There are three powers in Egypt now: The Army, led by the Military Council, the Muslim Brotherhood (MB), and all the other opposition groups and organizations.
As in all such strategic situations the outcome depends on which two powers get together against the third. Whoever stands alone will eventually lose.
Of course after two forces cooperate and succeed in defeating the third they will then each try to come out on top.
Now the Army - or security forces - are clearly in control of the country They may think they have enough power to rule by themselves - although they are probably less strong than is usually assumed. If they do decide to take the risk of going it alone they would try to keep the other two powers divided, as Mubarak did until that strategy stopped working. But the Army, which is now governed by a committee of practical 60 year-olds, is likely to recognize its need for a civilian opposition partner, although it may not have the patience to get through the difficulties and uncertainties of such a partnership.
An alliance between the Brotherhood and the Army is not possible. Therefore the Brotherhood - which is the second strongest power right now - has to try to work with all the other opposition forces - and outside supporters of democracy - to weaken the military's power and establish civilian control and prompt elections.
A Brotherhood victory would be death to the other two powers. The MB would gradually or quickly establish a religious dictatorship. They are an 80-year-old international organization with a strong ideology, based on their understanding of Islam, and they have learned how to survive and operate despite great efforts by the Egyptian and other governments to suppress them. Part of their motto is "jihad is our way; dying in the way of Allah is our highest hope."
The Brotherhood knows two things about its political position in Egypt. First, that most Egyptians do not want the kind of regime the MB will create if it comes to power. Egyptians want to live in a free society, not in a fear society where it is dangerous to say what you think. Egyptians don't want the government telling them how to practice their religion. And Egyptian women don't want to be second-class citizens. The Brotherhood also knows that the Egyptian army is their enemy and must be defeated before they can succeed.
Therefore the MB doesn't have a choice about its strategy about the triangle; they must work together with all civilian opposition forces to end the military's power.
The Brotherhood must try to have elections as soon as possible, to take advantage of their current popularity before other parts of the Egyptian community have a chance to get organized and to build support. This requires that they put on a "liberal" face to be accepted into the coalition of those trying to force the army to yield to civilian control and to hold prompt elections, taking advantage of the wishful thinking of those who don't want to recognize the real character of the Brotherhood.
So it is the diverse collection of civilian opposition movements and groups that probably will determine which two sides of triangle will join against the third. This non-centralized decision may well determine the outcome of the current turbulence in Egypt.
The "natural" and obvious alliance is of all civilians against military control. But if that is how Egypt's strategic triangle develops the virtually inevitable outcome will be Brotherhood control of the country and a long and bitter religious dictatorship probably postponing Egypt's freedom and development by a generation or more.
The opposite alliance, of "liberals" and others with the Army against the Brotherhood, would postpone full democracy and civilian control for some years, and let many of the economic beneficiaries of the Mubarak regime keep their positions,
Since the natural inclination of the diverse opposition movements and their international supporters will be to join with anyone against the Army's control of the country - and against substantial continuity with the discredited Mubarak regime - it will require patience and wisdom to make instead the strategic choice of joining with the military in treating the MB as the main enemy.
But the only way to prevent Egypt from becoming a religious dictatorship is for the liberal and other independent opposition voices to do what they can to preserve military power for enough years to build their organizations so that Egyptian voters can have a real alternative to the Brotherhood.
The other wise but difficult choice that the opposition organizations need to make is cooperation between religious and "secular" groups. No group can succeed in competing with the Brotherhood if they are seen by the Egyptian population as anti-Islam. Even in the cities the Egyptian masses have a deep attachment to Islam. If the Brotherhood is to be defeated Egyptians must believe there is a Muslim alternative to the Brotherhood.
Muslim moderates are now very weak in Egypt, but it is not unreasonable to believe that if they were free to operate without government suppression, and were protected from violence by the MB and other religious extremists, the strength of this element of Egyptian society would grow rapidly. The hopeful scenario depends on both the "liberals" and the moderate Muslims seeing each other as rivals who need each other and are on essentially the same side, initially against the MB and eventually against military control. Egyptian democracy cannot work until Muslim religious and secular groups (not including the MB) develop the ability to work together.
Much in the early stages of the Egyptian "revolution" provides inspiring hope that a new generation of Arabs cares about freedom and may be able to avoid the pitfalls along the long path to stable democracy. The Iraqis have succeeded for longer than almost anyone thought they could in governing (badly) their divided country with politics instead of bullets. If the Egyptians are wise enough to make the strategic decision of joining forces against the Brotherhood they too may do much better than expected.