Custom Rules for Risk

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Overview

This document contains an appendix and footnotes at the end.

The objective of this rule update is to deal with a couple of issues with the classic rules of Risk and pull in a few elements from Castle Risk and add some "political gambling" and alliances. A primary concern is the way turning in cards produces larger and larger armies, which seems unrealistic and makes the game unstable. It may be meant to bring the game to a reliable conclusion, but probably leads mainly to a drawn-out oscillation (2) between the last two players who are by the way forced to use the army pieces of defeated players to represent the ridiculous numbers of armies produced by card turn-ins at the end game.

This custom set of rules consists of several new elements:

1. All six armies are placed on the board. Up to four of them are "allied armies."

2. Cards work as in classic Risk, but are turned in for either armies or for "factories." 

2.1. Army turn-ins do not accumulate, but are always based on a die roll.

2.2. Factories produce armies every turn on the same spot (which may be conquered by others).

3. Players can use allied armies, but may have to play poker against other players for the right to do so.

3.1. Players bet their future armies when they play poker.

3.2. If a player loses all their armies at poker, they get none when their turn comes (except for factories).

Setting up The Game

1. When the process is done, all six armies will be on the board, player armies and allied armies. The allied territories will have two armies each, but three randomly selected territories shall have and additional three armies each.

2. First, deal Risk cards to all players and all allied armies. Every army that is not assigned to a human player shall be an allied army. Each real player shall count out twenty armies to be distributed at will.

3. On each Risk card territory of an allied army, place two armies. Then choose three cards at random from the stack of cards for that army and place three more on each of these three territories. This gives each allied army 7 x 2 = 14 plus 3 x 3 = 9 for a total of 23 armies. Every real player starts with 20, then immediately gets three at the start of their turn. This makes things about even.

4. There will be at most four allied armies. This will be explained later, but players play poker for the right to use the allied armies after their own turns. As such, each allied army is assigned at least one poker suit ♥ ♦ ♠ ♣, hearts, diamonds, spades, clubs (3). The idea is that one must not only win a poker hand, but also have at least one card in the suit of that army in order to take control of that army.

5. Shuffle all the Risk cards together and put them into a pile. The player with the high dice roll goes first, and play proceeds clockwise.

How to Play

1. When it's your turn, first tally up your armies. If you took part in a poker game since your last turn, you'll already have armies counted out and you must play with what you have on hand. This will be explained later. Regardless of poker play, if you have any factories, place two armies on each territory with a factory. 

2. If you have five Risk cards in your hand, you must turn in a set of three cards. Otherwise, if you have a matching set (1) you may turn it in at this time, and place two extra armies on the territory for each card for which you control the territory on the card.

3. Place your armies. Begin your campaign. You are free to attack any territory you can, including all allies. If you are playing an allied army, however, you cannot attack your own territories.

4. At the end of your turn you may:

4.1. Perform one troop transfer (see "Troop Transfers" below).

4.2. If you conquered at least one territory, draw one Risk card and one poker card.

4.2.1. Do not draw a poker card when playing an allied army.

4.2.2. If you already have five poker cards, you can choose to either discard one before drawing, or not draw.

4.3. You may turn in sets of Risk cards at the end of your turn to buy factories and place them on any of your territories you wish.

4.4. If you have at least one poker card, you may make a bid to play an allied army. If you have five poker cards, then you must choose an allied army to play.

Using Allied Armies

1. Announce your intent to use which allied army. If no other players challenge you, you are free to use the army. Skip the poker playing and count out the allied armies in exactly the same way as your own army, counting out armies, using cards, factories, etc.

2. If challenged, a player is chosen to be the dealer.

2.1. All players taking a hand in the game count out their armies (including factories) to make their betting pools, or, if they already counted a pool, use those armies. If they already lost all their armies gambling, they cannot take a hand.

2.2. All players ante up.

3. You must choose one or more cards from the pile you've accumulated (a maximum of two for Texas Hold 'Em, for instance. See below for Texas Hold 'Em rules). Set the rest of your cards aside. Other players may choose from their poker piles in the same manner.

4. The dealer deals per the rules of the game.

5. If you win the hand, you get the pot. If you have at least one card of the suit of the army you declared for in Step #1, you may use it, otherwise your turn ends and you keep the pot.

