You are playing the following game. You can ask the host of the game to tell you a number. Each number is an independent random uniformly distributed real number between 0 and 1. After the host tells you the number you can ask for more or just stop. When you stop, your score is equal to the sum of all numbers which the host has given to you. Let $0 < x < 1$ and suppose that you're trying to get a score in the interval from x to 1. What is the probability of winning, assuming that you are using the best possible strategy? Find the value of probability of winning for $x=0.334568$
Edit: so i ask my friend the complete problem. And re edit this to be more clear
First i use monte carlo method, but i have hard time to solve this riddle. Thank you.