I’m a little hesitant to post this, because Monopoly is my favorite board game and I like to win. But here are two great webpages with way too much quantitative information about probabilities of hitting spaces on the board and rolls to recoup an investment:
Probabilities in Monopoly by Truman Collins
How to Win at Monopoly by Tim Darling

Here are a few of my strategies:
-Ideally, be the first to get a monopoly. Any monopoly, though the ones on the second side are preferable. Build 3 houses ASAP on each property.
-Trade. Always trade. (I also employ lots of trading in fantasy football). Be willing to give up bit pieces to get monopolies. Or even to get pieces that give you the CHANCE of picking up a monopoly. Be willing to give expensive monopolies to people that are cash-poor if it gives you a monopoly you can build on.
-Railroads are only good early in the game, in my opinion. Trade them later on for anything that increases your chance of a monopoly.
-Until <5 properties are available, get out of jail ASAP. After that, never pay to get out of jail early. -I mortgage more bit pieces than the average player to get cash to build houses. -Try to be the person who knocks others out of the game, because then you get their property, which is almost always valuable, even it it's mortgaged. Position yourself in the end game to knock people out. -Sometimes it's wise to trade a bit piece for cash if it both gives you needed cash and starves someone who has an expensive monopoly of cash to build with. -Know which properties others are likely to hit with their next roll. Build there if possible.