# Monopoly/Strategy

STRATEGY
Monopoly involves a substantial portion of luck with the roll of the dice to determinine whether a player gets to own key properties or lands on squares with high rents. Even the initial misfortune of going last is a significant disadvantage because one is more likely to land on property which has already been bought and therefore be forced to pay rent instead of having an opportunity to buy unowned property.
There are, however, many strategic decisions which allow skilled players to win more often than the unskilled. The fundamental strategic point is that securing monopolies (all the properties in a colour group) is the way to amass wealth, but monopolies arise more through trade than through chance. In a standard six-player game, there is a fair probability that none of the players will be able to buy all of one colour group without trading. If no monopolies emerge by chance, and the players do not trade, it is rare for anyone to be eliminated. The game could last indefinitely with the ₩200 for passing Go, thus keeping the poorer players from going bankrupt.
Since monopolies are the key to victory, and monopolies arise by the exchange of property from one player to another, a well-played game of Monopoly is from start to finish a game of trading, negotiation, and diplomacy as well as the occasional well-timed "tactical dirty trick" (such as creating a building shortage).

## Trading and blocking

Players must be aware of the strategic value of each property at any particular time, considering who needs it to complete a monopoly and which properties in that group are as yet unowned. As soon as two players between them own all the properties in two colour groups, they are likely to make some sort of bargain whereby each of them obtains a monopoly because, if they are the first to be able to build houses and hotels, they each have a much better chance of winning.

## Cash management

Apart from property trading, the most important strategic decisions involve cash management. There is great pressure to acquire properties and to build houses and hotels as soon as possible in order to collect large rents. On the other hand, a player who does not have the cash to pay a large rent may be forced to tear down houses, getting only half the invested cash back. It can be as dangerous to build as it is to refrain from building.
Furthermore, holding cash is important when unowned property is landed on and must be auctioned, as well as important when there is a shortage of houses and the remaining houses are auctioned. Being cash poor can lead to frustration when another player gets a good deal in an auction in which you cannot compete. Also, holding cash allows one to cut favorable deals with a player who is cash poor. For example, a player who would be forced to undevelop their property to pay a large rent might decide to sell some other undeveloped property for cash, even though they would normally be reluctant to trade property for anything other than property. If only one player has significant cash reserves, that player has considerable negotiating leverage.
Because of the importance of cash, many players treat any ungrouped property they own primarily as a cash source through which they can develop their monopolies. Holding unmortgaged and undeveloped property is rather similar to holding a cash reserve because mortgaging is relatively inexpensive. To de-mortgage a mortgaged property costs only 10% more than the cash received for mortgaging whereas to rebuild a house one has torn down costs 100% more than the cash received for tearing it down.
Another thing to be considered when it comes to cash is that a player is not required by the official Monopoly rules nor the Official Tournament Rules to disclose to opponents how much cash he or she has. This is important because in many situations opponents can take an advantage when estimating how much cash the other player has. For example, a player may be more willing to trade an opponent the final property in a color group (thereby giving that opponent a monopoly) if the player sees that the opponent doesn't have enough cash to place buildings on that monopoly.
While the route to victory in Monopoly is clearly to build houses and hotels to take maximum rent, a player is unlikely to be able to acquire a complete set of properties in a game with four or more participants, except by trading. It is therefore very useful to be able to determine which colour groups are more valuable.
The overall value of any property is determined by a combination of four factors:
* Buying cost (not usually important as players can't choose where they land and players usually buy everything they land on)
* House/hotel cost
* Rent charged
* Position on the board (visitation frequency)
The first three factors are obvious: valuable properties have a better ratio of expenditure to return. The fourth factor is more interesting because it determines how often players will land on each property and thus pay rent to its owner. In recent years, computer simulations have allowed a probabilistic analysis of the frequency with which each square is visited during the average game.
For instance, the Jail square is the most commonly visited space in the game because of the "Go to Jail" square, the chance and community chest cards directing a player there and the rule that a throw of three successive doubles also sends a player there. Combined with the fact that a player is most likely to throw 6, 7, or 8 when moving away from Jail than he is to throw 2, 3, 4, 5, 9, 10, 11 or 12, this means that the overall probability of visiting an orange property is far higher than that of visiting a light purple/pink property, for instance. Similarly, because there are only two properties in each of the dark blue and dark purple/brown sets, these sets are visited correspondingly less often, although Boardwalk does have a chance card.

