# Will you win the game?

You play a gambling game. On 100 folded pieces of papers are written 100 different values. You cannot see the numbers written on the folded pieces of paper, which are grouped in a pile. You pay 10 dollars to play the game. You may pick any piece of paper at a time, without returning it to the pile of pieces of paper, you unfold it and see the amount written. You need to decide if it is the largest of the pile – you know what numbers/values were selected by you before but you do not know what is ahead (the values could be of any amount and not limited to the maximum of 100 – let us assume that numbers varies from 1 to 1,000,000,000). When you select the “highest value” the game stops.

If you select the highest value – the value where you stop – you win the game and receive \$100. You may play up to 10 games.

Will you play the game? How you plan to win? What is the best strategy to go about – winning the most out of 10 games?

• This is the famous secretary problem (en.wikipedia.org/wiki/Secretary_problem). While the problem is nice, I don't think the solution is simple enough for this to qualify as a puzzle. Also, it probably deserves a citation. – Eric Tressler Dec 25 '18 at 4:53
• I was not aware of that source. Thanks for the insight. The reason for this to be a puzzle is that it requires a "discovery light". When you have it - basic mathematical tools could lead to the solution. – Moti Dec 25 '18 at 5:47
• At the start a new game, is the pile of numbers the same or could they be a brand new set of numbers? – hexomino Dec 26 '18 at 1:31
• Every time, a new pile is created so you don't have any prior knowledge of the numbers used. – Moti Dec 27 '18 at 2:09