The Open-Ended Machine
The Open-Ended Machine (TŒM ) uses narratives to create and to rule on the outcomes of a conflict or plan by drawing from the knowledge and imagination of players and umpires. Anything can be modeled. The fidelity of the model depends on the ability of the participants to identify what matters in the resolution of initiatives. TŒM provides statistically-based mechanics to determine the outcome of player’s initiatives. Gamers familiar with the MATRIX system will recognize the principle of assigning probability to an argument on the basis of its soundness.
A game is made of a scenario and a set of directives on the scope of each initiative. A game begins with a scenario describing the setting and objectives of individual factions. Through conducting initiatives, players command a faction to position themselves to achieve these goals. Positioning is the gradual process by which a scenario evolves from setup to completion through the alteration of the situation.
The participants are either players or umpires. Each player is assigned a goal and may be assigned an individual, a group or some other kind of organization which they control. What is controlled by a player is thereby referred to as afaction. A umpire doesn't control a faction but is instead in charge of the narrative, and is responsible for moderating the discussion and adjudicating initiatives by applying the TŒM game mechanics.
A player propose an initiative, which is an action (or event), an outcome, and any number of supporting or counter-arguments. Arguments are facts that either provided in the scenario briefing, or are made true by previous initiatives.The player who has the right to propose the next initiative is said to hold the initiative.
This section describes the flow of a game from the point when each player is assigned a faction to the moment when the scenario ends.
The player who proposes an initiative is said to be "holding the conch", in reference to the mechanism to designate the speaker in William's Golding's "Lord of the flies". Only the player holding the conch can propose an initiative. However, the analogy ends here since all players/umpires are encouraged to provide arguments and counter-arguments when appropriate.
The scope refers to the set of allowable initiatives that a player can propose; it can be open-ended or drawn from set of allowable actions. Scope can be changed as the result of an initiative if the umpire allows it. Another possible way to define the scope of an initiative is to associate a time span in which both the event and the outcome will be observed (e.g. an initiative per day).
As a general principle, the conch remains in the hands of the holder for a subsequent initiative if the proposed outcome is ruled true. Once an initiative fails, the conch is passed to the player for which it makes the most sense from a narrative perspective. For example: The mayor failed to pass a bylaw because of the action of a citizen group in a sub-argument, therefore, it makes sense to give the conch to the citizen group if it is a playing faction). In situations where all players hesitate or refuse to take up the conch, the umpire should intervene in a logical fashion, moving the overall situation toward a crisis point. This crisis point should move the narrative away from the objectives of all players.
- The conch holder proposes an initiative.
- All contribute arguments to the initiative, each argument is added if 1) it is orthogonal to other arguments 2) is certain to be true or has been resolved as true as a sub-initiative.
- The arguments are tallied and a probability is determined.
- The conch holder rolls 3D6.
- The umpire provides a narrative outcome.
- If the initiative was successful, the conch holder may keep the initiative, give it to any one player or give it back to the umpire. In the event that the initiative was unsuccessful, the umpire pass the conch to the player of his choice.
- Goto 1.
This game type rewards thoughtful gameplay and only rarely rewards far-fetched gambles. Furthermore, all other players must use the argument building phase to draw the conch in their direction in order to gain the initiative.
A initiative is one event, one action or an implicit set of actions that alter the course of a narrative. Each initiative is made of one event/action, a set of pro and counter-arguments and an outcome. The roll of 3D6 determined whether the event causes the outcome to be true. In absence of information, all events have a 50% chance of success (sum of 3D6 is equal or less than 10). Each supporting arguments increases the target number by one, each counter arguments decrease the target number by one. This roughly implies that each argument respectively doubles or halves the chance of a success. Everything can be used as an argument as long as all arguments are relevant and orthogonal to each other. The outcome of a past argument can be used to shape the likelihood of future arguments. The player that can make the best use of the developing situation is the most likely to take control of the narrative.
The procedure is described here in four steps The remainder of this section expand on the mechanics.
