3 Food Economy

Food is the primary constraint in Caverna. Every harvest, each dwarf must be fed $2$ food (plus $1$ per offspring). Failure to feed produces begging markers worth $-3$ points each. This chapter formalizes the food conversion system and proves the universal food crisis that shapes all viable strategies.

3.1 Food values

Definition 3.1 Animal food values

✓

Sheep convert to $2$ food, wild boar to $3$, cattle to $4$. Donkeys have a superlinear pairing bonus: $1$ donkey gives $1$ food, but pairs give $3$ food (a $+1$ bonus per pair).

Theorem 3.2 Donkey pair bonus

✓

$\text{donkeyFoodValue}(2) = 3$ and $\text{donkeyFoodValue}(2) {\gt} 2 \cdot \text{donkeyFoodValue}(1)$, confirming the superlinear pairing bonus.

Proof ▶

By computation: $3 {\gt} 2 \cdot 1 = 2$.

\begin{tikzpicture} [
res/.style={rounded corners=4pt, minimum width=1.8cm, minimum height=0.7cm,
font=\small, text=textDark, draw=textDark, thin, align=center},
food/.style={res, fill=pastelMint, font=\small\bfseries, minimum width=2.0cm,
minimum height=0.9cm},
arr/.style={-{Stealth[length=5pt]}, thick, color=textDark},
rate/.style={font=\scriptsize, text=accentTeal, fill=white, inner sep=1.5pt},
]
% Food node (center)
\node[food] (F) at (0, 0) {Food};
% Source nodes
\node[res, fill=pastelSky] (cattle) at (-5.5, 2.0) {Cattle};
\node[res, fill=pastelSky] (boar) at (-3.0, 2.0) {Wild Boar};
\node[res, fill=pastelSky] (sheep) at (-0.5, 2.0) {Sheep};
\node[res, fill=pastelLavender] (donkey) at ( 2.0, 2.0) {Donkey};
\node[res, fill=pastelLemon] (veg) at (-4.5, -2.0) {Vegetable};
\node[res, fill=pastelLemon] (grain) at (-2.0, -2.0) {Grain};
\node[res, fill=pastelPeach] (gold) at ( 0.5, -2.0) {Gold};
\node[res, fill=pastelCoral] (ruby) at ( 3.0, -2.0) {Ruby};
% Arrows with conversion rates
\draw[arr] (cattle) -- (F) node[rate, midway, above, sloped] {4};
\draw[arr] (boar) -- (F) node[rate, midway, above, sloped] {3};
\draw[arr] (sheep) -- (F) node[rate, midway, above, sloped] {2};
\draw[arr] (donkey) -- (F) node[rate, midway, above, sloped] {1 or 1.5/ea};
\draw[arr] (veg) -- (F) node[rate, midway, below, sloped] {2};
\draw[arr] (grain) -- (F) node[rate, midway, below, sloped] {1};
\draw[arr] (gold) -- (F) node[rate, midway, below, sloped] {$n{-}1$ (lossy)};
\draw[arr] (ruby) -- (F) node[rate, midway, below, sloped] {$\geq 2$};
% Donkey annotation
\node[font=\tiny, text=textDark, anchor=west, align=left] at (3.3, 2.5)
{1 donkey $\to$ 1 food\\2 donkeys $\to$ 3 food\\(superlinear)};
% Gold annotation
\node[font=\tiny, text=accentAmber, anchor=north] at (0.5, -2.7)
{1 gold wasted};
\end{tikzpicture} — Figure 3.1 Food conversion network. All resources ultimately convert to food at varying rates. Cattle is the most efficient animal source; gold conversion is lossy (1 unit overhead); rubies serve as emergency food ($\geq 2$ each). Donkeys exhibit a superlinear pairing bonus.

Theorem 3.3 Cattle is most efficient

✓

Cattle gives strictly more food than wild boar and sheep per animal.

Proof ▶

$4 {\gt} 3 {\gt} 2$.

Theorem 3.4 Vegetable over grain

✓

Vegetables give $2\times $ the food of grain (2 vs. 1).

Proof ▶

By definition of food values.

3.2 Gold-to-food conversion

Definition 3.5 Gold to food

✓

Converting $n$ gold to food yields $\max (0, n-1)$ food. This is lossy: $1$ gold is wasted as overhead.

Theorem 3.6 Gold conversion is lossy

✓

$\text{goldToFood}(2) = 1$ and $\text{goldToFood}(1) = 0$.

Proof ▶

Direct from the formula $\max (0, n-1)$.

3.3 Feeding costs

Definition 3.7 Feeding cost

✓

$\text{feedingCost}(d, o) = 2d + o$ where $d$ is the number of adult dwarfs and $o$ the number of offspring.

Theorem 3.8 Two-dwarf feeding

✓

$\text{feedingCost}(2, 0) = 4$.

Proof ▶

$2 \cdot 2 + 0 = 4$.

Theorem 3.9 Five-dwarf feeding

✓

$\text{feedingCost}(5, 0) = 10$ and $\text{feedingCost}(5, 1) = 11$.

Proof ▶

By computation.

3.4 The universal food crisis

Theorem 3.10 Starting food is insufficient

✓

Player 1’s starting food ($1$) is strictly less than the first harvest feeding cost ($4$): $1 {\lt} \text{feedingCost}(2, 0)$.

Proof ▶

$1 {\lt} 4$.

Theorem 3.11 First harvest deficit

✓

$\text{feedingCost}(2,0) - \text{startingFoodP1} = 3$. Every player faces a 3-food deficit at the first harvest.

Proof ▶

$4 - 1 = 3$.

Theorem 3.12 Universal food crisis

✓

Both players face a food deficit at the first harvest: $\text{feedingCost}(2,0) - \text{startingFoodP1} = 3$ and $\text{feedingCost}(2,0) - \text{startingFoodP2} = 2$. This structural constraint forces every viable strategy to solve the food problem within its first $3$ actions.

Proof ▶

Player 1 starts with $1$ food and needs $4$, a gap of $3$. Player 2 starts with $2$ food and needs $4$, a gap of $2$.

Theorem 3.13 Ruby emergency food

✓

Rubies can be converted to at least $2$ food each, serving as an emergency food source.

Proof ▶

By the ruby conversion rules.