### Best improvable properties

Among improvable properties (properties that can have houses or hotels built on them), the orange set is far superior to any other: It is visited quite often (it is located at a moderate distance after the Jail square), and property costs are relatively cheap, and the prospect of collecting damaging rents without too much investment is excellent.
The runner-up for best improvable properties is the red set—statistics demonstrate that while the orange are landed on more often as a group, Illinois Avenue (Equivalent Property in U.K. Edition = Trafalgar Square) is landed on most often as a single entity. In addition, it catches many people who happen to overrun the orange properties on their way out of jail.
As a general rule, the second colour group on each side of the board has a far better cost-to-value ratio because the houses and hotels cost the same as the first colour group but yield higher rent. The major exception to this strategy is the red group over the yellow group for the reasons outlined above.

### Other improvable properties

Similarly to red, the light purple set gets many landings from people leaving jail but not getting very far. The light blue set, on the other hand, receives many hits from people coming from the Go square. The dark purple/brown set is far inferior; though inexpensive, is often skipped and collects little rent. The yellow set doesn't get nearly as many hits as the reds, but they can dominate later in the game. The Green set is very expensive, although with hotels it will collect the most income. The dark blue set has only two properties, so they are landed on less often than the other sets; however, their high rents can often cripple other players. A player who uses these relative values as a guide to trading ought to do better than chance in the long run.