- Formulate an initiative A player (or the umpire) formulates an initiative. This can be an event, a simple action (e.g. I withdraw across the river) or a multi-action initiative (e.g. I always make a point of throwing lavish parties when French knights ask for hospitality.).
- Gather supporting arguments Compile a list of all possible facts that significantly aﬀect the probability of success of this initiative. Finally, each pro argument is equal to +1 while counter-argument are worth -2. The final target value is 10 plus the sum value of all arguments.
- Resolve the outcome Compare the sum of 3d6 and the target number. If this number is less or equal than the target, then the initiative succeeds. Otherwise, it fails.
- Prepare the outcome The umpire prepares a narrative outcome which describes how and why the initiative failed or succeeded. The outcome must spell out how the initiative has changed the position of a faction (e.g. You have lost the conﬁdence of your ally.).
An ideal initiative states an event that is sure to occur and specify that this even is causal to a given outcome. If there is no doubt that both the event occurs and that the event automatically causes the outcome to be true, there is no need for providing arguments: it just happens. If either or both the likelihood of an event and it's causal effect on the outcome is uncertain, then the argumentation phase is required.
The probability of an event or action will be considered as a whole. This means that if a player propose a chain of event as the core of one initiative: either none of it or the entire chain will take place. Arguments can be made by all players against individual component of the chain of events. Long chains or chains with a weak link are less likely to occur: it may be best to break down this chain into multiple initiatives.
The most simple outcome is a single statement which can be used later in the game as an argument. If the roll of dice indicates a success, the outcome is considered to be true and the event considered to have happened.
A player can propose more than one outcome to an event (or a chain of events). There is, however, a restriction on the relationship between outcomes that must be met. If a player choose to state two outcomes to an event, the second outcome must be possible ONLY if the first outcome is true. If a subsequent outcome is added, this latter outcome's truth must be conditional to any of the previous outcomes. The order in which the outcomes are stated is important, and cannot change once all other players are allowed to argue on the current initiative. Also, all players are allowed to argue on the causality between the event and each of the outcomes.
An initiative that fails doesn’t imply that the action didn’t take place but rather that another faction assumes the initiative; it no longer dominates the narrative and the expected outcome have failed to be realized.
An argument is a statement that describe a factor that enhances or decreases the probability of either an event/action from happening or the causality of an event to its outcome. Each argument must meets the following two properties: signiﬁcant and orthogonal to all other arguments.
An argument is relevant if it is logically linked to both the initiative and the desired outcome. A relevant argument is signiﬁcant if its inclusion can credibly support or obstruct the likelihood of an outcome. Anything can be used as an argument, unless restricted by the umpire.
All arguments, regardless of cardinality, must be able to stand alone. The umpire should be able to imagine a situation where every possible subset of arguments would make sense. In other words, no argument should be true conditionally to another argument used in the same initiative. An example of non-orthogonal arguments would be: because I am small and because I am not tall, or because I am small AND because I weight less than the average.
All arguments in TŒM should have equal weight. The umpire can assign alternative values to an argument (it is his/her game after all). However, there is another way to do this which may enrich the narrative outcome. However, playtesting indicated that a game flows more fluidly if counter-arguments weigh more than pro-arguments. As a result, counter-arguments have a weight of -2 while pro-arguments have a weight of +1. This weighing scheme ensures that the initiative change hands more often when gambles are made, and also compensates for the fact that counter-arguments usually are more deleterious that positive factors in real life.
The target number for all arguments is 10 + [number of pro-arguments] - [2 X number of counter-arguments]. The sum of 3D6 must be less or equal than the target number for the outcome to be true.
Expected consecutive successes
As a rule, ...
It is possible to shape the narrative by adding constraints. In these cases, the base target number is something different than the "neutral" narrative level. These constraints are either:
- Stated in the scenario briefing.
- Supported by external information.
- Set as the outcome of a previous initiative.
Example - A hand of poker
An initiative calls for a faction to draw a two pairs hand in a round of poker. There is no existing narrative constraints on poker playing in this scenario. However, a player demonstrate that the probability of this hand is 4.75%. The nearest narrative level to this value is "very unlikely" (rounding up rather than down). This means that this player can argue that the base target number for this initiative should be a 6. It will remain 6 for the rest of the game.
