This strategy is designed to be used with unrestricted leaders, so that you can combine the Egyptian obelisk with a philosophical leader. You could still do it with a non-philosophical leader, but it won't be as good.
The basic idea, as you've probably guessed by now, is to produce an extremely early great prophet. The obelisk is by far the easiest way to do that, since it doesn't require a religion. The monument/obelisk is also extremely cheap (just 30 hammers on standard speed) and you'll probably want to build it early on anyway, in the cities you first settle. Often it's the first building you construct.
So, let's look at the math to see whether it's worth taking advantage of the special feature of the obelisk (to run 2 priests). Here's a picture of what it might look like:
It's a size 2 city, with two improvements- the desert hill riverside gold mine, and the farmed flood plains. Working both of those would give 4 2 9 . Working two priests produces only 2 2 , which starves the city a bit. Since it's too early to have any multipliers, gold and science and commerce are all equivalent.
So, clearly the regular tiles are better than the priests. On the other hand, with philosophical, we only need to run the 2 priests for 9 turns to produce a great prophet. Actually we can take one off on the last turn, too. After 9 turns, we'll have a prophet who can be settled to produce 2 and 5 . Let's see whether this is worth it.
Right now we have slavery, but the city doesn't have a granary yet. There's not really any other tiles we want to work there yet (the best are an oasis and an unmined desert hill gold) so we'll probabaly use that food for slavery. At size 2, 24 is worth 30 , so the 4 which the flood plain produces is worth 5 . With 8 turns without working the flood plain, and 9 turns without working the gold mine, we lose 8*5 , 8*1 , 9*2 and 9*8 , while producing (9 + 8 = 17) and . The total loss is 41 and 80 . A great prophet will pay back the after just 16 turns, and will pay back the after 21 turns. So let's say that after 20 turns, the prophet pays for itself, and becomes prophetable (huck!).
I consider anything that pays for itself in less than 50 turns a good investment, especially in the early game. 20 turns is definitely a good deal. And, in this particular case we have a gold mine that we're missing out on- a lot of city sites won't miss as much by running a priest. However, without philosophical, you have to run the priests for twice as long, so it's probably not worth it.
The real question of course, is what other alternatives are available? You could get an early great scientist instead, but you won't be able to get it as soon as the prophet, and in the very early game I think the prophet is actually better. You could use the extra production to build a worker or settler instead, but usually the capital can handle expansion by itself. You could work cottages, but without financial it will take a long time for those to be better than the prophet. In my opinion, the early prophet is the best option for a philosophical Egyptian leader.
The basic idea, as you've probably guessed by now, is to produce an extremely early great prophet. The obelisk is by far the easiest way to do that, since it doesn't require a religion. The monument/obelisk is also extremely cheap (just 30 hammers on standard speed) and you'll probably want to build it early on anyway, in the cities you first settle. Often it's the first building you construct.
So, let's look at the math to see whether it's worth taking advantage of the special feature of the obelisk (to run 2 priests). Here's a picture of what it might look like:
It's a size 2 city, with two improvements- the desert hill riverside gold mine, and the farmed flood plains. Working both of those would give 4 2 9 . Working two priests produces only 2 2 , which starves the city a bit. Since it's too early to have any multipliers, gold and science and commerce are all equivalent.
So, clearly the regular tiles are better than the priests. On the other hand, with philosophical, we only need to run the 2 priests for 9 turns to produce a great prophet. Actually we can take one off on the last turn, too. After 9 turns, we'll have a prophet who can be settled to produce 2 and 5 . Let's see whether this is worth it.
Right now we have slavery, but the city doesn't have a granary yet. There's not really any other tiles we want to work there yet (the best are an oasis and an unmined desert hill gold) so we'll probabaly use that food for slavery. At size 2, 24 is worth 30 , so the 4 which the flood plain produces is worth 5 . With 8 turns without working the flood plain, and 9 turns without working the gold mine, we lose 8*5 , 8*1 , 9*2 and 9*8 , while producing (9 + 8 = 17) and . The total loss is 41 and 80 . A great prophet will pay back the after just 16 turns, and will pay back the after 21 turns. So let's say that after 20 turns, the prophet pays for itself, and becomes prophetable (huck!).
I consider anything that pays for itself in less than 50 turns a good investment, especially in the early game. 20 turns is definitely a good deal. And, in this particular case we have a gold mine that we're missing out on- a lot of city sites won't miss as much by running a priest. However, without philosophical, you have to run the priests for twice as long, so it's probably not worth it.
The real question of course, is what other alternatives are available? You could get an early great scientist instead, but you won't be able to get it as soon as the prophet, and in the very early game I think the prophet is actually better. You could use the extra production to build a worker or settler instead, but usually the capital can handle expansion by itself. You could work cottages, but without financial it will take a long time for those to be better than the prophet. In my opinion, the early prophet is the best option for a philosophical Egyptian leader.