There is a regular deck of 52 playing cards and 5 cards are placed face-down on the table. The cards have values ranging from 1-13. The dealer secretly checks all face-down cards, i.e. you do not get to see them. The dealer then removes the lowest value card, without showing anyone the value, and replaces it with a new face-down card.

My friend was asked this question in an interview recently.

I know the initial expected value is simply 7 * 5 = 35. But now how de we find the new Expected Value conditional on the fact that the lowest value card has been removed and replaced

The interviewer after while gave a hint and mentioned using the Standard Deviation of a single card = $\sqrt 14 $ but I'm unsure what the logic of using std here is and how to proceed

There is a regular deck of 52 playing cards and 3 cards are placed face-down on the table. The cards have values ranging from 1-13. The dealer secretly checks all face-down cards, i.e. you do not get to see them. The dealer then removes the lowest value card, without showing anyone the value, and replaces it with a new face-down card.

My friend was asked this question in an interview recently.

I know the initial expected value is simply 7 * 3 = 21. But now how de we find the new Expected Value conditional on the fact that the lowest value card has been removed and replaced

The interviewer after while gave a hint and mentioned using the Standard Deviation of a single card = $\sqrt 14 $ but I'm unsure what the logic of using std here is and if its correct to use std and how to proceed