Risk Board Game

Risk is a turn-based strategy board game focused on world domination. The objective is to conquer all of the territories of the world by eliminating one or more opposing players. For the digital version on PC and mobile, please see https://risk-global-domination.fandom.com/wiki/Risk

Standard
Setting up the Risk board for play is more involved than in many other games. An Alternate way to do this is to deal out the Risk territory cards with each person getting assigned to different Territories.
 * Each player first counts out a number of playing pieces or "armies" for initial deployment. The number of armies that begins the game depends on the number of players: 40 armies for two players: 35 armies each if three players; 30 armies each if four players; 25 armies each if five players; and 20 armies each if six players.
 * Players then take turns claiming territories by placing an army on an unoccupied territory until all the territories are occupied.
 * Players then take turns placing their remaining armies on their territories.For each star on the card put down a troop. After all armies have been placed the actual game begins with another roll of a die used to determine the playing order.

Player turn
There are five phases to a player's turn: placing reinforcements, turning in Risk cards, attacking, fortifying, and receiving Risk cards.

Drafting troops
At the beginning of a player's turn, the player drafts new armies (troops) and then distributes these pieces around the board to reinforce any territory occupied by that player. The number of armies drafted is determined by summing the following several rules (official versions have varied with various editions):
 * Territories and Cities formula; draft armies equal to the number of occupied territories plus the number of cities in those occupied territories divided by three and rounded down to the nearest integer. If this result is less than three, round up to three armies.
 * Continent Bonus; The player receives additional armies for occupying an entire continent, equal to the continent bonus shown on the game board.
 * One additional army for every capital within the player's occupied territories.
 * Any armies gained from turning in Risk Cards.

Turning in Risk cards
The player may receive armies by turning in a set of three Risk cards. A set of Risk cards consists of one of the following: If a player has five cards before the end of his turn, he must trade in a set immediately. The player places the armies on any of his territories.
 * three cards depicting the same unit (e.g. all three cards have cavalry pictures)
 * three cards showing one of each type of Risk unit (soldier, cavalry, artillery).

The first set to be turned is worth 4 reinforcements; the second is worth 6; third 8; fourth 10; fifth 12; sixth 15 and for every additional set thereafter 5 more armies than the previous set turned in. Also, if a player owns one or more of the territories depicted on the set of turned in cards, the player may choose one of these territories to be awarded two additional armies that must be placed in that territory.

Attacking
Attacks can only be originated by the player currently having a turn, and must be launched from one of the attacker's territories, against an adjacent or sea-lane connected territory occupied by an opposing player. The outcomes of battles are decided by rolling dice. Each dice roll determines the outcome of an individual attack, however a player may repeat this process during the attack phase of the turn, attacking any number of territories any number of times before yielding the turn to the next player. Attacking is optional; a player may decline to attack at all during the turn.

The attacking player attacks with one, two, or three armies, rolling a corresponding one, two or three die. At least one army must remain behind in the attacking territory not involved in the attack, as a territory may never be left unoccupied. The defending player must resist the attack with one or two armies (using at most the number of armies currently occupying the defended territory)[4 ] by rolling a corresponding one or two die. If an attack successfully eliminates the final defending army within a territory, the attacking player then must occupy the newly conquered territory with an equal or greater number of armies as used in the attack. There is no limit to the total number of additional armies that may be sent in to occupy, providing at least one army remains behind in the original attacking territory.
 * The attacker's highest die number is compared against the defender's highest die. The highest number wins, with the defender winning in the event of a tie.
 * The attacker's next highest die is compared against the defender's second-highest die (assuming the defender committed a second army).
 * Any extra dice (dice not matched against a defending army) are disregarded and do not affect the results.
 * With each dice comparison, the loser removes one army from his territory from the game board.

If an attacking player occupies a defender's last territory, thus eliminating them from the game, the attacker acquires all of the defender's Risk cards. If the conquering player now has five or more cards, he must trade in sets until he has fewer than five. The gained armies are placed immediately.

