Raj Board Game

Players are given an equal deck of cards from one to fifteen. Each turn, a prize tile is randomly selected from a pool. The prize tile either has positive or negative points, and each player is attempting to gather the most positive points from these prizes. Players secretly select one of their remaining fifteen cards, and reveal them simultaneously. The highest card gets the prize (if positive), or the lowest card get the prize (if negative). However, if two people play the highest (or lowest) card, they cancel each other out and the prize goes to the next in line...