So, should I use calculus/linear algebra etc.. to find out what is the best strategy for Google Map powered Monopoly City Streets? Note* this is the perfect way to start the game with the most money, not the most score! (scores are calculated differently) No, its not necessary. Here is my guide for making the most money out of your rent: First let me just list some data that I found out: 1. You start with a certain amount of money, 2. Everyday you get paid by a FIXED constant 1million and your rent. 3. Longer streets' houses makes more money. 4. Shorter streets are less offensive. 5. There is a tax system. 6. The way the rent is calculated : Let's use the basic 50,000 one as example, its equation of rent is: 50,000*x/1,000,000 where x is the street value. lets call it daily housing fee. (DHF) That is, if you build n houses on this street, your next day rent will be : Rent (x, n) = x*.1+n*DHF Because you want the most money, you wanna use up all your money. and the number of houses that you will build is limited by your street money. That is, f_x(n)=3,000,000-n*500000 Then you can substitute x into the Rent equation, and without taking the derivative, the answer is already obvious by the graph: Link: http://www.edisonwang.com/2mj (wolfram alpha) approx. 30 houses would be the best. by substitute this back to the f_x(n) equation, we get the optimized x is approx. 1,500,000 Wow, isn't this 50% of your money? Yes, it is. Splitting your money into half half for buying long streets and house. Notice that the 50,000 value house occupies more space than some other buildings, but its def the best thing to build at the start. I will not discuss cheating methods here, but I can say....CHEATING JUST GOT MORE EFFICIENT.
Good luck and Have fun.