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I write down 4 numbers on four cards and you should choose one card. After seeing the card you can decide to throw away this card and pick another one without replacement. You can stop anytime you want, but if your card has the highest number among four you will win 6$. Calculate the expected value. Say what is the best strategy. I solved this problem for n=2 and the expected value is 1.8. However, I could not generalize the answer for n=100. Could you please help me to do that.

Alen
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    This looks related to the Optimal Stopping problem https://en.wikipedia.org/wiki/Optimal_stopping or https://en.wikipedia.org/wiki/Secretary_problem – turkeyhundt Jul 12 '15 at 03:16
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    It's exactly the same as the Secretary problem, but slightly different from the Optimal stopping problem. So according to the table on Wikipedia, the best strategy is to throw away the first card, and then pick the first card that has a greater value than the one on the first card. The probability of winning is 11/24, making the expected value 11/4. – msinghal Jul 12 '15 at 03:29
  • I vote to leave this closed since the question is a duplicate of Secretary problem - why is the optimal solution optimal?. –  Jul 12 '15 at 15:42
  • I did not know the name of this game so I could not find it in the previous posts, so I ask it again. Thank you! – Alen Jul 12 '15 at 17:41

1 Answers1

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Mihri, what do you think about this calculation of the expected value:

$$\left(1\times \frac{1}{4}\right)+\left(2\times \frac{1}{4}\right)+\left(3\times \frac{1}{4}\right)+\left(4\times \frac{1}{4}\right)=\frac{10}{4}$$

Harish Chandra Rajpoot
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rezzz
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