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Outcome Enumerator for Mass Effect 2

This document assumes the reader is familiar with the entirety of Mass Effect 2, including references and terminology that may be considered spoilers. You have been warned! :)

This Python package models a decision tree for all player actions affecting the survival of allied characters at the end of Mass Effect 2 and, to a certain extent, Mass Effect 3 (see Limitations). The output of the decision tree is a mapping between unique outcomes and ordered pairs containing the following data:

  1. The number of unique traversals that lead to the outcome
  2. An example of one such traversal encoded as an integer

An outcome encodes the following information into a single integer:

  • Which allies survived?
  • Which surviving allies were loyal?
    • An ally becomes loyal if the player successfully completes their loyalty mission.
  • Was the surviving crew of the Normandy SR2 rescued?
    • For the purposes of discussion, "the surviving crew" refers to the group that is still alive when Shepard arrives to rescue them.

A traversal encodes a path through the decision tree, which is discussed further in its own section. The output can be used to find answers to some interesting questions, such as

  • How likely is it for a particular ally to survive the final mission?
  • How likely is it for Shepard to die?
  • How many outcomes can only be achieved by making a unique set of decisions?
  • How many different outcomes can be achieved?
  • What is the most likely outcome?

See Interesting Facts for some answers to these and other questions.

Some player actions and their consequences are not considered in the scope of this project. See Limitations for a discussion of the rationale behind the exclusions.

Interesting Facts

  • The decision tree covers 39,600,351,708 traversals!
  • There are 697,887 achievable outcomes of 1,417,176 potential outcomes.
    • That means there are 719,289 outcomes that are impossible to achieve.
  • 111 outcomes are uniquely achievable (i.e., they have only one traversal).
    • These outcomes have the following in common:
      • Miranda survives and is loyal.
      • Garrus is not loyal.
      • Jacob is not loyal.
    • Note that Garrus, Jacob, and Miranda are all ideal leaders. That is, if they are loyal when selected as a leader during the final mission, a death will be avoided.
  • The greatest number of traversals for any outcome is 62,147,162.
    • Unsurprisingly, that outcome spares only loyal Jacob, loyal Miranda, and the crew.
  • The ten most common outcomes cover 373,227,856 traversals.
  • The one hundred most common outcomes cover 1,767,031,966 traversals.
  • The one thousand most common outcomes cover 6,807,718,024 traversals.
  • Morinth is more likely to survive than a loyal Samara.
    • Loyal Samara's survival rate is 87.1% of Morinth's.
  • There are 324,677,659 ways to prevent Shepard from surviving the final mission. This can only happen if less than two allies survive.
    • In other words, Shepard survives 99.18% of all traversals.

Ally Survival Rates

Name Relative Absolute
Miranda 1.000 0.705
Jacob 0.840 0.592
Zaeed 0.780 0.549
Garrus 0.647 0.456
Grunt 0.623 0.439
Mordin 0.508 0.358
Samara 0.489 0.345
Kasumi 0.443 0.312
Legion 0.433 0.305
Tali 0.425 0.299
Thane 0.422 0.297
Jack 0.389 0.274

NOTE: Morinth is not included in the table above due to her dependence on Samara's loyalty mission.

NOTE: Survival implies recruitment. That is, if an ally is not recruited, they are not regarded as surviving.

Decision Tree

The decision tree is not strictly modeled as a tree in the mathematical sense. It is akin to a directed, acyclical graph (DAG) with a root node, and traversing the graph accumulates state. That state is the traversal encoding which maps onto a unique root-to-leaf traversal of the analogous tree.

Some decisions affect the availability of future choices. The decisions that are considered are described below in "plain English." The bare logic can be found in the DecisionTree class in the dt module.

