A box is filled with 'N' slips of paper. On each slip of paper is written some positive integer (note that any positive integer may appear on the slips - not just the integers from 1 to 'N'). The integers do not necessarily appear in any sequence or pattern. Each of the slips has a different integer on it, so there is just one slip with the greatest integer.
A person who has no prior knowledge of which numbers appear on the slips - but who does know that there are 'N' slips - is to blindly pull slips from the box one by one. The person looks at each slip, then either agrees to accept that number (of Rupees) and quit or decides to go on and choose another slip.
Note that the person looks at each slip as he/she proceeds, and then decides whether to quit or to go on. That person can go forward, but cannot go back. If no choice is made by the time the 'N'th slip is reached, then the person must accept the number (of Rupees) on the 'N'th slip.
Does there " EXIST " a 'Best Strategy' for the person ? If " YES ", then what is that strategy ? (Here the term " Best Strategy" means that the person will get the greatest amount of Rupees).
(In reply to
re: Monte Carlo Simulation (continued) by Charlie)
Your guess, as you have mentioned Charlie "....I chose to simulate bypassing a certain number at the beginning to determine a max to try to exceed....", is absolutely correct, but when you try to prove it, you will find that you are also considering the case when the possibility of the slip with the highest/maximum number is there within the first few that you have rejected. So i don't think you are to consider just one particular case when such a thing occurs. I mean where the numbers drawn are found to be in descending order as mentioned in your comment.
re(2): Monte Carlo Simulation (continued)
