A target board consists of four parts, and each part has different numbers on it. You will make at most $10$ shots, and every shot's point will be added to your score. If you get a score of $20$ points at any point while you are shooting, you win the game.
The most interesting part of this game is that you decide what numbers are on each part of the target board, and you know that your probabilities of hitting each of these parts and missing the board are equal.
What numbers you should put on each part of the board to maximize your chance to win?
What is your chance to win the game?