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A recent Board Games with Scott episode [Breaking Up the Monopoly] has brought up an interesting question: When someone that you know asks to play Monopoly with you, what game do you suggest playing with them? I assume that you don't end up playing Monopoly with them. If so, that's cool, just tell me why you do that instead (alternative rules, versions, etc.).
Try to limit your answer to one game, and explain the mechanic or "hook" that you use to entice them away from the dreaded Boardwalk, Park Place, and Free Parking.
For adults, I would suggest Settlers of Catan, since it's a much better game to me and a lot more fun to play. If your willing to play a full game of Monopoly, then Catan is a prefect fit since it's actually shorter. There's also a much more nuanced trade mechanic, and a board to stack our your share of. I see it as a great chance to introduce them to Euro games if they haven't played one before.
For young kids, if they want to play Monopoly, I wouldn't dare be a spoil sport and suggest something else.
I am surprised no one has mentioned this classic (back in print as of 2008) which is quite thematically similar (paper money, real estate). Except, it is shorter, more strategic, and has no dice rolling (but still some randomness from tile drawing). It is also pretty easy to learn.
A card game based on the board game, everyone wins here -- they get to play something in the spirit of Monopoly, and you don't have to deal with a long, drawn-out game of landing in Jail and haggling for properties, or worse, reaching a stalemate where no one will budge.
The card game is fun, very inexpensive to purchase, and plays quickly. It works better with multiple players, but is just as fine playing with two players.
For me, it has to be Power Grid. It has many of the attributes of Monopoly, such as bartering of which power station to buy and is economically driven, plus the rules are pretty simple. Furthermore, it is such a great game, it is a brilliant introduction to the world of strategic board games, and I have known a few players hooked in this way.
I like the limited resources and bidding to get different rooms. It can get pretty competitive, depending on the group, but I enjoy the mechanics and think of it as Monopoly only a little more fun and with a definite endgame.
So sue me, it's technically a videogame (for the original Playstation), but it's basically monopoly set in a mall, translated to Japanese and then back into English. It's a heck of a lot of fun, and plays pretty much just like a boardgame. Up to six can play at a time.
If you land on an empty square you can open a store. If you land on an opponent's store you have to buy at least one item, but can buy two. If there are no items in a store you've landed on you can take over it. If you land on your own store you can restock ANY one store you own. There are random events, and points you get that will let you do various game changing events.