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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?"

What will be your answer?

My friend and I had an argument about this. My answer is you will say - "I don't care whether you shuffle or not".

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'.

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  • $\begingroup$ Do you know what cards he has, or no? $\endgroup$ – Saketh Malyala May 13 '17 at 4:04
  • $\begingroup$ Yes. But we do not know the order of cards in the deck $\endgroup$ – Mathai May 13 '17 at 4:05
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    $\begingroup$ 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. $\endgroup$ – Ross Millikan May 13 '17 at 4:07
  • $\begingroup$ 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'. $\endgroup$ – Mathai May 13 '17 at 4:09
  • $\begingroup$ 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. $\endgroup$ – Ross Millikan May 13 '17 at 4:11
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There is no advantage to shuffling for either player. You replace an unknown permutation of the remaining cards with another unknown permutation. The fact that each player has drawn certain cards may give and advantage to one or the other, but shuffling has no effect unless you know something about the order of the remaining cards.

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  • $\begingroup$ Thanks, My friend is really picky about the choice of words. I took several classes in statistics (and my answer is also I don't care whether its shuffled or not), but he just wants to hear the answer from someone else. So I assume you are going to say "I don't care" $\endgroup$ – Mathai May 13 '17 at 4:21
  • $\begingroup$ By the way, how does it matter what kind of game it is? Regardless of the objectives, won't a player who is a mathematician say "I don't care whether you shuffle the deck or not" $\endgroup$ – Mathai May 13 '17 at 4:24
  • $\begingroup$ If you convince him of the mathematical truth that there is no advantage to shuffling or not, he may fall back on nonmathematical reasons for the preference. That is what I was hinting at by my comment about liking the sound of shuffling. Maybe it makes him feel lucky to specify whether the deck is shuffled. Maybe he likes to make you do work. Maybe he hopes to get a glance at some of the cards as you shuffle. He might still care. $\endgroup$ – Ross Millikan May 13 '17 at 4:30
  • $\begingroup$ It's just that he feels 'lucky'. I couldn't quite argue on what he feels - it's just like saying in a game of Chute and ladder, some one else throwing the die for him affects his luck. So we agreed that hearing a mathematician say "I don't care" is enough. $\endgroup$ – Mathai May 13 '17 at 4:33

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