Optionally, a task-oriented scenarios can define certain tasks to be either Simple, technical or complex and define each faction into one of four possible training level at completing a task (Naive, Trained, Experienced or Elite).Simple tasks can be completed with a 50% probability even by an untrained faction, technical tasks require some training but no exceptional aptitude to complete. Finally, complex tasks are considered to be consistently doable only by masters or experts. The target values in the last three column of the table set the base probability for each combination of task difficulty and skill level.
For example, if a regular unit of riflemen (experienced) are told to apply cover fire (technical task), the base target number will be 12 instead of 10.
In the most simple case, if a die roll is more than the target number, the event as described fails to produce the outcome that was stated by the conch holder. There are ways to enrich the narrative of an outcome. This section describe how this can be done.
The number of possible successful outcomes equals the positive difference between the target number and the sum of the dice roll used to determine the success of the initiative. Outcomes becomes true in the order in which they were proposed by the conch holder.
Example: An initiative is made with four outcomes. The target number is 11 and the sum of 3D6 is 9. The first three (11-9) outcomes are said to be true, leaving the last one false.
One way to interpret a failure with n increments is to assume that: "had n fewer counter-arguments be significant, the outcome would have been different". To determine which arguments are primarily to blame, the umpire may select up to n counter-arguments as explanation for the initiative’s failure.
Player A proposes to lower all sails at the approach of a large gray cloud. And that the outcome is that the ship is ready to weather the storm. This is a task for his trained crew (10) which is complicated by high winds (-1) but reasonable as a reaction because of recent experience with the local weather(+1).
Total: 10 roll: 11.
Outcome: There would be one increment of failure. The umpire announce that had the strong wind not interfering, this would have been possible. Also, that the crew is now stranded up high in the rigging as the sea gets very rough.
A quantitative initiative is an initiative that attempts to set a numerical value from a more abstract context. In this situation, the event and the outcome is the same. The number of increments is used to modulate the factor by which the proposed figure is wrong. A success modulates the figure in the direction favourable to the interested party.
The factor by which the quantity in the estimate is affected is 2 per increment. A two increments success will multiply the estimate by (22= 4), while a failure by one increment would multiply the estimate by (2-1= 0.5). Less extreme factors can be used model better a situation.
An umpire is asked how much tax money was collected from a newly annexed village in the last year. From the scenario design, the umpires pulls the relevant facts:
- A typical village contains 100 hearth.
- The hearth tax is set to 1/2 Florin per year.
Initiative/outcome: A typical year would yield 50 Florins.
- The harvest was very good in the last two years (+1)
- People are resistant to the new lord (-1)
- The tax collectors are corrupted (-1)
Total: 9, roll: 10, collector's corruption is determined to be the top factor.
Outcome: Only 25 Florins were collected because the tax collectors are skimming the treasure.
Gameplay should proceed with as a little detail as possible. This is desirable because of the fractal nature of a TŒM game; where it is not possible to know beforehand which details are important and how finely they need to be defined. The quantitative argument is a kind of backfilling argument that attempts to pin a quantity from an abstract context. However, it is possible for a player to specify a detail from a more abstracted context. The limitation is that the details cannot be inconsistent with the narrative from the scenario and previous initiatives. The probability of these initiative is purely on the account of the backfilled detail since there is no need to specify an outcome for these initiatives.
Initative: I own a personal computer powerful enough to run most modern software.
- +1 Most household include one or more computers.
- +1 I’m technically savvy.
- +1 Computers are cheap nowadays and thus replaced often.
Total : 13, roll : 14, failure by 1 increment.
Outcome: You do own a computer, but it is an old clunker which can barely run the web browser. [Note how the umpire chose to use the blame rule to explain why the argument failed. The umpire could as well have denied the existence of the computer altogether, but he/she is in a good mood today.]