5.1. To use an allied army, play it the same as your own, started at Step #2 under How to Play above. Turn in cards, get armies for territories and factories, deploy them where you will, campaign, then get Risk cards and troop transfers. Note that only players that play an ally have the right to look at that ally's Risk cards.

6. If you lose the poker hand, the winner gets the pot (converted to their own army color). You may choose to keep playing, if you have any armies left in your pool. At this point you still have the option to start with poker cards from your stack, or just be dealt in entirely by the dealer.

Card Turn-ins

Factories vs. Immediate Armies from Cards

Cards work differently in the New Rules. There is no "perpetual growth" of values of turn-ins, for one. You can either turn in a set of cards at the start of your turn for some number of armies determined by two-die roll (2-12 armies), or at the end of your turn to get a factory on one of your territories. Factories produce two armies on the territory where they are located, forever, but they may be conquered by other players, who then get the armies. For immediate armies from a card turn-in, roll two dice.

Allied Armies

Playing Poker for Control

All armies are on the board at all times (until they are wiped out). If there are only two players, then four of these armies will be allied armies, able to be used by any and all "live" players. Each allied army is assigned at least one poker suit, i.e., hearts, diamonds, clubs, spades, or ♥ ♦ ♣ ♠. At the end of every successful turn, in addition to a Risk card, a player draws a card from a poker deck.

NOTE: The queen shall be the high card in the hearts and diamonds, ♥ ♦ the red suits (3).

The right to use an allied army is accomplished by winning a hand of poker against the other players, or being unchallenged. The way a poker game works is that at the end of your turn you can declare the intent to use one of the allied armies. If challenged, you must win the hand, and your winning hand must contain at least one card in the suit of that army you want to control. If you lose a hand, you can keep playing as long as you have armies to bet with.

Any poker game (five card draw, seven card stud, Texas Hold'em, etc.) may be played--it's the dealer's choice. Players may begin with any number of poker cards they have in their already drawn poker card pile, if they so choose, and be dealt the remainder. For instance, for five card draw a player may elect to use up to five of their accumulated cards, while for Texas Hold'em one may choose to use up to two accumulated cards as one's "hole cards." Any additional cards are dealt by the dealer. With every new hand, the player again has the option to go to their accumulated cards, if any remain.

Betting Future Armies

A player bets with armies they will get on their next term. By doing so they forfeit a new levy of armies at the start of their next turn (except for factories). They are, in effect, raising their levy now. Their next levy occurs on the turn after their next turn.

Before the first hand, each player taking a hand in the poker game must compute the number of armies they would receive for territory, continent bonuses, and factories and place that in their betting pile. If a player previously played poker and still has armies left over from that, the leftover armies are their betting pool, that is, no new army count. Any new player can join the game at the beginning of a hand.

The ante is one army.

Texas Hold'em

Also known as Eastern United States Hold'em.

For Texas Hold'em, a player can select up to two cards from their accumulated pile of poker cards. Any additional cards are dealt by the dealer. For each new hand, a player has the option of starting with cards from their collection.

For Texas Hold'em, players ante up one army, then are dealt up to two "hole cards" (depending upon how many accumulated cards each player starts with). The dealer then burns one card before turning up one card ("the flop"). Betting begins with the player whose turn it is, going around giving all players the chance to check, call, raise, or fold. The dealer burns a card and lays out the next face-up card ("the turn") and betting resumes. A player may go all-in, and all players must call this bet, any raises going into a side pot. The final burn-and-turn card is "the river." The best 5-card hand made from a player's hand and the two "hole cards" wins the pot. If hands are tied, the pot is split, but if the player whose turn it is wins, and their winning hand contains the suit of the allied army they selected, they gets to use that allied army. Winning players convert all armies in the pot into their own color(s).

Simplified Poker Play

The dealer may decide to play a simpler game like five card draw. All players may build their hands from their accumulated cards in any case.

Playing an Allied Army

An allied army is played just like your own army. You accumulate Risk cards (but not poker cards), and may play them as normal to gain armies for the allied army. Only players that win the right to play an allied army may look at that army's cards, or, of course, anything else. Allied armies collect territory and continent bonuses as well as two armies for any factory on its territory.

