Hi there,
I'd like you to comment on this strategy, since I haven't yet found the time to try it in practice.
Let's suppose we're philosophical, running caste system, and have a city with enough food to run a specialist.
1. Run a merchant in this city.
2. When a great merchant pops, settle him in this city (+6G, +1F).
3. For every two great merchants settled, run an additional merchant specialist off their extra food. Repeat.
Now for the math behind it. For the sake of simplicity, let's assume that we will have popped only GMs, and they have all been settled in our merchant city. Let's further assume that the GP threshold will increase by 100 for each great person, ignoring the +200 change in increase at 1000 GPP.
Let n denote the number of great people we have generated so far. Thus, we will be able to run at least
M(n) := 1 + (n/2)
merchant specialists in the city. Generating the next great person will cost
requiredGPP(n) := 100 * (n + 1)
points, and our merchant specialists will generate
producedGPP(n) := 6 * (1 + n/2)
points per turn.
Now, we can estimate the number of turns it takes to pop the next GM:
rounds(n) = requiredGPP(n) / producedGPP(n) = (100*(n+1)) / (6 * (1 + n/2)) = 100/3 * ((n + 1) / (n + 2)).
As you can see, for an increasing n, the second term ((n + 1) / (n + 2)) will tend to cancel out, leaving us with a near-constant number of turns (roughly 33 turns) to the next GP throughout the game. What's more, even if we assume that roughly one in two generated great persons is not a GM, or is a GM which we don't settle, this linear-time property still holds (although the turn count 'rounds(n)' will differ, obviously). Other effects (threshold increase by 200 GPP past 1000 GPP, being non-PHI, pacifism, golden ages, parthenon, national epic...) will also only impact the turn count, not the underlying model.
So much for the theory anyway. Does this sound feasible in a real game, am I missing something, have I only managed to re-state common knowledge?
I'd like you to comment on this strategy, since I haven't yet found the time to try it in practice.
Let's suppose we're philosophical, running caste system, and have a city with enough food to run a specialist.
1. Run a merchant in this city.
2. When a great merchant pops, settle him in this city (+6G, +1F).
3. For every two great merchants settled, run an additional merchant specialist off their extra food. Repeat.
Now for the math behind it. For the sake of simplicity, let's assume that we will have popped only GMs, and they have all been settled in our merchant city. Let's further assume that the GP threshold will increase by 100 for each great person, ignoring the +200 change in increase at 1000 GPP.
Let n denote the number of great people we have generated so far. Thus, we will be able to run at least
M(n) := 1 + (n/2)
merchant specialists in the city. Generating the next great person will cost
requiredGPP(n) := 100 * (n + 1)
points, and our merchant specialists will generate
producedGPP(n) := 6 * (1 + n/2)
points per turn.
Now, we can estimate the number of turns it takes to pop the next GM:
rounds(n) = requiredGPP(n) / producedGPP(n) = (100*(n+1)) / (6 * (1 + n/2)) = 100/3 * ((n + 1) / (n + 2)).
As you can see, for an increasing n, the second term ((n + 1) / (n + 2)) will tend to cancel out, leaving us with a near-constant number of turns (roughly 33 turns) to the next GP throughout the game. What's more, even if we assume that roughly one in two generated great persons is not a GM, or is a GM which we don't settle, this linear-time property still holds (although the turn count 'rounds(n)' will differ, obviously). Other effects (threshold increase by 200 GPP past 1000 GPP, being non-PHI, pacifism, golden ages, parthenon, national epic...) will also only impact the turn count, not the underlying model.
So much for the theory anyway. Does this sound feasible in a real game, am I missing something, have I only managed to re-state common knowledge?