At the end of the game, yes, but if players don't try to bankrupt each other it probably won't happen.
Early in the game the expected value of a trip around the board is positive because of low rents of undeveloped properties and the net gain from Chance and Community Chest, plus passing Go. Cash flow into the game is positive as a whole.
Later in the game, when property is developed you're going to be paying bigger rents. This is going to cause players to mortgage or sell houses to pay the big rents (also their own liquid cash supply is likely lower from developing their own properties), each of which is a money sink since you don't get full value for these. This causes money to exit the game, eventually leading toward bankruptcy.
However, this requires that players actually get to develop their properties. If the game hits a lock due to no one trading and no one getting a natural monopoly, the game can go pretty much indefinitely.
> If the game hits a lock due to no one trading and no one getting a natural monopoly, the game can go pretty much indefinitely.
Yeah, I once played with someone whose strategy was "Never trade". In an act of desperation, I offered him $1,000 for a light-blue property, and he refused. The game lasted for nearly an hour before I quit out of extreme boredom.
A typical 4-player game of Monopoly should only last around 30 minutes, but people often have terrible strategies or play with ridiculous house rules that constantly inject money into the game, prolonging it. A lot of people don't even know that the house rule they're playing is even a house rule because it's what they were taught when they first learned to play.
> Yeah, I once played with someone whose strategy was "Never trade".
That's the right strategy for strong play. You should never trade property for mere money. If you absolutely have to, trade property for property if the trade gives you a monopoly, or if (in a more-than-two-player game) doing so gives you a net increase in the number of groups for which you hold at least one property (so you can block anyone from getting a monopoly in those groups without trading with you).
It's not an especially fun strategy, either for you or the people you're playing with.