  1. How many optional allies will be recruited?
    • Garrus, Jack, Jacob, Miranda, and Mordin (five) are required. All others are optional, but eight is the minimum number of allies necessary to complete the game, so at least three must be chosen.
  2. Which optional allies will be recruited?
    • Do not consider Morinth in this decision (see #4).
  3. Which allies' loyalty missions will be completed?
  4. Will Morinth replace Samara?
    • This decision is only considered if Samara is recruited and loyal.
  5. Will the Silaris Armor upgrade be purchased?
    • If not, Jack dies.
  6. Will the Cyclonic Shields upgrade be purchased?
    • If not, an ally will die according to a certain priority.
  7. Which allies will join the squad that defends the cargo bay?
    • This decision is only considered if the shields were not upgraded because the allies in your squad will not die even if they would have been prioritized for death.
  8. Will the Thanix Cannon upgrade be purchased?
    • If not, an ally will die according to a certain priority.
  9. Which ally will act as the first tech specialist?
    • If they are not loyal and one of Kasumi, Legion, or Tali, they will die.
  10. Which ally will lead the first fireteam?
    • This decision is only considered if the first tech specialist would survive according to the previous decision.
    • If the first fireteam leader is not loyal and one of Garrus, Jacob, or Miranda, the first tech specialist will die.
  11. Which ally will act as the biotic specialist?
  12. Which ally will lead the second fireteam?
    • If they are (1) not Miranda, (2) not loyal or one of Garrus or Jacob, they may die. They will not die if there are fewer than four allies remaining to choose for your squad for the final battle (see #16).
  13. Will an ally escort the crew?
    • If there are four or fewer total allies remaining, no one is allowed to escort the crew.
  14. Which ally will escort the crew?
    • This decision is only considered according to the previous choice.
    • If they are not loyal, they will die. Otherwise, they are guaranteed to survive the final mission.
  15. Which allies will join your squad under the protection of the biotic specialist?
    • This decision is only considered if the biotic specialist is not loyal and one of Jack, Samara, or Morinth because an ally in your squad will die according to a certain priority.
  16. Which allies will join your squad for the final battle?
    • Any disloyal ally in your squad will die after the final battle.
    • All remaining allies (except the crew escort, if applicable) are left behind to hold the line. Their survival is dependent on a formula that is too complex to describe here. See the References for a flowchart, or check out get_defense_victims() in the death module.

All of the choices made for each decision above are decodable from an encoded traversal, which is stored as a single integer.

Decision #15 was the most technically challenging to implement due to the fact that not picking an ally for your squad can spare them from the consequence of choosing a bad biotic specialist.

Usage

Most of the code in the me2 package can be treated like documentation. The interesting part is probing the data that has already been generated and included in this repository. The easiest way to get started is with an interactive Python session.

$ python -im me2 me2.dat
The decision tree is fully generated!
Use outcomes to view the decision tree outcome dictionary.
>>> len(outcomes)
697887
>>> print(next(iter(outcomes)))
(160, (341198, 562069081815085676543))

outcomes is a view of dictionary items, and all data is encoded as ints. You can get human-readable output like so:

>>> item = next(iter(outcomes))
>>> print(describe_outcome(item[0]))
Survived: (2) Grunt and Legion
Loyal:    nobody
Crew:     dead
>>> print(describe_traversal(item[1][1]))
No Normandy upgrades.
Recruit: Grunt, Kasumi, Legion, Morinth, Samara, Tali, Thane, and Zaeed
Loyalty Missions: Garrus, Jack, Jacob, Samara, Tali, and Thane
For the cargo bay squad, pick Kasumi and Legion.
Choose Jacob as the tech specialist.
The second fireteam leader does not matter.
Choose Miranda as the biotic specialist.
Choose Morinth to lead the diversion team.
Do not send anyone to escort the crew.
For the squad in the biotic shield, pick Garrus.
Pick Miranda and Zaeed for your final squad.

You can also request a brief description of an outcome.

>>> print(describe_outcome(item[0], brief=True))
2 allies survived.

More intelligent queries currently require knowledge of the outcome encoding. For example, this is how one would ask, "What percentage of traversals result in Jacob's death?"