Fortifying!
When finished attacking and before passing the turn over to the next player, a player has the option to maneuver any number of armies from a single territory occupied by the player into an adjacent territory occupied by the same player. Under an alternate rule, the maneuvering armies may travel through as many territories to their final destination as desired, providing that all involved pass-through territories are contiguous and occupied by that same player. As always, at least one army must be left in the originating territory.

Receiving a Risk card
If the player has conquered at least one territory during the turn, the player draws a Risk card from the deck, and then trades it. Play then proceeds clockwise to the next player.



Strategy
Risiko (Italian version) in play Basic strategy

The official rulebook gives three basic strategic tips for the classic rules: Alliances
 * First, players should control entire continents to get the bonus reinforcement armies.
 * Second, players should watch their borders for buildups of armies that could imply an upcoming attack.
 * Third, players should build up armies on their own borders for better defense.

The rules of Risk do not endorse or prohibit alliances or truces. Thus players often form unofficial treaties for various reasons, such as safeguarding themselves from attacks on one border while they concentrate their forces elsewhere, or eliminating a player who has grown too strong. Because these agreements are not enforceable by the rules, these agreements are often broken. Alliance making/breaking can be one of the most important elements of the game, and it adds human interaction to a decidedly probabilistic game.

Dice probabilities
Defenders always win ties when dice are rolled. This gives the defending player the advantage in "one-on-one" fights, but the attacker's ability to use more dice offsets this advantage, as indicated in the dice probability charts below. Actually capturing a territory depends on the number of attacking and defending armies and the associated probabilities can be expressed analytically using Markov chains,[5][6][7] or studied numerically using stochastic simulation.

It is advantageous to always roll the maximum number of dice. (Exception: In some cases, an attacker may not wish to move men into a 'dead-end' territory. If this is the case, he might choose to roll fewer than three.)

The table below states the probabilities of all possible outcomes of one attacker dice roll and one defender dice roll:

Thus when rolling three dice against two dice (the most each player can roll), or two against one, the attacker has a slight advantage, otherwise the defender has an advantage. When large armies face off, a player will tend to gain a greater advantage over his opponent by attacking rather than defending. (Multiple opponents can change the prudence of such a strategy, however.)

The following table shows the probabilities that the attacker wins a whole battle between two countries (a sequence of dice rolls): The number of attacking armies does not include the minimum one army that must be left behind in the territory (i.e. so if the attacking territory has 10 armies total, it has maximum 9 attacking armies). Lime green indicates an advantage to the attacker, (i.e. that the probability to win is larger than 50%), and red an advantage to the defender.

A common situation is that the attacker wants to take over a whole region of countries during the same round, by a series of battles. After each successful battle, the attacker leaves one army in that country, and continues with the remaining attacking armies into next country. The following table shows the average number of countries that the attacker can take over, as well as the 90 percentile, starting with a certain number of attacking armies in the first battle. A fixed number of armies is assumed to defend each country.

Rule variations
Over the years, Parker Brothers and Hasbro have published many different editions of rules for the game.

one-player Risk
The rules for this 1-player game were developed by Michael Levin of Philadelphia, Pennsylvania, and were included within the Official Rules published in 1975.[9]

This 1-player version is played according to the traditional rules of Risk. Each player takes 40 armies and alternately places one army on an unoccupied territory until each has occupied 14 territories. The remaining armies are alternately distributed on the occupied territories. The remaining 14 territories are occupied by a force called the Allied Army. These armies are composed of playing pieces different in color from those used by the two players. Two Allied Armies will be placed on each unoccupied territory for a total of 28 armies.

Each player accumulates armies in the traditional manner. At the beginning of each turn, the Allied Army is entitled to one half the number of armies the player receives, rounding down. So, if a player obtains a total of nine armies, the Allied Army is entitled to four. Each player places the armies on the board according to the traditional rules. After a player has accumulated his armies, placed them on the board and completed his attacks (but prior to the fortifying phase) the opposing player places the number of Allied Armies (determined above) in Allied occupied territories.

