Let's suppose we have a button that indicates a random number from 1 to 30 (including 1 and 30). There are 30 people who play the game, only one person wins.
Game rules A: Each person is enumerated from 1 to 30, the button is pressed once. The one whose number is rolled wins the game.
Game rules B: Each person pushes the button. The one who gets the highest number wins. If two or more people get the same largest number, they play among themselves and press the button again until one of them gets the highest number.
It is clear for me that for game rules A probability to win is 1/30 or 3%. What is probability to win the game using game rules B, is it 1/30 as well?