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For Geeks & Brainiacs #28- The Game Of Googol -

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Puzzle Image There are 20 slips of paper in a stack, each with a different number written on it (so 20 unique numbers). The papers are face down with the numbers concealed. The papers are in no particular order. The numbers on the papers can be any positive number ranging from small fractions to a googol (1 followed by a hundred zeroes) or even larger.

You win the game if you manage to guess the largest number among all 20 papers. The game goes as follows. Turn over one paper at a time and each time you do, you may choose to stop and select the number on the paper that you just turned as what you believe to be the largest number among all 20 papers. The CATCH is that you can only ever choose the number on the paper you just turned. If you choose to keep going and turn over another paper, you cannot choose the number on any previously turned over paper. And if you turn over all 20 papers, then you MUST choose the number on the last paper.

What strategy do you use to maximize the probability of guessing/choosing the largest number? And what do you think the probability is of being right?

Credit: This is a variation of a puzzle created by Martin Gardner in 1960.
Do you have a suggestion for this puzzle (e.g. something that should be mentioned/clarified in the question or solution, bug, typo, etc.)?
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