The Amber gamemaster is required to be the eyes, ears, nose, hands and tongue of the PCs. He or she is also required at times to be the mind, which is the most difficult thing to represent of all.
A large part of the problem is that, in theory, even if the PC has merely Amber in Warfare (the default), he or she is still an infinitely better tactician and strategist than the player is. The PC can beat Napoleon on the battlefield and Kasparov at chess; beyond even that active use of tactical abilities, they have passive tactical skills just as great. This is with only the default in a stat; even 10 additional points beyond Amber puts the PC into levels of ability as regards tactical skill and foresight that are beyond anyone who has ever lived on earth in the recorded history of humankind.
How to represent this disparity between the tactical abilities of the player and the tactical abilities of the character is one of the central difficulties of Amber as an RPG setting, particularly as regards issues of player choice and control.
The players must ultimately be given free choice in the actions of their characters, but they must also feel they have been given a fair choice. They must feel that they were given enough of an understanding of the situation their characters faced that they could make an informed decision. Sometimes (very often, in fact, particularly in combat situations) this will involve the players probing the gamemaster for some time to get information or tactical evaluations that their characters can make in seconds, and sometimes this will have to involve the GM alerting the players to things (even very obvious things, things he or she thinks are so obvious that they should not have to be informed of them) that they appear to be overlooking, but that their characters certainly would not overlook.
It is often the most apparently obvious things that are the most problematic for this. Common sense, as has been said, is not common. Assuming your players ought to know something that you consider obvious works fine until you hit the "obvious" thing that was not, for whatever reasons, obvious to them, but that ought to have been obvious to their characters.
There is no feeling more frustrating in an Amber game, nothing more likely to breed the resentment that turns what was once a stress-relieving entertainment into a stressful chore, than the feeling that the gamemaster is not being fair in making sure the players have the resources at hand to make an informed choice for their characters. When significant and long-term consequences come about because the player has overlooked some detail that their characters ought to have considered, the players feel cheated. They stop trusting their characters, and they stop trusting the gamemaster.
Trusting the character is very important in Amber, and by this I mean that the players must believe in the potency of their characters' abilities, in their competence to handle a situation, in their experience, in their skills. If they do not, the tendency to micromanage every situation comes forth, slowing down the game tremendously. If the characters fail in their endeavours or encounter serious difficulties because their players do not note trivial details that the characters ought to be made aware of due to their much greater skill, experience and immersion in the setting, the players begin to become obsessed with trivial details.
Trusting the gamemaster is even more important, and by this I mean that the players must believe the gamemaster is being fair to them. They must believe that the presentation of the game world they are given is one adequate to allow them to make informed decisions for their characters. The gamemaster must not only present the physical details of a setting, but the mental ones, the ones that the characters (with, as mentioned, their superior tactical abilities, greater experience and greater immersion within the world of the game) would have to be aware of in order to make informed decisions about what to do and what to say and when. Without this feeling of trust, the gamemaster becomes an adversary to be overcome, someone from whom the necessary information must be extracted painfully and unwillingly, rather than a partner in the collaborative storytelling that is the heart of the Amber DRPG's philosophy.
The responsibility of the gamemaster is ultimately to guide the player in such a way that he or she can make informed decisions about character actions, not control character actions. This guidance must, however, often come in the form of warnings or advisories, sometimes about the things the gamemaster considers extremely obvious, because what seems obvious to one person is not obvious to another.
Being told it was assumed you would know to consider something after you have performed actions with your character demonstrating you did not consider it is extremely frustrating and somewhat belittling. It is short steps away from being told you are stupid. Players have vastly different experiences and abilities and priorities than their characters, and often from their gamemasters. This must be taken into account. Do not assume the players necessarily know things you consider obvious, and do not act as though their characters deserve whatever they get because their players didn't consider obvious what you did.
Lacking true immersion within the minds of their characters and the world they inhabit, the players must rely on the gamemaster to compensate for them in this respect. Lacking tactical abilities superior to Napoleon, the players must rely on the gamemaster to compensate for them in this respect as well.
Failures and missteps by the characters can and ought to happen, but they should happen because it was possible for the character to fail or misstep in the situation, not because the player overlooked (for whatever reason, be it ignorance or distraction or stress or weariness or the position of the stars) a detail the gamemaster considered obvious, or could not foresee consquences (this is particularly a problem when dealing with the usage of character powers which the characters are intimately familiar with the workings of and the players almost entirely ignorant) their characters ought to have foreseen, or did not take into account something their vastly more competent and knowledgeable and aware characters would have known to take into account.
The game ceases to be fun if the players have to constantly worry about whether they're being told things their characters should know automatically, if they begin to feel they cannot trust the gamemaster to present the situations faced by the characters in such a way that they can make informed decisions about their characters' actions, and if they begin to feel they cannot trust their characters to avoid missteps without being led by the hand like children. The danger lies not merely in this actually being the case within the game, but in the players fearing it may be the case in each and every situation their characters are in. It is a stifling atmosphere to play under, constantly fearing you may get burned by the fire again unless you (the player, not the character) take certain "obvious" things into account.
Because presenting the game world and every situation the characters find themselves in as they would appear in their whole to the characters is impossible, the gamemaster simply has to compensate by means of warnings or advice when the players begin to do things their characters would know not to do in that situation. This sometimes must include giving the players a chance to take back an action they have already ordered performed if it becomes clear they would not have ordered the action had information available to their characters been available to them.
This is most important in two situations: when the character faces serious immediate danger in a situation (generally combat), or when serious long-term consequences and alterations to the course of the campaign can come about because of what the characters choose to do and say in their interactions with others. The first is generally easy to judge, and the second not so easy. Where is the line to be drawn between presenting the situation fairly to the players and between guiding them by the hand? A large part of the problem is that the second case can sometimes only be seen in hindsight, after so many things have happened because of it that it cannot simply be gone back to and altered; in this situation, there really is nothing more that can be done than to grin and bear it, and try to make sure it does not happen again in the future.
However, in situations where it is immediately obvious to the gamemaster that the characters are in danger of making (or are making) serious missteps because their players may not be considering an aspect of the situation their characters would know to consider, it is the responsibility of the gamemaster to make sure the players are aware of what they are doing. To do otherwise is to engender suspicion and mistrust in the players in all future situations, and to put upon them too much of the burden that they thought was to be borne by their characters: to be aware enough of the setting and competent enough in their abilities that kingdoms will not be lost for want of an obvious nail. And if the kingdom is to be lost for want of a nail, then the players must feel that they were aware of the nail's want if their characters would have been.