When we start playing, we have some villagers, and we may want to advance to the next age as quickly as possible (this is an hypothesis...). To upgrade we need some food, and building villagers also need food. We also need more villagers to get food faster.
Now, there are two opposite forces here: If we want to go quickly, we need lots of villagers. But if we only build villagers every 100 food we get, we will never get our 800 or 1200 food units we need to upgrade. So, the question is: what is the OPTIMAL number of villagers we need to build before starting to save the food to the upgrade?
The math is not very complex. Itīs just n villagers getting food at the rate n*phi, until reaching 100 and a new villager is built (n=n+1), until we reach a threshold, and then we collect 800 ou 1200 food.
Itīs just a sum of the harmonic series IF the amount of food needed to the upgrade was equal to the amount needed to build a single villager, than the optimal solution would be a single villager gathering food. To build a second villager instead of upgrading would be obviously wrong... But what happens when the amount of food needed is much larger than the price of building a villager??... RESULTS According to what I calculated, starting with a single villager (who costs 100) and 0 food, and needing 800 food (not a very realistic scenario, I know!...), the optimal solution is 7 or 8 villagers (the same time!). If the amount needed is 1200, the optimal is 11 or 12. So, it looks like the optimal would be the amount needed divided by the price of the villager (minus 1). I have to prove this yet... Iīm curious about the optimal solution in the russians case! =) With less villagers, we take longer because of the reduced speed. With more villagers, we take longer because we spend too much food building villagers instead of saving to the upgrade. This kind problem is very frequent in AOE in general, I believe a good analysis of it is important... There ARE optimal solutions to this problem!... But we still need to study more complex and realistic scenarios to see wether the optimal solutions are better than the "null" solutions or not... In our case here, 7 is the optimal, but +- 3 or 4 did not make a huge difference. To the beginning of a regular game it doesnīt make a differencee, because we already start with lots of food and villagers, and the upgrade is cheap. But this would be important to know if your food is over, someone killed many of your villagers, and the next upgrade is far away... Anyway, itīs an interesting problem, and it may be worthy to study it, so we can find an optimal AOE strategy! Think about it!! (of course I canīt believe Iīm the first person to think this. Has aybody here ever tried this?)
CONCLUSIONS