[Gator]

Here’s the proposition. You have 1,000 identical slips of paper. You write a distinct number on each piece of paper. There is no bound. The only limitations are that each number be unique and that a person of high school intelligence can quickly determine that one number is higher then another (i.e. 1.5345 is permissable as is 9,999,999.02 as is - 53 -- but i-squared is not). These 1,000 slips of paper are then mxed up in a hat. You randomly select a number and read it out loud. After reading a number, I either tell you to stop or go ahead and read the next number. I win if I stop you after you've read the highest number (before reading another number). I lose if you read the highest number and I tell you to go to the next number. I am only allowed to stop you one time. What percentage of the time will I win this proposition using an optimal strategy (and what is that strategy). There are no tricks (i.e. reading body language, marking the cards, etc.).