Perfected Monopoly

From Summa Bergania

Theory

There's no doubt that Monopoly is a fun and classic game. Anyone who is even the least bit interested in actuarials, probabilities, speculative investments, and deal-making is immediately and permanently attracted to Monopoly. I was hooked on it in the 3rd or 4th grade, using my primitive math skills to bang out calculations regarding how many times opponents would have to land on a certain property to recoup the cost of buying 3 houses. And I also remember actually shaking dice repeatedly and tallying which properties the markers landed on, thinking that data from 4 tokens moving about the board 10 times established a scientific conclusion that the Greens were the most landed on property. Dad looked at my report and suggested that I needed about 1,000 more trips around the board... and that's how I learned about sample sizes and margins of error.

Monopoly was a huge part of our growing up (parents: this game is great for teaching arithmetic), but once we were smart enough to enjoy strategy games, we realized that Monopoly's strategy level is pretty low. Read the comments of anyone who ever won a national Monopoly tournament... they usually credit their win to something like "selecting the dog token" and "trying to avoid landing on the Railroads." After a few games you'll realize the Golds are far-and-away the best set (Jail is the most landed-on square, and anyone in Jail hits a gold with a 6, 8, or 9), and that there's no point to investing in houses unless you get to the three-level. Once everyone knows those two concepts, the dice play the rest of the game and the people are just observers.

Somewhere down the road a few years, while playing Monopoly for old time's sake, it occurred to us that one of the lesser-used events in the game might make it a little more interesting. According to the rules, you're only supposed to auction a piece of property when the player landing on the property declines to buy it at face value. What if instead, every piece of property had to be auctioned when landed on? We tried playing a game that way, and suddenly Monopoly was resurrected. No longer could someone get a set just by landing on each of the properties and paying face value (no strategy could beat that kind of luck). But when every property has to be auctioned, it's all fair game and you really have to evaluate what that deed is worth. Pay too much, and you won't have enough to run up a set your rival is eyeing... or enough to bid on the others in your set.

That one change opened the game back up to all the risk-reward concepts we love. But as we played on, we discovered other areas to improve... other little pieces of luck that interfered with sound strategy and calculation: If the dice land you on income tax coming past Go, you're $200 behind the other bidders in the auctions. If a Chance card puts you in jail, you're stalled from collecting your salary for 3 - 5 additional turns. If Community Chest gives you $200, you pretty much can finish any set you want.

With this in mind, we stripped Monopoly of all the luck elements we could by turning all the non-deed squares into do-nothings. The only luck left is the actual movement of markers using 2 six-sided dice... and it's impossible to conceive of any kind of interesting variant with fixed or arbitrary movement... risk-reward needs some randomness to work with. And we even considered using one 12-sided die instead of the 6-sided dice... but the two 6-sided are better because they form a nice balance between the more and less probable. Having a "7" be six times more probable than a "12" (using two 6-sided dice) makes things more strategic than if the two were equally probable (using a 12-sided die)... you'll buy houses on properties that are 6, 7, or 8 squares away with two 6-sided dice. With one 12-sided die, anything from 1 to 12 is just as likely to be landed on... you'll have to develop the whole strip to catch your prey. (Although, now that I think of it, three 4-sided dice or four 3-sided dice might be interesting... their probability curves are a little closer to a normal distribution. A computer program that returns random values using a true normalized distribution might be even better...)

The other major enhancement is a virtually fool-proof system to prevent the cheap revenge tactic whereby one player sells all his stuff to third party for $10, and thereby imbalances the game against the guy who is putting him out.

Using these rules, Monopoly is almost a top-tier game. It's certainly a lot of fun, but there is still an element of luck that you just have to live with. For example, you might hit a hotel and then roll snake-eyes to hit another one in the same color group... and that pretty much decides the whole game. You might take yourself down to your last $20 bidding on the last property for your set, and with 8 lucky shakes survive long enough to collect 2 salaries and start developing that group (when no one else was able to consolidate a color). The only ways I can think of to work around this involve drastic and tedious changes... like making a new board with 10 times as many squares and using 20 six-sided dice to further normalize the moving probabilities. Even then, there would still be luck, it would just be of a more controlled sort... like that of poker or blackjack. But even in poker you can get a bad beat. I just don't see how it's possible to eliminate that element in any game that's fundamentally actuarial.

