Statistical modelling for the Assassins' Guild
In the current version of AutoUmpire, the targeting graph will undergo "breakdown". When an assassin is killed, it is unable to fix the underlying targeting graph.
The objectives of this research is to determine factors that impact targeting graph breakdown.
Creating the Graph
The graph must meet a few requirements:
- Every player targets three assassins and is targeted by three assassins
- A player cannot target themselves
- The graph cannot be easily reverse-engineered
It was thought that breakdown could be delayed by varying the initial graph state. This has not (yet) been demonstrated.
Retargeting Assassins
When an assassin dies, we must modify 7 nodes:
- one node for the dead assassin
- three nodes that attack the assassin
- three nodes that assassin used to attack
To illustrate this, we can plot a subset of the original graph:
When a particular node is removed:
- Three assassins are missing a target
- Three targets are missing an assassin.
This is the simplest case, and there are a total of six possible solutions:
Solution #1: Solution #2: Solution #3:
1 -> 3 1 -> 14 1 -> 155
21 -> 14 21 -> 3 21 -> 3
98 -> 155 98 -> 155 98 -> 14
Solution #4: Solution #5: Solution #6:
1 -> 3 1 -> 14 1 -> 155
21 -> 155 21 -> 155 21 -> 14
98 -> 14 98 -> 3 98 -> 3
Analysis becomes more difficult when there are pre-existing relationships between nodes. Consider a more complicated problem:
We model this particular problem with a matrix, which is successively simplified down:
Problem:
6 13 16
----------
2 | 1 1 1
4 | 0 0 1
7 | 0 1 1
Assassin 4 targets 16.
6 13 16
----------
2 | 1 1 0
4 | 0 0 0
7 | 0 1 0
Assassin 7 targets 13.
6 13 16
----------
2 | 1 0 0
4 | 0 0 0
7 | 0 0 0
Assassin 2 targets 6.
The corresponding object returned would be:
RetargetingState(
bitmat = 0×0 BitMatrix,
attack_indexes = Int64[],
target_indexes = Int64[],
attack_counts = UInt8[],
target_counts = UInt8[],
pairs = [(4, 16), (7, 13), (2, 6)]
)
This method of retargeting is effective because it generalizes to processing multiple kills in a batch.