Each player attacks according to the traditional rules. A player may attack the other player or the Allied Army. When a player attacks the Allied Army, the other player rolls the dice for the Allied Army. Immediately after the Allied Armies are placed, the player who placed them may act as the Allied Army and attack the other player's armies. He need not use the armies immediately but may allow them to accumulate in a territory. However, if they are not used, the other player may use them to his advantage when he gets the use of the Allied forces. When a player is commanding Allied forces he may not attack his own territories. Allied forces do not pick up Risk cards, and they accumulate armies only in the manner described above.

The first player may take his free move only after the second player has stopped attacking with the Allied Army. The Allied Army is not entitled to a free move.

The game ends when one player loses all his territories. If the Allied Army loses all its territories it may no longer obtain additional armies and game play is continued according to the traditional rules.

Capital Risk
Each player has a "capital" in one of the initially-occupied territories. The player to capture all capitals wins. Capital Risk often leads to much shorter games.

Secret Mission
The "Secret Mission Risk", which was the standard game in European editions for some decades[2] until 2003, gives each player a specific mission short of complete world domination. Players do not reveal their missions to each other until the end of the game, which is after the first player to complete the mission shows the Secret Mission Card and wins the game.

The missions are: In 2003, a different "Secret mission" version of the game was released, in which each player received four (easier) secret missions to complete.
 * capture Europe, Australia and one other continent
 * capture Europe, South America and one other continent
 * capture North America and Africa
 * capture Asia and South America
 * capture North America and Australia
 * capture 24 territories
 * destroy all armies of a named opponent or, in the case of being the named player oneself, to capture 24 territories
 * capture 18 territories and occupy each with two troops

Alternate card turn-in rules
In some editions, the cards display either one or two stars. Cards may be exchanged to draft a number of armies depending on the sum of these stars (limited from 2 to 10 stars) according to the table below.[10] Cards may be accumulated as long as the player wishes. The new armies are immediately deployed in any combination across the player's occupied territories.

One common house rule follows the same ratios of troops, but simply uses cards instead of stars. This "currency" method prevents the wild escalation of reinforcements that occurs with the traditional rules. Players are forced to turn in their cards if they have a full set of ten.

If an Objective has been accomplished on the player's turn, that player is prohibited from also drawing a Risk card on that turn. The territory on the card is irrelevant when drafting troops. An additional card exchange regime is to offer a fixed number of armies depending on the emblem on the card. Three cannons would receive four armies, three infantry would receive six armies, three cavalry would receive eight armies, and one of each emblem would receive 10 armies.

Yet another card exchange regime follows the escalating exchange rules, but after awarding 15 armies for the sixth exchanged set the number is reset to the original four armies before increasing again with each exchange.

Other rule variations
The official rulebook suggests variations to the game-play mechanics for "Risk experts," any or all of which can be used depending on player preference.[4] These suggestions include: In addition to these official variations, many computer and Internet versions have different rules, and gaming clubs often use house rules or competition-adjusted rules. These may include structure such as forts, freeplay (players take turns simultaneously), or other rules.
 * Reducing the rate at which Risk card sets increase in value so that they only go up by 1 each time
 * Allowing for armies to move to any controlled territory if it has contiguity between it and its destination. (Rather than only an immediate neighbor)
 * Granting an attack advantage (the option to re-roll one die per battle) when attacking from or to a territory for which the attacker holds a Risk card.
 * Granting attackers the ability to change one of the dice rolled so that a six is showing. An attacker may do this only once per turn.

Territories
The following is a typical layout of the Risk game board, with a table of the corresponding continent and territory names.[11] Each territory on the typical Risk game board represents a real-life geographical or political region on Earth. As such, the territoryborders are drawn to resemble the geography of those regions. This provides an interior space on which to place the army units, adds an element of realism to the game, and also adds complexity.

A representation of the Risk game board, showing the different territories, an approximation of their borders, and an approximation of their usual coloring.