## Tactics

* The most likely number to roll is 7 (given that you are using two dice each with 6 faces). As you depart from 7, the probabilities decrease piecewise. In other words, the probability of rolling 6, or 8, is slightly less than 7; the probability of rolling 5 or 9 slightly less, still, until you reach 2 and 12, with the least probabilities. Use this information to predict where both you or your opponents will land on their next roll. If an opponent is approaching a street you own, the best property to build an extra house on is the one located as close to seven spaces distant from his as possible.
* Early in the game when many properties are unowned, it is a disadvantage to be in Jail. A player should pay the fine and get moving with an eye to landing on unowned property or at least passing Go. Later in the game, when properties are highly developed, it can be an advantage to be in Jail so as to avoid paying high rents. At that stage it is better to refuse to pay the fine and to attempt to roll doubles.
* The average income a player receives from one round of the board is ₩170. This includes rent earned, rent paid, money from Go, fines and rewards.
* When landing on the Income Tax square, a player is not allowed to calculate his assets before deciding whether to pay ₩200 or 10% of his assets. However, there is a simple rule of thumb that works well in practice. Since players start with ₩1,500 and collect ₩200 for passing Go each time, it is generally better to pay 10% until passing Go for the third time. Barring exceptionally good or bad fortune, the third time past Go is the time when a player's assets exceed ₩2,000, and once above ₩2,000, a player is not likely to dip below until late in the game when he has paid some drastic rents and is on the verge of elimination.
* The increased rent for houses takes a long time to pay off the initial investment if there are only one or two houses per property. Starting with the third house, rents rise dramatically and pay off the investment correspondingly faster. If a player owns two colour groups, it is much better for them to put three or four houses on each property in one group (leaving the other group undeveloped) than it is to put two houses everywhere. Similarly, it is unwise for a player to deeply mortgage themselves to develop a monopoly unless they can build to at least the third house.
* If there is a shortage of houses, players should consider buying the last houses rather than buying hotels because each hotel built returns four houses to the bank for other players to use. When there are no houses in the bank, no one else can build houses. Also, players with hotels can't easily convert them to cash in this situation; they would have to strip an entire colour group of its hotels to raise money since buildings must be removed evenly from a colour group and because the hotels cannot be exchanged for houses since there are no houses in the bank. The owners of inexpensive monopolies should be particularly eager to use this tactic to prevent the owners of expensive monopolies from fully developing.
* Occasionally, when there is a housing shortage, it can pay to tear down houses on one colour group to immediately build them on a different colour group. However, if another player declares an interest in buying the houses you have torn down, you will have to outbid that player for them, so this tactic pays off only when you are buying the torn down houses for expensive properties anyway, and you have much cash, and the other likely bidders are cash poor.
* If the game is deadlocked with players holding properties of different color groups, the railway stations and utility properties can prove to be a great source of income. A crafty player who is able to acquire all four railroads collects ₩200 every time another player lands on them. In addition, the railroads are very frequently landed on as one is located on each side of the board and the presence of chance cards which directs a player to a certain railway station.. This can prove to be a real thorn to other players, as the ₩200 rent robs them of their ₩200 collected from passing the GO Square. Even in games with monopolies being developed, this can severely hinder an opponents cash flow in developing their monopoly, sometimes forcing them to tear down houses or mortgage other properties. The utility properties are not as universally useful. In games with four or more players, they can be a cost-efficient way of collecting rent if the player owns both utilities and monopolies have yet to be established. Their value however, drops considerably if monopolies have been fully established, the player only owns one of the set or in a game with only two or three players.
* In a game with many players, it is advantageous to make trades even if you are "getting the short end of the stick" because the trade will be a burden for your opponents. For example, there is a four-player game and player 1 is going to trade with player 2. They are going to give each other properties so that each will then have a monopoly. The space that player 1 will get is worth a little less than the space he is going to give player 2. Should he go ahead and trade? Yes. Let’s say that player 1 is trading away a space worth 4 units in return for one worth 3 units. Although he will net -1 units initially, the other two players in the game (players 3 and 4) will be forced to pay for player 2’s newly acquired monopoly. This will offset the -1 unit disadvantage of the trade. In other words, player 1 is getting the advantage because the trade, although initially bad for him, will hinder the other 2 players in the game. When in doubt, it is usually best to go ahead and trade (if not for any other reason, just to keep the game moving. Many games are ruined because all four players are stuck in a stalemate, refusing to trade anything).
* When building houses in a colour group, a player should usually build the first house of a level of houses on the last property of the colour group. The second house of the level should be usually built on the first property of the colour group, unless the colour group is the light-blue or orange colour group. The same applies to hotels (which, for practical purposes, can be considered as five houses or four houses when the standardized Rules for a Short Game are used). This tactic is based on the fact that usually the rent mathematical expectancy (the average of the expected rent) is higher when houses are built in that order.
       Example for the light-purple colour group:
| Step | Property 1 | Property 2 | Property 3 |
| 1 | | | House |
| 2 | House | | House |
| 3 | House | House | House |
* A player should always be diplomatic with players because, especially at the end of the game, opponents who are likely to lose can take revenge of players who are likely to win and make them lose against other players who are also likely to win. For example, let us say there is a player who cannot pay his debt without making trades; but, because of his situation of being likely to go bankrupt in the next few turns anyway, sells all his properties at a relatively low price to an opponent other than the creditor of that debt. Then the player who gets the properties is also likely to form complete colour groups with the newly acquired properties and is likely to defeat the creditor of the debt. Such a player who decides who wins or loses the game is sometimes referred to as a "king-maker" because that player decides who gets "crowned".
* An interesting strategy when the auctioning rule is in play is to carefully monitor the cash flow of the other players when you are buying property. Generally early in the game, when players are busy buying properties, they get rather low on cash rather quickly. This is normally not that bad since the rents for properties are of minor value in the beginning, but you can turn this situation in your favor. When you land on a property, instead of buying it from the bank at the price listed, you can take advantage of the fact that the rest of the players have little money and decide to auction instead. By doing this you can actually buy properties for less than the assessed value (the value listed on the board). Doing this can give you a substantial tactical advantage by increasing your assets without spending as much money and gain money earning properties as well. This can be risky however, as other players may try to outbid you anyway by mortgaging properties or "pull a rabbit out of their hat" and come up with some cash you didn't notice earlier (like hiding a ₩500 note under a stack of ₩1 notes, for instance). This strategy works best if you are in a cash-strong position when the other players have small amounts of cash and when there are fewer players in the game, especially just two players.

## External links

* Monopoly Revisited by Ian Stewart
* Probabilities in the Game of Monopoly
* Probabilities in the Game of Monopoly (UK Edition)
* How to win at Monopoly - a SureFire Strategy
* Good strategy of monopoly
* Interesting Discussions of General and Specific Monopoly Strategies
* Free, Online Monopoly Simulator