There seems to be a lot of confusion about great people, how they are generated and the odds involved, so I thought I’d try to explain that a bit.
1. Generating Great People
Great people are generated by accumulating great people points (GPPs) in your cities. Every city has its own counter that keeps track of how many GPPs have been produced in that city already, which can be seen in the lower right corner of the city screen. Once a city has reached a specific threshold, a great person will be generated, and the GPP counter of that city will be reset to zero. This threshold is a civ-wide one, and will increase each time a great person is born so that the next one will be harder to get.
For normal game speed, you need 100 GPPs in one of your cities to generate your first great person. From then on, every great person thereafter will cost you an additional 100 GPPs until 1000, then the threshold will be increased by 200 for every great person, making it even harder.
So you need 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, then 1200, 1400, 1600, 1800, 2000, 2200, … GPPs to generate a new great person.
For Epic game speed, you need 150% of the required GPPs, so it’s 150, 300, 450, 600, …
For Quick game speed, you need only 67% of the required GPPs, so it’s 67, 134, 201, …
Note again that the threshold is civ-wide and the same for all cities, while the GPP counter is individual for each city. For example, you have city A with 80 GPPs and +2 GPPs per turn, and another city B at 99 GPPs and +3 GPPs per turn. So city B will reach the threshold of 100 GPPs next turn. This will produce your first great person, and sets the GPP counter of city B back to 2 (2 excess GPPs are carried over). Additionally, the new threshold for producing a great person is set to 200, so city A, now at 82 GPPs +2 GPPs per turn, will need much longer than before to produce a great person!
For the question whether it’s better to concentrate all your GPP production in one city, or spread it over multiple cities, see an article by Vol here.
Note that you will also receive specific great persons if you are the first to discover certain techs (Music, Economics, Physics, …). This does not effect the threshold for your GPP production in any way. The same is true for great people generated by other civs: They won’t effect your threshold either.
2. Sources for GPPs
Normally, a city won’t produce any GPPs on its own. There are two sources to produce GPPs, specialists and wonders.
Specialists produce +3 GPPs per turn, except the citizen specialist which will produce none. Great wonders generally produce +2 GPPs per turn, and small wonders +1 GPP per turn. Once a wonder becomes obsolete, it will no longer produce any GPPs.
These GPPs per turn can be further boosted by “+x% birth rate” enhancers. The most obvious one is if you play a philosophical leader, which provides +100% birth rate for all cities. Then there’s the Pacifism civic that comes with Philosophy, which adds +100% birth rate for all cities as well. Finally, there are some wonders that provide a similar bonus, like the Parthenon (+50% birth rate for all cities) and the National Epic (+100% birth rate for the city it was built in only). Note that these boni are additive, so if you are a Philosophical leader, have adopted Pacifism and have the Parthenon, you will get +250% GPP production in all cities.
3. Odds to Get a Specific Type of Great Person
There are five types of great persons: Engineers, merchants, scientists, prophets, and artists. The odds of which type of great person will be generated once one of your cities has produced enough GPPs, depends on which types of sources contributed to the GPP pool of that city. The odds can be displayed by mousing over the GPP bar in the lower right corner of the city screen.
Each type of specialist counts as one source for the respective great person type, and each wonder has noted in its description which type of source it is. For example, the Great Library counts as a source for great scientists, while the Parthenon counts as a source for great artists.
If you have produced only one type of GPPs in your city once it has reached the threshold, then you are guaranteed to get a great person of that type. For example, if your city has the Parthenon (source for great artists) and you had hired an artist specialist to increase GPP production, you will be guaranteed to get a great artist.
If you have different types of GPP sources, it gets a little more complicated. For each turn, the game notes what types of sources had produced GPPs in the city (regardless of how many GPPs each source had contributed!). This determines the odds of which type of great person would be produced for that turn. The overall odds are the average values of all the turns since the last great person was generated in that city.
Note that difference: The number of GPPs will determine when a great person will be generated, and the number of sources will determine what type it will be.
* You have the Parthenon (great artist source) and a priest specialist (great prophet source) in the city the whole time. Your chances will be 50% to get a great artist and 50% to get a great prophet. Note that it’s irrelevant that the Parthenon produced only 2 GPPs while the priest produced 3 GPPs per turn; they both count as one source.
* A city has the Great Library (great scientist source), an engineer, and an artist specialist, plus the two free scientist specialists from the Great Library. So you have 5 sources (one wonder and four specialists). This will give you a 3/5 = 60% chance of getting a great scientist, a 1/5 = 20% chance of getting a great engineer, and a 1/5 = 20% chance of getting a great artist.
* You have the Pyramids (great engineer source) in a city. One turn before the city reaches the threshold to produce a great person, you hire a scientist. What happens? Well, the game remembers that for every turn but the last, the great engineer source had been the only source of GPPs, and that only on the last turn there had been a different source present. So it is a 100% chance of getting a great engineer during all turns but the last, and a 50%/50% chance for the last turn. Since it averages the odds over all the turns, you will have a 99% chance of getting a great engineer, and a 1% chance of getting a great scientist.
* Assuming normal game speed, no great person generated yet: You hire a priest specialist for 22 turns. Then you fire him, and hire two scientist specialists for 11 turns. Intuitively, one would assume that because you had 22*1=22 sources for a great prophet and 11*2=22 sources for a great scientist, this would give you a 50%/50% chance. But because the game averages over turns, the odds will be 22/33 = 67% for a great prophet and 11/33=33% for a great scientist instead, because you had 22 turns with only great prophet sources and 11 turns with only great scientist sources.
(Thanks to Roland Johansen for suggesting this!)
Once the threshold is reached and a great person is generated, the city “forgets” which types of sources there had been before and starts anew. So if you hire a scientist to produce a great scientist, and after generating that great scientist remove the scientist specialist and hire a priest instead, you will have a 100% chance of getting a great prophet as the next great person, since the city will have forgotten that there had been a great scientist source in the city during the previous cycle.
If you have comments, questions, or found any mistakes, feel free to comment!