This was in my drafts folder but due to the lackluster performance of my latest few posts I decided it doesn't deserve to be a top level post. As such, I am making it a comment here. It also does not answer the question being asked so it probably wouldn't have made the cut even if my last few posts been voted to +20 and promoted... but whatever. :P

Perceived Change

Once, I was dealing a game of poker for some friends. After dealing some but not all of the cards I cut the deck and continued dealing. This irritated them a great deal because I altered the order of the deck because some players would not receive the cards they were supposed to be dealt. One of the friends happened to be majoring in Mathematics and understood probability as much as anyone else at the table. Even he thought what I did was wrong.

I explained that the cut didn’t matter because everyone still has the same odds of receiving any particular card from the deck. His retort was that it did matter because the card he was going to get is now near the middle of the deck. Instead of that particular random card he will get a different particular random card. As such, I should not have cut the deck.

During the ensuing arguments I found myself constantly presented with the following point: The fact of the game is that he would have received a certain card and now he will receive a different card. Shouldn’t this matter? People seem to hold grudges when someone swaps random chances of an outcome and the swap changes who wins.

The problem with this objection is illustrated if I secretly cut the cards. If they have no reason to believe I cut the deck, they wouldn’t complain. Furthermore, it is completely impossible to perceive the change by studying before and after states of the probabilities. More clearly, if I put the cards under the table and threatened to cut the cards, my friends would have no way of knowing whether or not I cut the deck. This implies that the change itself is not the sole cause of complaint. The change must be accompanied with the knowledge that something was changed.

The big catch is that the change itself isn’t actually necessary at all. If I simply tell my friends that I cut the cards when they were not looking they will be just as upset. They have perceived a change in the situation. In reality, every card is in exactly the same position and they will be dealt what they think they should have been dealt. But now even that has changed. Now they actually think the exact opposite. Even though nothing about the deck has been changed, they now think that the cards being dealt to them are the wrong cards.

What is this? There has to be some label for this, but I don’t know what it is or what the next step in this observation should be. Something is seriously, obviously wrong. What is it?

Edit to add:

The underlying problem here is not that they were worried about me cheating. The specific scenario and the arguments that followed from that scenario were such that cheating wasn't really a valid excuse for their objections.