How does the out-of-order sequencing rule apply when an out-of-order shortcut would generate a legal but obviously-unintended gamestate? This came up in the recent Leonin Arbiter discussion, as to whether "I crack a fetch and pay 2 for the Arbiter" should allow you to search your library or not - clearly the player making this statement intends for this to happen but strictly speaking this sequencing would not allow it.

I assume you mean that you would be using the cracked fetch to pay for the Leonin Arbiter? If that is the case, out of order sequencing isn't allowed, because the sequence is giving you access to information that you wouldn't otherwise have if things were done in a correct/legal sequence. If you mean that you crack a fetch and then tap a sol ring to pay for Leonin Arbiter, that's fine - Leonin Arbiter's rule is a sort of "special action" effect and so you're technically doing things in a fine order anyway.

How complicated are shortcuts allowed to be? Can you propose expansive conditional shortcuts where the outcome of certain individual actions might be unpredictable (ie. shuffling your library and revealing the top card), but you can guarantee a win no matter what outcomes occur without any interaction from the opponent? I remember having a long argument about this over an Eggs-style deck or something, I believe. What if the conditional shortcut only has a 100% chance of success in the limit as the number of times you shuffle your deck approaches infinity (ie. you need to shuffle your deck and get a certain order of cards, and if this doesn't happen you reshuffle. Given a sufficient number of reshuffles as part of your loop, however, this will happen.)

This is the same problem with the Four Horsemen deck in Legacy; you are not allowed to simply demonstrate the ability to repeat an action or series of actions and then declare what your desired end will look like without being able to describe how many times it will take to get there - you cannot rely on entropy to give you an eventuality. If you can define that doing sequence X exactly Y times will result in Z, then you're fine. If you would have to write a flowchart with branching points for actions you might take, depending on how the randomness comes up, that's not okay.