Rules

All standard rules apply except:

1) The Luxury Tax square is a Free Parking. (Free Parking as defined by the Monopoly rulebook... nothing gained nor lost by landing on the square.)

2) The Income Tax square is a Free Parking.

3) The Go To Jail square is a Free Parking.

4) The Jail square is a Free Parking.

5) All Chance and Community Chest squares are Free Parkings.

6) Doubles do not let you shake again.

7) All monetary figures are rounded to the nearest $10, except when multiple houses and hotels are sold, and properties mortgaged in one turn. (For example, you don’t get $30 for each house you take off the light blues.)

8) All property the bank owns is automatically auctioned when it is landed on. [We use a silent auction (all players write their bid on a piece of paper and then reveal), but a verbal (normal) auction also works fine.]

9) Any player may make a bid in an auction for any amount. However, if they win the auction, they are required to pay the full amount of the winning bid – which may mean taking down houses or mortgaging property. The property that was just won cannot be mortgaged to pay for its own auction. If a player does not have enough in assets to cover his or her bid, that player is bankrupt.

10) When a player is bankrupt, the bank receives all his or her cash and property (which goes back on auction when landed on). The player that put him out then gets cash from the bank to cover the rent in full. (example: I land on John’s Boardwalk for $2000. I can only raise $500 through selling houses and mortgaging, so I am bankrupt. Everything I have goes to the bank, and the bank pays John the $2000 he is owed.)

11) When a player lands on unmortgaged property that another player owns, he must settle the debt in full with that player before he may negotiate any trade with any other player for cash or property.

12) To unmortgage property you must pay the face value (instead of mortgage value + 10%).

13) Free passes are not allowed.

14) All people are responsible for paying all debts incurred on all property, regardless of who notices it. There is no penalty for snitching.

15) Strike the rule that players have to pay 10% on acquired mortgaged property.

16) If there is a shortage on houses or hotels, tokens, trinkets, or coins may be used in their place. The bank never runs out of houses and hotels.

17) If there is a shortage on money, write sums down on a piece of paper, or use some other means to keep track of your value. The bank never runs out of money.

18) Any player may declare “Hold!” on any person’s turn. The player who is holding then has the opportunity to mortgage/unmortgage or buy/sell houses and hotels. The hold stops the current player from moving unless the dice had actually reached the playing surface before the hold was called. In a close call, the dispute will be over whether the word “Hold” was heard first or the sound of the dice hitting the table.

19) Rolling dice: Cocked dice will be re-rolled only if it is impossible to tell which number is mostly facing up. Dice that fall off the playing surface (ie. on the floor or in someone’s lap) will be re-rolled. Both dice must leave the hand at the same time or else they will be re-rolled. (Not allowing a player to roll one die and then trying to hit it with the second one.)

Vulnerable player (defined): A player that is unable to pay rent on the most expensive property on the board by his or her own means (includes being able to take off houses, mortgage, etc.).

Vulnerable value (defined): The value something is worth when you are calculating whether you are vulnerable or not. (The most you can get from it from the bank.) For unmortgaged property, it is the mortgage value price. For mortgaged property, it is $0. For houses and hotels, it is half the cost to build the house/hotel.

Face value (defined): For unmortgaged property, it is the price on the board. For mortgaged property, it is half the price on the board. For houses and hotels, it is the cost to build the house/hotel.

Unfavorable trade (defined): A trade that leaves a player at a net loss in face value.

20) When a player is vulnerable, he may not make an unfavorable trade.

21) To enforce rule 20, a third player may audit when he sees an unfavorable trade if and only if the rent of the most expensive property on the board is at least $300. The audit applies only to the player in the trade that is at a net loss. In order for the trade to continue, the audited player must show enough assets to prove he is not vulnerable or else balance the trade.

22) If a player wishes to resign, all his assets return to the bank.

Other Options

Other things we have thought of but don’t currently use:

a) Whenever someone makes an offer of cash alone for property, any other player may make a higher offer of cash. The player with the property is then bound to make a decision either to not sell his or her property or else sell it to the player with the highest offer.

b) Non-bluff variant:

No one may make an auction bid for more than the amount of actual cash they have on hand.

Any player at any time may audit another player, at which point the audited must give a full and truthful report of all of their cash on hand.

c) Make the mortgage value of all property equal to $100, and face value equal to $200.

d) Make the player that has the second-highest bid in an auction also pay the bank the amount of his bid, even though he doesn’t receive any property.