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).
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.
edit: As far as the math goes, here's one such article that goes over it: https://ideas.ted.com/heres-how-to-win-at-monopoly-according...
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).