>>> jacob_dies = sum(e[1][0] for e in outcomes if ~e[0] & Ally.Jacob.value)
>>> total = sum(e[1][0] for e in outcomes)
>>> jacob_dies / total
0.40816029779691876

So, roughly 41%, as it turns out. This is not user-friendly, but at least it is not impossible to do.

Generating Data

Full disclosure: On my machine, it took several days to generate the data file. If you are curious enough to try anyway, read on.

To run the decision tree, point the me2 package at a non-existent or incomplete file.

$ python -m me2 path/to/file
# or interactively
$ python -im me2 path/to/file

In non-interactive mode, the decision tree will run until an interrupt signal (Ctrl-C) is issued. In interactive mode, you can manually request progress information with progress() or a running total of traversals with counts(). Use quit() like usual when you want to stop.

In either case, ending the program will pause the output generation. All information required for the script to pick up where it left off is saved in the file along with the actual outcome and traversal data. The file is considered incomplete, but restarting with the same file will automatically continue generating data.

Limitations

The following subsections discuss some of the known and perceived limitations of the design.

Partial Data

Each outcome was achieved via one or more traversals of the decision tree, but only the traversal count and one encoded traversal is included with each outcome in the output data. Why?

It comes down to speed and storage constraints. Some quick math shows that even with an ideal serialization scheme, the size of the output data would quickly become unreasonable.

  1. There are ~39.6 billion traversals.
  2. The shortest traversal encoding is 48 bits (6 bytes) long.
    • They are at most 70 bits (8.75 bytes) long.
  3. In the best case, 39.6 billion times 6 bytes is about 220 GiB.

By today's standards, that is still considered a gigantic amount of storage, especially for such a trivial use case. Forget about trying to load and query a file of that size, too.

In the end, the outcomes are the most interesting data to analyze, and the most interesting traversals are the ones that led to rare outcomes. By including one traversal for each outcome, we get the best of both worlds.

Scope

The scope of this project is limited to only the parameters that affect the fate of Mass Effect 2 allies when carried over to Mass Effect 3. If an ally survives ME2, they will be encounterable in ME3. Furthermore, if the ally was loyal, they may become a war asset in ME3. If they were not loyal, however, they would die in ME3.

However, there is one member of the crew of the Normandy SR2 who is not specifically addressed in this implementation: YN Kelly Chambers. Outcomes only encode whether the crew was rescued, but that is only part of the story. Some of the crew may die before they are rescued based on the number of missions completed after the installation of the Reaper IFF.

Missions Result
0 Everyone in the crew survives.
1–3 Half of the crew dies, including YN Kelly Chambers.
>3 Everyone except Dr. Karen Chakwas dies.

Both Chambers and Chakwas return in ME3 if they survive the final mission of ME2, and Chambers even has an "implicit loyalty" in ME2 that factors into her fate in ME3. So, why are they not explicitly considered in the decision tree? In Dr. Chakwas's case, her survival is entirely dependent on whether an escort is selected, so one could argue that the crew survival encoding in the outcome should be called the "Dr. Chakwas survival bit." For YN Chambers, this is just an unfortunate gap. To address this, I would make the following changes:

  • Add a Kelly Chambers loyalty decision (true/false).
  • Add a post-Reaper-IFF mission completion decision (0/1–3/>3).
  • Reinterpret the existing crew survival outcome bit as the Dr. Chakwas survival bit.
  • Add a Kelly Chambers survival bit to the outcome encoding.
  • Add a Kelly Chambers loyalty bit to the outcome encoding.

Usability

It is painful to query encoded outcome data. This project is missing a well-designed query module/API.

References

This project was made possible by the amazing folks in the Mass Effect community, particularly those who took the time to answer some esoteric questions on the Mass Effect subreddit. Of particular importance was this flowchart for which I regrettably am unable to find any attribution, though I believe that particular version was distilled from a primary source unknown to me.