This sample game is a Tactical-styled game with the time scope of argument set to one week. Arguments can be recursive. Players can also propose initiative of a narrative nature. Three players are going to oppose each other: Farrag is a tribal leader whose livelihood depends on poppy crops, Ali is the Taliban leader in the region and CPT Killroy is an newly arrived ISAF unit commander which is tasked to eradicate the culture of poppy in the area. The conch is given to CPT Killroy as per the scenario dictate.
- As a rule, Farrag will not meet with either Ali nor CPT Killroy.
- It is very unlikely that Farrag will give up the culture of poppy.
- Farrag sells his poppy crop to Ali each season, and thus depend financially on this economic partnership.
Initiative 1 (CTP Killroy, a narrative argument)
The valley where Farrag lives is plagued by poor water quality since the 1980's invasion of the USSR where the watershed was poisoned.
Outcome: This affects the quality of the crops, and makes both livestock and human sick. The inhabitants see this as a real problem.
- The soviets did poison wells in the 80's (+1)
- The government since then never addressed the situation because of a lack of resources (+1)
- The poison diluted in 30 years and is no longer in dangerous concentrations (-1) [proposed by Farrag]
Target = 11
Roll = 15 (failure by 4)
Narrative Outcome: No, the water in the valley is just fine. Even though the Soviet poisonned many water sources and some are still contaminated, this is not the case in Farrag's valley.
The conch is passed to Farrag.
Initiative 2 (Farrag)
I send some of my men ahead to talk to the ISAF people and figure out what kind of material advantages they can provide me.
Outcome: My men convince ISAF to donate a generator for the village.
- ISAF wants to make contact (+1)
- ISAF has the resources to make donation, and this is good COIN practice (+1)
- The Taliban oppose such kind of interaction through intimidation (-1) [proposed by Ali]
- ISAF can be brought to donate only if a contact can be made with the tribal leader himself (-1) [proposed by CPT Killroy]
Farrag doesn't agree that the Taliban can intimidate him enough to make a difference. This spawns a sub-initiative where Ali is the conch holder.
The Taliban opposed any meeting between Farrag's men and ISAF using threats of reprisal, both monetary and through armed intimidations.
Outcome: The Taliban's opposition is a significant factor in preventing the contact between the tribe and ISAF.
- The Taliban is the main economic partner to Farrag (+1)
- The Taliban has a track record of intimidation (+1)
- Farrag's would see it as a dishonor to be interfered by a third party (-1)
Total : 11, roll: 8 (success by 4)
Outcome: Clearly, the action of the Taliban are significant, despite Farrag's sense of pride.
Total: 10, roll: 11 (failure by 1) The Taliban's argument preceded over the ISAF one as determined by the flip of a coin.
Outcome: No generator is obtained, mostly because the Taliban interfered, but also because ISAF wasn't trusting about dealing with an intermediate. Had these factors out of the way, it would have probably worked.
Both Ali and CPT Killroy made a difference but Ali's precede over CPT Killroy's. The conch is passed to Ali.
Initiative 3 (Ali)
The Taliban make sure that ISAF has a hard time to tell who are legitimate intermediate of Farrag's from Taliban agents.
Outcome: ISAF is likely to trust the Taliban sympathizers more rather than the legit representatives of Farrag.
- Farrag's legit representatives are seen as free loaders after the generator incident (+1)
- ISAF is new to the region and hasn't built a clear picture of the social networks in the valley (+1)
- The Taliban uses this trick all the time with new ISAF units (+1)
- Farrag's elusiveness frustrates ISAF and blurs the line between good and bad guys on the field (+1)
- Legit reps can be vetted by cooperative folks from rival tribes (-1) [CPT Killroy]
Total: 13, roll: 7 ( success by 7 )
Outcome: ISAF, unknowingly, are dealing with the wrong people in trying to approach Farrag. Even with the help of folks from rival tribe, the result would be the same.
Ali keeps the conch.
Playtesters and Input
Sandy Mackay, Christopher (Neville) Taylor and Michael Veniez, Terrence Rideau, Neal Durando.
Game system (inspiration)
Chris Engle (Hamsterpress.net)
The Open-Ended Machine by Christian Blouin is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 Canada License. Based on a work at www.opcon.org.