This is an interesting trick I discovered while thumbing through the rule book of Monopoly and realizing that I had no chance of winning against my friend (who owned the entire board, save for the three properties I had a few houses on.) The idea is, if you are forced to default to a certain player, you can give them the absolute least amount of money possible. This trick also works if you purposely want to lose to somebody (i.e., you don't want to give all your properties to the person who is kicking ass), but you have enough money to pay off your debt. It works like this:

1. You begin by selling all the buildings you have on your properties. In most cases, you are losing so bad you don't have to worry about this, but if you are going to follow through with this, the rules state that you need to remove the buildings anyway.

2. Mortgage all of your properties. Figure out what 10% of the least valuable property's mortgage value is and use that number for the variable Y.

3. Take all the money you have (including the profit from the sale of the houses/hotels and mortgages) and count it up. This total will make up the variable X.

Make sure that the only assets in your possession are mortgaged properties and cash. For reference, the following is out of the Monopoly Official Rule Book:

Unimproved properties can be mortgaged through the Bank at any time. Before an improved property can be mortgaged, all the buildings on all the properties of its color-group must be sold back to the Bank at half price. The mortgage value is printed on each Title Deed card....

In order to lift the mortgage, the owner must pay the Bank the amount of mortgage plus 10% interest...

...If you have mortgaged property you also turn this property over to your creditor but the new owner must at once pay the Bank the amount of interest on the loan, which is 10% of the value of the property.

With this in mind, basically what you are going to do is unmortgage and re-mortgage your least valuable property several times before you pay anything to your creditor. Every time you unmortgage your property, you pay 10% of the original mortgage value, or 10% of half the face value of the property. If you do the math, you are losing this 10% every time you unmortgage and re-mortgage. If you keep doing this long enough, you will lose a substantial amount of your money. Using the variables above, use this formula to find the value you will have when you can no longer afford to unmortgage all of your properties:

`( (X/Y) - mod(X/Y) ) * Y`

This value is essentially the integer remainder of the value (X/Y). Once you've calculated this value, you should have a figure that is significantly less than your original sum of assets, X. At this point, if you were to physically flip the property over the times required and calculated out the mortgage/unmortgage values, the property would end up unmortgaged (i.e., you just paid the unmortgage price to the bank, and you are nearly broke.) Mortgage the property one last time. When you do this, you will end up with the mortgage value of your least valuable property (10 * Y) plus the remainder figured out above, which will not be enough to pay off the unmortgage fee. Now you are ready to give your properties to your creditor.

One last stinger: if you read the above rules, you will realize that your creditor will have to pay the 10% from all your mortgaged properties anyway! So if Z is the total mortgage value of all your properties, your creditor would have to pay the bank by the following formula:

`Z - ( ( (X/Y) - mod(X/Y) ) * Y ) + 10 * Y )`

If you are really lucky (though chances are that, because you just lost, you are not) this will put your creditor in bankruptcy as well, causing him to default to the bank!

The official rules of monopoly do not clearly state if one can do what PaSTE describes:
A player is bankrupt when he owes more than he can pay either to another player or to the Bank. If his debt is to another player, he must turn over to that player all that he has of value and retire from the game.
This would imply that unless you can come up with the money everything goes to the owed player as is. I take the phrase "than he can pay" to mean that the player can do whatever they want to do to come up with the money. This includes selling houses, making trades and mortgaging. BUT, if at the end of all this, you can't actually pay the person it is all cancelled. They get all your assets in their original form, minus the housing.

I think this reading of the rules is the most "fair", and is probably what is used in tournaments. This also avoids a player selling all his property to someone else for \$1. It tends to be pretty easy to really screw over the person you owe by doing this because most likely you can complete a competitors monopoly for them.

The most important thing to do whenever playing Monopoly is to discuss how the rules will be interpreted, or more commonly, completely ignored. Otherwise, when PaSTE decides to try this out you'll simply get in a long argument over the ambiguous rules.

Of course, if we want to beat the system in Monopoly and still stay legit, we could start by working out the probabilities of landing on the various squares. The easiest method of doing this is to run many computer trials; the result of 10 million moves shows roughly the following chances of landing on each property:

Pink & Light Blue: + 0% chance
Green & Yellow: + 5% chance
Orange & Red: + 22% chance
Brown & Deep Blue: + 2% chance (adjusted for only 2 properties)

The reason Orange is so popular is because of the "Go to Jail" square; this effectively means a player has twice the normal chance to be on the "Jail/just visiting" square... throwing a 6/8/9 from here lands you on an Orange

Or, we could find the amount of money you need to spend on each set of properties before the rent is 750:

Brown: n/a
Light Blue: n/a
Orange: 1760
Pink: 1940
Deep Blue: 1950
Yellow: 2150
Red: 2330
Green: 2720

(adopted from the book "Taking Chances" by John Haigh)

Note: I'm assuming the following colours when progressing around the board from "GO"; these are used in most European versions anyway: Brown, Light Blue, Pink, Orange, Red, Yellow, Green, Dark Blue.

Actually, according to the official rules, PaSTE's strategy doesn't sting as much as he might suggest, but it does hurt quite a lot. It's not effective in a one-on-one game, but if there are multiple players still alive, you can at the very least, cause your creditor some grief.

What causes the major hurt is that your creditor has three options for each property when you declare bankrupcy to him/her:
A) Pay the mortgage right now
B) Pay a 10% "transfer fee" then later, unmortgage for mortgage value + 10% again
C) Pay nothing now, then unmortgage for mortgage value + 2 seperate 10% mortgage value fees.

So either you deny them use of the property for a longer time or they blow a lot of cash at once. It's not a Super Weapon, but if your creditor is barely in the game, you keep him/her from becoming much stronger from your property.

In conclusion, Monopoly is good, I need to get more sleep, and boredom is a Good Thing

From the Official Rules of Monopoly, "... he must turn over to that player all that he has of value and retire from the game." A bankrupt player cannot do anything at all including mortgage any properties. Some like to allow a player to trade after being declared bankrupt *if* they can get enough funds to payoff the debt but that is not allowed by the rules -- there are no provisions for coming out of bankruptcy. The moment a player is bankrupt there is nothing left for them to do.

Prior to throwing the dice a player could in theory use the tactic described to reduce their net value but we (the group of people I play with) expect every player to always improve their overall position with every action taken. Likewise, prior to throwing the dice, a smart player could make trades to improve their cash position enough in order to avoid bankruptcy; again with the same expectation.

If a player takes an unreasonable (in the sense that they aren't improving their overall position) action we won't play with them again in the future. A trade can obviously be deemed reasonable even if the player ends up with less cash. A trade can be deemed reasonable even if the player ends up with less net worth (in fact, this is almost always the case for one of the traders (exactly even trades are unlikely, unnecessary, and could even be deemed unreasonable)). A trader can obviously over-value a trade out of a simple lack of experience and this is not necessarily deemed unreasonable. If the trader is honestly attempting to improve their overall position but just makes an error in judgment then that is not deemed unreasonable although it would be good to help the player learn and improve later. Taking advantage of an inexperienced player is mean spirited. It is possible for a trader to improve their net worth yet still be deemed unreasonable, e.g. if they own the unimproved and not mortgaged orange monopoly and trade New York Avenue for \$201. Obviously breaking the monopoly for a net worth gain of \$1 is unreasonable.

There is no option C.

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