A player cannot play poker as an allied army.

Poker Tricks

Playing poker for allied control can have interesting side-effects. One is that one can win more armies above and beyond the normal levy one gets at the start of one's turn. By the same token, one can take away armies from one's opponents, thereby weakening them. Another interesting side-effect is that if one plays poker, one counts out one's armies as they are now, which may allow one to avoid the effects of territorial losses over the course of the game until one's next turn.

Troop Transfers

At the end of a turn, a player is able to transfer any number of armies from one territory to another over any contiguous path through territories controlled by the player. Allied armies may also make the same sort of transfer once campaigning is over.

The path may be of any length, but only one of these "contiguous transfers" may be made per turn, at the end of the player's turn.

Getting Armies

At the start of a turn, a player is always awarded two armies for every factory on every territory that they control, regardless of whether they played poker since their previous turn. These armies, of course, are deployed on the territories where the factories are located.

Next, if a player played a poker game since their last term, they get the "betting pile" (which may now be empty, or contain poker winnings) which they counted out for the game. In other words, their "troop levy" already happened, so they get no new one until next turn (or poker game).

Barring poker play, at the beginning of their turn, a player receives the total count of territories divided by three plus continent bonuses, as in classic Risk. Next, they receives two armies for every factory on any territory they controls. They can play any Risk cards in exchange for armies (by roll of two dice).

At the end of his turn, a player may play cards to buy factories (which start to pay off the following turn).

AGAIN: If a player has already counted up his betting pile for a poker game prior to his turn, he does not count up his territory and continent bonuses again upon the start of his turn. He simply places all armies (if any) left in his betting pile. He does, however, get factory armies and may turn in Risk cards for armies, regardless of previous poker participation.

If a player fails to get territory and continent bonuses on their turn due to poker losses, they will get them at the start of his next turn or at the next poker hand they joins, whichever comes first.

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APPENDIX

Values of Factories and Turn-in Armies

The relative value of a factory versus a set of armies for a card turn-in are both computed based on the average number of turns required to get another set of cards to turn in. I'm guaranteed to get another set to turn in after five cards. If a factory gives two armies a turn, that's 10 armies. Turning in for armies immediately should be somehow "equivalent."

The way I'm working out whether these are equivalent is based on how long it takes to collect another set of cards to turn in. In other words, I want the average number of armies a player gets over time to be the same, regardless of building a factory or getting armies immediately.

I can either get a factory for the turn-in at the end of my turn, which starts to give me two armies per turn forever after, or I can turn in at the beginning for some number of armies immediately. I am thinking rolling for the armies, two dice, for 2-12 armies, with an average of 7.

At the start of a turn when I turn in cards, I have an average army levy value of 7, which I can use now. If I turn in for a factory, it's at the end of a turn, so I get six armies by my next soonest card turn-in, eight by four cards, and ten by the guaranteed turn-in of five cards.

By the same token, I may get up to 12 armies which would be two more than the ten I get by worst-case turn-in with a factory.

The details of the maths need to be worked out. Basically, it depends upon the probability of drawing a complete set of cards (three-of-a-kind or one-of-each (1) ) which becomes guaranteed at five cards. One is guaranteed armies from a factory. We need to match that against the probability distribution of how many armies one gets from two Vegas die rolled in either three, four, or five turns.

Instability of Classic Risk Card Turn-ins

One premise of this new system is that a) accelerating card turn-in levies are unrealistic and b) they destabilise the game (2) rather than bring it to a timely, guaranteed conclusion.

I need to document the way in which card turn-ins go HERE (1).

This may be an interesting math problem. I'm not sure which branch of mathematics is involves. Game Theory, obviously, but along with the factory versus army problem, might represent some kind of problem in economics...who knows?

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Footnotes

(1) A set of Risk cards is one-of-each or three-of-a-kind. There are infantry, cavalry, and artillery cards. 

(2) Exponential card turn-ins in classic Risk may lead to instability. This would be an interesting system to model mathematically.

(3) The queen is the high card in the red suits (hearts, diamonds ♥ ♦ ), while the king is still the high card in black suits (clubs, spades ♠ ♣)