Conspirator Combinations

The nine cards in the Conspirators deck are Theodosia (1), Blennerhasset (1), Jackson (1), Merry (1), Irujo (1), and Wilkinson (4).

Drawing three cards from a nine-card deck involves the combination formula: a way to calculate the total number of combinations where the order of the cards within each combination does not matter.

The forumla to calculate combinations is:

C(n,r) = n! / r! * (n - r)!

where
n = number of items
r = number of items being chosen at a time

In Hero of Weehawken the formula becomes:

C(9,3) = 9! / 3! * (9 - 3)!
  = 84 possible conspiracy combinations.

This can also be read directly from Pascal's triangle. Next to last row, showing possible combinations of 0 through 9 items selected randomly from a nine-item set.

Pascals

In the game as published, 29 combinations out of 84 (34.5%) result in plan I: Settle the Ouachita Valley (see table below).

The above variant conspiracy combinations chart greatly reduces the impact of Theodosia on the conspiracy and evens out the chances of each plan occurring (with slightly less at the ends of the range). In this variant, the likelihood of Burr settling the Ouachita valley is the same as for a coup d'etat. Historically he was tried for VI (Detach Western U.S.) but his actual goal was most likely IV (Invade Spanish Southwest).

Plans are assigned to each combination based on the following assumptions:

  • Wilkinson is the catalyst for the conspiracy.
    > If he is not involved, there is no defined goal. Burr fails to gain any support on vague generalities, and retires from public life (I).
    > With one Wilkinson card in the conspiracy, a filibuster is the most likely outcome (II through V). The exception being when both foreigners (de Irujo and Merry) are involved, pumping up Burr's visions of empire (VI).
    > With two Wilkinsons in the conspiracy, New Orleans (II) is out of the mix, and a coup d'etat (VII) becomes a possibility.
  • Burr's devotion to Theodosia does not trump his ambition, but her presence at least guarantees that Burr will not turn traitor. Theodosia's influence depends on Wilkinson's involvement:
    > Theodosia + Wilkinson x 2: she is unable to mitigate Wilkinson's sway on Burr and the "historical" plan (IV) is used.
    > Theodosia + Wilkinson + other: they "cancel each other out" (in terms of their influence on Burr), and the third conspirator becomes the determining factor in which plot is used (which Wilkinson supports in spite of Theodosia).
  • Neither foreigner (de Irujo or Merry) is interested in a coup d'etat (VII), but will gladly egg on Burr's ambitions of empire (VI).
    > de Irujo (Spanish minister) will not involve himself in plots against Spanish territory or Mexico. He is particularly interested in the New Orleans (II) plan due to a personal disdain for all things French.
    > Merry (British envoy) is interested in eroding Spanish influence in the Caribbean, so he supports the Mexico plan (III) or the Florida invasion (V).
  • Jackson will have no truck with treason but will join Burr in any filibuster, especially the Florida plan (V).
  • Blennerhasset is Burr's sycophant, flatterer, and instigator. He will go along with any of the filibuster plots, and is willing to join Wilkinson and Burr in a coup.

Conspiracy Objectives Table (as published)

Comparison of plan combinations

Plan As published This variant
I. Ouachita valley 29 10
II. New Orleans 9 12
III. Mexico 10 14
IV. Southwest 13 14
V. Florida 8 14
VI. Western empire 5 10
VII. Coup d'etat 10 10

Guilt level of all combinations

Verdict As published This variant
Innocent 29 10
Filibuster 40 54
Treason 15 20