# Shuffling in the middle of a card game

Let's say we start with a deck of shuffled cards numbered 1 to 100.

This is a two player game in which, in each round, each player takes one card from the top of the deck in a particular order. Let's say the game proceeds like this

## Round 1

You take a card from the top of the deck I take a card from the top of the deck

## Round 2

You take a card from the top of the deck I take a card from the top of the deck

Continues like this until let's say half of the deck is drawn.That at the end of round 25.

Before round 26, we know what cards are in the deck, but obviously we do not know the order.

Now I ask you, "Are you okay with shuffling the deck now?"

He says you will say "I don't want it to be shuffled. "

Who is right?

Edit: Sorry I didn't specify the rules, because it seemed to me it really didn't matter what the objective the the game is. The game is 'Race for the Galaxy'. If you don't know the game, let's say there are some advantages in getting certain combinations let's say a '6' and '35'.

• Do you know what cards he has, or no? – Saketh Malyala May 13 '17 at 4:04
• Yes. But we do not know the order of cards in the deck – Mathai May 13 '17 at 4:05
• You have not defined the objectives of the players. Without that, there is no reason to care whether the deck is shuffled. As described, there is nothing to the round structure or who draws which card, so we might as well just look at the top $50$ cards. Maybe I love the sound of shuffling, so my answer is "please shuffle". -1 for a poorly thought out question. – Ross Millikan May 13 '17 at 4:07
• This is actually the game 'Race for the Galaxy'. If you don't know the game, let's there is some advantage in getting certain combinations, lets say '1' and '35'. – Mathai May 13 '17 at 4:09
• Then you should say that. Still there is no advantage to shuffling for either player. You replace an unknown permutation of the remaining cards with another unknown permutation. – Ross Millikan May 13 '17 at 4:11