10 Degenerate Combos and Edge Cases
This chapter analyzes specific furnishing combinations and resource chains that could potentially break the dominance result. We show that each apparent exploit has a natural ceiling, confirming that the payoff matrix remains valid under extreme play patterns.
10.1 Beer Parlor
The Beer Parlor converts grain to gold: \(2\) grain yields \(3\) gold (or \(4\) food). It is rate-limited by grain stockpile.
\(\text{beerParlorGold}(g) = \lfloor g / 2 \rfloor \times 3\) for \(g\) grain.
\(\text{beerParlorGold}(20) = 30\). Even with \(20\) grain (an extreme stockpile), the Beer Parlor produces at most \(30\) gold.
\(\lfloor 20/2 \rfloor \times 3 = 30\).
\(\text{beerParlorGold}(10) = 15\) and \(\text{beerParlorGold}(4) = 6\). In practice, a farming player might accumulate \(\sim 10\) grain, yielding \(15\) gold, not an unbounded engine.
By computation.
10.2 Weapon Storage
Weapon Storage gives \(+3\) per armed dwarf: theoretical max is \(15\) (all \(5\) dwarfs armed). Realistically, \(3\) armed dwarfs yield \(9\).
\(3 \times 5 = 15\) and \(3 \times 3 = 9\).
10.3 Ruby economy chain
Mining \(8\) rubies over a game yields \(4\) ruby mine activations (at \(2\) rubies each). Those \(8\) rubies can convert to \(16\) food as emergency rations.
\(8/2 = 4\) and \(8 \times 2 = 16\).
Converting rubies to gold for State Parlor: net yield is \(12 - 2 = 10\) points after accounting for conversion overhead.
By the conversion chain arithmetic.
10.4 Blacksmithing Parlor
\(\text{blacksmithingParlorGold}(5, 5) = 10\). With \(5\) rubies and \(5\) ore, the Blacksmithing Parlor produces \(10\) gold (\(1\) ruby \(+ 1\) ore \(\to 2\) gold \(+ 1\) food per activation).
\(\min (5,5) \times 2 = 10\).
10.5 Writing Chamber
The Writing Chamber prevents up to \(7\) gold points of negative scoring, regardless of how many penalties exist. \(\text{writingChamberReduction}(24) = 7\), \(\text{writingChamberReduction}(57) = 7\), \(\text{writingChamberReduction}(8) = 7\).
The reduction is capped at \(7\) by definition.
10.6 Dog-sheep stacking
\(\text{dogSheepCapacity}(n) = n + 1\) and \(\text{dogSheepCapacity}(10) = 11\). Even \(10\) dogs only house \(11\) sheep, making this a weak scaling path compared to stabled pastures.
Direct from \(f(n) = n+1\).
10.7 Breeding and mining output
Over \(7\) harvest phases with breeding, total food output is \(35\).
\(7 \times 5 = 35\).
A Miner produces \(10\) ore over \(5\) activations (\(2\) per activation). Ore trading yields at most \(6\) per use (\(3 \times 2\)).
\(2 \times 5 = 10\) and \(3 \times 2 = 6\).
10.8 Combined exploits
The theoretical maximum from combining Beer Parlor, Blacksmithing Parlor, and Hunting Parlor is \(30 + 10 + 20 = 60\) gold. This is a ceiling, not an achievable value, because the required input resources (grain, rubies, ore, boar) compete for action tempo.
By addition of individual ceilings.
With one growth at round 4, total placements are \(47\). This finite action budget prevents any exploit from running unbounded.
\(\text{totalPlacementsOneGrowthRound4} = 47\).
Arming \(3\) dwarfs at strength \(4\) each costs \(3 \times 4 = 12\) ore. The ore investment caps the weapon snowball effect.
\(3 \times 4 = 12\).
The “furnish cavern” loot option is worth \(\sim 4\) points. At maximum strength \(14\), total available loot value is \(\sim 13\) points. Expeditions are valuable but capped.
By enumeration of loot items and their point values.