RobinZ ventured a guess that their true objection was not their stated objection; I stated it poorly, but I was offering the same hypothesis with a different true objection—that you were disrupting the flow of the game.
I’m not entirely sure if this makes sense, partially because there is no reason to disguise unhappiness with an unusual order of game play. From what you’ve said, your friends worked to convince you that their objection was really about which cards were being dealt, and in this instance I think we can believe them. My fallacy was probably one of projection, in that I would have objected in the same instance, but for different reasons. I was also trying to defend their point of view as much as possible, so I was trying to find a rational explanation for it.
I suspect that the real problem is related to the certainty effect. In this case, though no probabilities were altered, there was a new “what-if” introduced into the situation. Now, if they lose (or rather, when all but one of you lose) they will likely retrace the situation and think that if you hadn’t cut the deck, they could have won. Which is true, of course, but irrelevant, since it also could have gone the other way. However, the same thought process doesn’t occur on winning; people aren’t inclined to analyze their successes in the say way that they analyze their failures, even if they are both random events. The negative emotion associated with feeling like a victory is stolen would be enough to preemptively object and prevent that from occurring in the first place.
However, even if what I said above is true, I don’t think it really addresses the problem of adjusting their map to match the territory. That’s another question entirely.
When you deal Texas Hold’em, do you “burn” cards in the traditional way? Neither I nor most of my friends think that those cards are special, but it’s part of the rules of the game. Altering them, even without [suspicion of] malicious intent breaks a ritual associated with the game.
While in this instance, the ritual doesn’t protect the integrity of the game, rituals can be very important in getting into and enjoying activities. Humans are badly wired, and Less Wrong readers work hard to control our irrationalities. One arena in which I see less need for that is when our superstitious and pattern-seeking behaviors let us enjoy things more. I have a ritual for making coffee. I enjoy coffee without it, but I can reach a near-euphoric state with it. Faulty wiring, but I see no harm in taking advantage of it.