Tim Darling is a math expert, who studied billions of computer simulations of Monopoly games, to figure out, mathematically, how you should play to have the best chance at winning the game. 

#1.)  ALWAYS BUY RAILROADS, NEVER BUY UTILITIES.  The revenue from railroads is much more constant over time. 

#2.)  ONLY BUY PROPERTY TO COMPLETE A MONOPOLY, OR KEEP AN OPPONENT FROM COMPLETING ONE.  Owing one or two properties in a group is useless, unless it stops Monopolies . . . because you need to build houses to win. 

#3.)  ALWAYS GET A “CHEAPER” MONOPOLY.  Get one of the four monopolies on the first two sides of the board:  The purples, light blues, light purples or oranges.  And get it quickly . . . trade if you have to. 

#4.)  ONLY BUILD THREE HOUSES.  As soon as you get a Monopoly, put THREE houses on each property.  Exactly three.  Based on the math, three houses is the sweet spot . . . they’ll pay off the most over time, without being too expensive up front like hotels. 

#5.)  ONCE YOUR FIRST MONOPOLY STARTS MAKING MONEY, GET A MORE EXPENSIVE MONOPOLY.  And put three houses on each of its properties. 

#6.)  STAY IN JAIL.  Once your opponents have monopolies, moving around the board will, most likely, cost you money.  So, stay in jail as long as you can.  But, until they have monopolies, get out of jail quickly so you can get back to buying property.  (Amnesta.net)