Not necessarily. The games rules include an auction that is frequently removed in house rules. What's supposed to happen is if the player who lands on the space (Player A) doesn't buy it from the bank, the property is auctioned to all players.
Maybe no one owns Boardwalk yet, and Player A doesn't want to try and get the Park Place/Boardwalk monopoly. Or maybe Boardwalk is owned by Player B but Player B doesn't have any cash, so Player A thinks they can block the monopoly while paying less to the bank. Or maybe Player B does have the cash but Player A knows that B is desperate for the monopoly, so they want to drive the price up and force them to pay more.
There's more to than just rolling dice and landing on spaces.
You can calculate the game-theoretic value of all of the properties (I'm a little surprised that no one seems to have actually done this AFAICT -- maybe a project for next weekend). At that point the game reduces to pure luck: players who land on properties whose list price is less than their game-theoretic value will buy those properties and gain a (small) edge. The auction clearing price for rational players will be the game-theoretic value, which will have no effect on the outcome. The rest is pure luck (modulo some other obscure rule that I've forgotten then allows players to make decisions), and that is the overwhelmingly dominant factor.
It's not just property values/landing percents. If you can get a "low value" monopoly more quickly through the auction, because combined players happened to land on all the orange spaces first time around the board but they're all "rationale" and "know" that orange is low-value (I don't know if it is, just an example), then that opens up an opportunity for you to swoop in.
That might not happen every game but it is advantageous to get a monopoly sooner rather than later. Like I said earlier you can also factor in how much money your opponents have when deciding whether to go to auction or pay list price. If everyone is cash poor that opens up opportunities for you to get deeds for low cost, increasing the properties future rate of return.
The randomness in the game means you can't just pick one optimal strategy and apply it to every game and every opponent. And if your opponents change strategy (or your opponents change), you need to adapt your strategy to accommodate for that as well.
another edit: There's also a limited amount of houses/hotels the bank has, so there's strategy around getting houses first and leaving your opponents unable to build up their monopolies (another frequent house rule is that there unlimited houses too buy from the bank). If multiple players are trying to buy houses at once and there's not enough, the houses are auctioned again to the highest bidder (hello capitalism housing shortages).
You can also sell properties you own, or choose to stay in jail (frequent house rule is that you can't collect money while in jail, but this isn't an official rule).
Liquidity is a thing, and trades are a combination of properties and cash passing between people who already have holdings of properties and cash that affect the subjective values of the properties being traded.
I think you're underestimating the complexity of your proposed calculation, and think is simply boils down to calculating how often particular spaces are landed on times the amount paid when they are landed on. I mean, it does, but the second part is not so simple.
What you have is a fairly complex strategy game, and the rest is pure luck (called dice.)
edit: I'd really be interested in seeing what you come up with (or imo, at what point you'd bail out) if you were to attempt to solve Monopoly. I'm at pessimizer@yahoo.com
I'd be interested in how you calculate it. Sounds like a great project. I've seen others that point out due to how the board is laid out which properties are most likely to be landed on, but don't think I've seen theoretical value based on rents.
An even better calculation would be how much it's worth to each player based on what they already have as well!
Usually people don't pass up the chance to buy property though. It's not that there's a house rule against the auction, it just never comes up unless you have someone who is already losing badly that lands on a space that has somehow not already been snapped up.
Other than maybe the utilities, when is it not advantageous to buy a property you land on? Until an opposing monopoly exists, there is a net positive value to each turn, so you have plenty of resources and if all you do is deny the property to someone else, you essentially get it at 50% discount by mortgaging it.
On the flipside of over-extending, last time my family played we included auctioning. Didn't take long for my brother to realize he could send it to auction, bid $1 (which no one challenged because we were focused on the partially-completed colors we had), and immediately mortgage it for free money to buy houses on the properties he did care about.
Not necessarily. The games rules include an auction that is frequently removed in house rules. What's supposed to happen is if the player who lands on the space (Player A) doesn't buy it from the bank, the property is auctioned to all players.
Maybe no one owns Boardwalk yet, and Player A doesn't want to try and get the Park Place/Boardwalk monopoly. Or maybe Boardwalk is owned by Player B but Player B doesn't have any cash, so Player A thinks they can block the monopoly while paying less to the bank. Or maybe Player B does have the cash but Player A knows that B is desperate for the monopoly, so they want to drive the price up and force them to pay more.
There's more to than just rolling dice and landing on spaces.