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Let's say there are 13 cards, labeled from 1 to 13, and 5 players, each who get a card at random. Every player can see their own card, and that is all. The players are trying to estimate the sum of the 8 remaining cards (say the remaining cards are put in a pile face down).

So initially, without having seen their own card, everyone would expect the sum of the cards in the pile to be 63 (EV of each card is 7, times 8 cards). However, let's say we now take a look at our own card, and we see it is a 10. How will this adjust the EV of the cards in the pile?

Eric Aldrin
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    Well, the missing cards sum to $13\times 7-10=81$, hence the average missing card has value $\frac {81}{12}$. So... – lulu May 28 '21 at 19:47
  • Expected sum of $8$ cards is $\frac{2(91-n)}{3}$ if a player sees their card to be $n$. – Math Lover May 28 '21 at 19:49

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