Post by MostWanted on May 18, 2017 12:22:21 GMT
Mathematical Exploration of Stronghold Crusader by MostWanted
Part 1 - Taxing
Taxes in SHC work very simple, you put a tax and you get specific amount of money per peasant. The point of part 1 is to show you that highest optimal tax is -8. Let's compare how much money we get on 10 and 24 peasants for each of the taxes:
What can we see from this table? A lot. Really, a lot.
- The tax revenue DOES NOT increase linearly with popularity. For those who don't know what this means, it means that "best" and "worst" tax will change with popularity, and be almost surely different for every game you play, except if you always make exactly the same popularity.
Ratio of the highest tax revenue / lowest tax revenue DECREASES when pop increases. They are inversely proportional. The constant of proportionality is not easy to estimate and is beyond the scope of my investigation.( i could do it but i am too lazy xd )
Highest tax revenue for 10 pop is 30 (-24 tax), and lowest is 8 (-2 tax). When you divide 30/8 = 3.75
72/21 = 3.43
Part 1 - Taxing
Taxes in SHC work very simple, you put a tax and you get specific amount of money per peasant. The point of part 1 is to show you that highest optimal tax is -8. Let's compare how much money we get on 10 and 24 peasants for each of the taxes:
| Tax | Profit per month (10 pop) | Profit per month (24 pop) | Profit per month (66pop) |
| -2 | 8 | 21 | 59 |
| -4 | 12 | 28 | 79 |
| -6 | 14 | 36 | 98 |
| -8 | 18 | 43 | 118 |
| -12 | 20 | 50 | 138 |
| -16 | 24 | 57 | 158 |
| -20 | 26 | 64 | 178 |
| -24 | 30 | 72 | 198 |
What can we see from this table? A lot. Really, a lot.
- The tax revenue DOES NOT increase linearly with popularity. For those who don't know what this means, it means that "best" and "worst" tax will change with popularity, and be almost surely different for every game you play, except if you always make exactly the same popularity.
Ratio of the highest tax revenue / lowest tax revenue DECREASES when pop increases. They are inversely proportional. The constant of proportionality is not easy to estimate and is beyond the scope of my investigation.( i could do it but i am too lazy xd )
Highest tax revenue for 10 pop is 30 (-24 tax), and lowest is 8 (-2 tax). When you divide 30/8 = 3.75
72/21 = 3.43
198/59 = 3.36
Now, which tax is the best and which one is the worst? Well, as you can see, it changes. On 10 pop, there is average of +2 increase in gold by -2 increase in popularity. This is easily proven by total increase in gold divided by total decrease in popularity/2 (because we are not intrested in uneven numbers since popularity decrease/increase is only presented in even numbers): 22/(22/1)= 2. Then take a look at -8 and -4 taxes. Compared to previous taxes, they give us +4 gold for -2 in popularity. It means that they are most optimal - profit maximizing taxes at 10pop. The worst tax is -12 since it gives us opposite, +2 gold for -4 in popularity. If it was this simple, oh I wish it was this simple... But no, I had to spend much more time working on this.... Because...
For 24 pop already, it changes. There is average of 51/11 = 4.63 increase in tax revenue per -2 decrease in popularity. The first thing to notice is that all taxes from -2 to -8 are great, and all taxes after them are quite terrible. From -6 to -8 there is a 6 gold increase in profit per only -2 in popularity which is much better than average, while all taxes after that has <4 increase in gold per -2 popularity... And finally, for 66 pop:
There is average of 139/11 = 12.63 increase in gold per -2 popularity decrease. Here we can notice something very, very interesting. If you look at the numbers, you can see that the increase in gold is almost always +20 for each new tax. (59-79, 98-118, 178-198), even when it's not, its 19. But... Starting from 12, we have negative economic profit since popularity started decreasing by 4, not by 2. This is the KEY of this exploration.
Conclusion : -12 tax, just like all higher taxes ARE BAD. -8 tax is the most OPTIMAL tax in SHC.
Additional notes:
- If you want to complete my investigation, do this for pops higher than 100, and do it also for positive taxes (generous taxes).
- This doesn't mean -24 tax is bed when you have 400 pop and then you do everything on -, that's completely another thing. I am talking about normal gameplay.
- How can you use this? For example, if you make cathedral+church on 10pt, dont tax -12, tax -8 and put food on -4, you will earn more gold.
---- End of Part 1---- by MostWanted, all copyrights reserved, 2017.
Part 2 - Click here
Now, which tax is the best and which one is the worst? Well, as you can see, it changes. On 10 pop, there is average of +2 increase in gold by -2 increase in popularity. This is easily proven by total increase in gold divided by total decrease in popularity/2 (because we are not intrested in uneven numbers since popularity decrease/increase is only presented in even numbers): 22/(22/1)= 2. Then take a look at -8 and -4 taxes. Compared to previous taxes, they give us +4 gold for -2 in popularity. It means that they are most optimal - profit maximizing taxes at 10pop. The worst tax is -12 since it gives us opposite, +2 gold for -4 in popularity. If it was this simple, oh I wish it was this simple... But no, I had to spend much more time working on this.... Because...
For 24 pop already, it changes. There is average of 51/11 = 4.63 increase in tax revenue per -2 decrease in popularity. The first thing to notice is that all taxes from -2 to -8 are great, and all taxes after them are quite terrible. From -6 to -8 there is a 6 gold increase in profit per only -2 in popularity which is much better than average, while all taxes after that has <4 increase in gold per -2 popularity... And finally, for 66 pop:
There is average of 139/11 = 12.63 increase in gold per -2 popularity decrease. Here we can notice something very, very interesting. If you look at the numbers, you can see that the increase in gold is almost always +20 for each new tax. (59-79, 98-118, 178-198), even when it's not, its 19. But... Starting from 12, we have negative economic profit since popularity started decreasing by 4, not by 2. This is the KEY of this exploration.
Conclusion : -12 tax, just like all higher taxes ARE BAD. -8 tax is the most OPTIMAL tax in SHC.
Additional notes:
- If you want to complete my investigation, do this for pops higher than 100, and do it also for positive taxes (generous taxes).
- This doesn't mean -24 tax is bed when you have 400 pop and then you do everything on -, that's completely another thing. I am talking about normal gameplay.
- How can you use this? For example, if you make cathedral+church on 10pt, dont tax -12, tax -8 and put food on -4, you will earn more gold.
---- End of Part 1---- by MostWanted, all copyrights reserved, 2017.
Part 2 - Click here
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