The following n-person optimal stopping game is considered. Each of n players gets a random number from [0; b], b > 1 as a score. A player has to decide whether to stop after the first draw or to continue to a second draw, in which case the value of a second random variable is added to their score. Players do not know the scores or the decisions of other players. The player with the largest total score not exceeding 1 wins. In the case the total scores of each player exceeds 1, the player with the lowest score closest to 1 wins. The objective of each player is to maximize the probability of one's win. Optimal strategies of the players are presented. The disorder version of the game is also investigated.