Old Maid, but that's not it. Old Maid is one game where the last player loses.
It's NIM
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The reason you cannot conquer someone's last city is because it would essentially eliminate that player from the game.
The game ends when all tiles have been drawn and one player uses all of his or her last tiles or when all possible plays have been made. The player with the highest final score wins the game.
In a game of poker, the order of play starts with the player to the left of the dealer posting the small blind, followed by the player to their left posting the big blind. The dealer is the last to act before the flop.
The game ends when all letters have been drawn and one player uses his or her last letter; or when all possible plays have been made. When the game ends, each player's score is reduced by the sum of his or her unplayed letters. In addition, if a player has used all of his or her letters, the sum of the other players' unplayed letters is added to that player's score. The player with the highest score wins the game. In case of a tie, the player with the highest score before adding or deducting unplayed letters wins.