I shuffle a deck of cards and deal them into two piles.

.

The first card I place in front of me

If the second card is lower in rank, I start a pile to the left of the first; otherwise to the right.
Now I have two piles [one card in each pile, with the lower ranked card on the left.]
I continue, until they are all dealt, as follows:

If a card is lower in rank than the previous card, I place it on the left pile.

If a card is higher in rank than the previous card, I place it on the right pile.

.

When I'm done, the left pile will tend to have lower ranked cards, and the right pile will tend to have higher ranked cards.

But not completely: a J that follows a K will be in the left pile and a 5 that follows a 3 will be in the right pile.

What is the expected highest ranking card in the left pile? Of the lowest ranking card in the right pile?

To make the rankings clear, I numbered the cards: from 1 [Club deuce] to 52 [spade Ace]. You can give the answer as a number or card, as you like.

## Question

## bonanova 84

I shuffle a deck of cards and deal them into two piles.

.

- The first card I place in front of me

- If the second card is lower in rank, I start a pile to the left of the first; otherwise to the right.

- If a card is lower in rank than the previous card, I place it on the left pile.

- If a card is higher in rank than the previous card, I place it on the right pile.

.Now I have two piles [one card in each pile, with the lower ranked card on the left.]

I continue, until they are all dealt, as follows:

When I'm done, the left pile will tend to have lower ranked cards, and the right pile will tend to have higher ranked cards.

But not completely: a

that follows aJwill be in the left pile and aKthat follows a5will be in the right pile.3What is the expected highest ranking card in the left pile? Of the lowest ranking card in the right pile?

To make the rankings clear, I numbered the cards: from 1 [Club deuce] to 52 [spade Ace]. You can give the answer as a number or card, as you like.

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