Sorry, those are division symbols. Apparently the forums can't display them...
THIS IS THE POINT PEOPLE(not you Belisarius)
Nicely done, best STABLE tax rate 50%
Best tax rate to MAKE GOLD 100% and work it.
I agree with Belisarius and think all of the BEST TAX posts should be ban (why beat a dead horse, it ain't going anywhere and you still look stupid) enough all ready
Lol, I just looked at the views and it was at 1776. Funny coincidence, and that's a LOT of views!
sooo in response to the original post. If you want to get fancy with the math try this one....
the total gold per unit time is x-x^2 that you have stated. now if we give x a time dependance, x(t) and integrate over some finite time T, we will have our total gold earned. for your explanation (which is quite true) you used a constant x, no time dependence (best when not playing). but alot of ppl are saying the best gold strats are letting your loyaly drop then raising it back up by dropping tax rate. I think they may be debunked if you really work out the math.
some short hand: int{0,T} f(t) dt=the integral from 0 to T of some function f(t) integrated over t.
our f(t)=x(t)-x(t)*x(t)
in terms of euler and lagrange type stuff, i think total gold can be thought of as our 'action' and f(t) is the Lagrangian. i think we can just use variational calulus to maximize the action, this will lead to an equation of motion for the x(t).
the thing I havent given much thought to is how to incorporate the rate of loyalty increase and decrease, because #1 they are NOT continuous (they change at discrete times). and I believe the rate the loyalty increases/decreases is independent on how high/low your tax rate is, so long as it is above the value that will make it go up/down. (this means that if your loyalty is at 100 and your tax rate is at 100, it will drop the same rate as if your tax rate was at 50, or 10, or 99, i think)
so at first glance, i think the THEORETICAL best tax plan is to keep it as close to 100 as possible as much as possible. to do this the rate at which loyalty falls is important. if it falls faster than 5%/15 minutes then you cant use comforting to keep it at 100% alone, in this case I think you want to drop your tax rate to 5%(or 4, 3,2,1,0) so that whenever your comforting cooldown is done, you can immediately use it to jump back to 100%.
so this is very (kinda) different from the let it drop to %50 plan then raise it back up. here your loyalty should NEVER drop below 95%!
anyway LOOOONG POST, i'm going to copy and paste it on its own thread, but I wanted to contribute my ideas to the theory-crafting discussion. if anyone out there has some good variational calc skills, see if you can set this up and find the best 'tax trajectory' x(t). it may be tough do to the non-continuous portions though, but I think if we consider everything to happen continously, we can figure out the discontinuous side from it easily.
this is really cool
=]
Take a look at the other tax threads some good info on just that topic was posted. Loyalty drops by 1 every 6 minutes, population falls behind that by 1% every 6 minutes, and it raises like that as well, no doubt both happen gradually over the 6 minutes.
You can however keep loyalty at 100 with Disaster Relief, but population will never reach max if you have the tax rate set lower, such as 100%. So you never quite get the max gold if you are cycling Disaster Relief with 100% tax rate.
I drew up some simple approximations in my thread comparing all the types, none of them are accurate except the 50% steady state rate as described in this post.
Hmm, so what will your Public Grievance be after you put it to 50%? Will it still be at 0?
Public Greviance only happen when things like riots, or being attacked happens.
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Fun stuff to do if you're bored- the impossible question.
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