Cooking Mechanics

Meal energy appears, at first glance, as though it should reduce to a simple sum over the chosen ingredients, though it does not, since the game first decides which recipe the ordered ingredients produce, then floors each ingredient's contribution separately, and only afterward applies the variety, recipe, and cooking-quality multipliers in turn.

The ordering matters enough that moving a single floor or multiplier to a position that looks more natural (summing first and flooring once, say) changes the displayed energy, sometimes by exactly one point.

Everything described as verified below is backed by a recorded in-game observation or a regression case in the research database. It should be noted, however, that some recipe conditions are still drawn directly from the in-game recipe table, and the full precedence between those recipes remains, at the time of writing, unresolved.

Variables

The variables used throughout this page are the following:

$E_i$ is its raw energy;
$M_i$ is its underlying cooking multiplier;
$C_i$ is its integer contribution to the meal;
$U$ is the number of distinct ingredient identities in slots 1–4;
$S=\sum_i C_i$ is the sum of the individually floored contributions;
$V$ is the variety multiplier;
$R$ is the recipe multiplier;
$Q$ is the cooking-quality multiplier.

In short, the calculation proceeds in the order below:

\text{ordered ingredients}\;\longrightarrow\;\text{recipe resolution}\;\longrightarrow\;\text{energy policy}\;\longrightarrow\;\text{energy calculation}

It should be noted that these three stages, recipe resolution, energy policy, and energy calculation, are kept genuinely separate by the game. Recipe resolution decides whether the ordered ingredients constitute a Mushroom Stew, Spaghetti, Burger, Smoothie, or an invalid meal; energy policy then takes that result and selects which variant of the energy formula applies, whether the normal interpolation described below or one of the recipe exceptions covered later on this page; energy calculation, finally, is the arithmetic itself, carried out according to whichever policy was selected.

Raw Energy and Identity

Every ordinary ingredient begins with a fixed raw energy Eᵢ, and its cooking multiplier Mᵢ describes the full cooked potential that ingredient can reach. A normal recipe, however, does not necessarily grant the ingredient all of that potential.

Modifiers change an ingredient's energy without necessarily creating a new identity for it. Arcane, for instance, triples the raw energy of an ordinary non-fish ingredient; fish, however, are treated differently, and an Arcane fish receives 1.5× instead. The verified fish-size modifiers are Small at 0.5×, Giant at 2×, and Massive at 3×, each applied to the underlying ingredient value before the meal formula is ever reached (Arcane Odyssey Wiki).

Note that Arcane does not create a new identity for the purpose of diversity: Boar and Arcane Boar still count as one and the same thing. Named Giant ingredients are a different matter entirely; Seacap and Giant Seacap are separate ingredients in the game's own bookkeeping, and are therefore counted separately here as well.

This distinction, it should be noted, is easy to miss: "Giant" refers here to the actual named ingredient category, not to some Arcane-enlarged version of an ordinary one.

Something of note is that zero-energy ingredients still count toward diversity. Samerian Ice contributes no energy whatsoever, yet it can still increase U when placed in slots 1–4. The dedicated seasoning slot belongs to a separate system entirely and does not count in this fashion.

Fish

Fish do not, in fact, require a separate energy formula of their own. The only unusual part is how their raw energy is determined in the first place, which comes from fish size rather than from any fixed per-species constant:

E_{\mathrm{fish}} = 5 \times \mathrm{AverageStuds}

Source: Arcane Odyssey Wiki.

After that raw value is established, any fish-size or Arcane modifier is applied on top of it. Salmon and Tuna each use a cooking multiplier of 1.2; Jellyfish uses 0.5; every other fish currently in the catalog uses 1.0.

Tuna is where matters grow somewhat stranger. Its verified contributions are 40, 43, 45, and 48 at U = 1, 2, 3, and 4 respectively, results that are only consistent if its hidden raw value lies within the following interval:

40.3125 \leq E_{\mathrm{Tuna}} < 40.\overline{5}

Simply substituting the displayed integer 40 for that hidden value produces one-energy errors throughout the curve. Indeed, this is exactly why the research database stores Tuna's verified curve as an ingredient-specific override rather than trusting the general formula. Full-potential recipes are noted to still give Tuna its full cooked contribution of 48.

Diversity and the First Four Slots

Only slots 1 through 4 determine diversity, as it happens:

U = \left|\left\{\text{distinct ingredient identities in slots 1--4}\right\}\right|

Slot 5 still contributes energy to the meal; it simply cannot increase U itself. Whatever value slots 1–4 have already established is reused when the fifth ingredient's own contribution is calculated.

The interpolation fraction is then given by

\alpha = \frac{U-1}{3}

one identity $U=1,\quad\alpha=0$

two identities $U=2,\quad\alpha=\frac{1}{3}$

three identities $U=3,\quad\alpha=\frac{2}{3}$

four identities $U=4,\quad\alpha=1$

Diversity, then, controls how far each positive cooking bonus is permitted to progress toward its full potential; it is not, as one might assume, simply another bonus tacked on after the ingredients have already been cooked.

Per-Ingredient Calculation

Positive Cooking Multipliers

With U established, each ingredient's contribution can now be calculated. For Mᵢ ≥ 1, a normal recipe interpolates between raw energy and full cooked energy according to the following:

C_i = \left\lfloor E_i\left(1 + \alpha(M_i-1)\right)\right\rfloor

Each ingredient is floored individually and on its own terms; moreover, the formula operates on the underlying multiplier directly, and it does not, as a subtly different implementation might, interpolate toward some already-floored solo value.

Raw Deer Meat serves as a useful illustration here. It has E = 45 and M = 1.5, and with three unique identities present, α = 2/3, giving

C = \left\lfloor 45\left(1 + \frac{2}{3}(0.5)\right)\right\rfloor = \lfloor 60\rfloor = 60

Its actual full potential is 45 × 1.5 = 67.5; if one instead stores 67 as the target and interpolates toward that already-floored value, the resulting calculation is simply wrong.

Negative Cooking Multipliers

Negative cooking multipliers are considerably simpler, thankfully. When Mᵢ is less than 1, the entire penalty is applied immediately, with no interpolation at all:

C_i = \left\lfloor E_iM_i\right\rfloor

Note that this case is entirely indifferent to U, as Coconut demonstrates: with E = 7 and M = 0.5, it contributes $\lfloor3.5\rfloor=3$ regardless of whether the meal has one identity or four.

Summing the Contributions

Once every ingredient's contribution has been calculated individually, the results are simply summed:

S = \sum_i C_i

It is to be noted that there is no additional floor applied at this stage, since every Cᵢ is already an integer by construction; slot 5 is included in this sum as normal, alongside the first four.

Variety and Cooking Quality

The meal as a whole then receives a separate variety multiplier, applied after the individual contributions have been summed:

V = 1 + 0.05(U-1)

one identity $U=1,\quad V=1.00$

two identities $U=2,\quad V=1.05$

three identities $U=3,\quad V=1.10$

four identities $U=4,\quad V=1.15$

This amounts to a flat five percentage points of bonus for each additional identity present; note that this bonus does not compound.

Cooking quality supplies the Q term. It begins at 1.0 and reaches 1.5 by level 8; the dedicated seasoning slot unlocks at level 7, while the fifth ordinary ingredient slot does not unlock until level 9.

Cooking level	Q	Ingredient slots	Seasoning slot
1	1.0	4	—
2	1.1	4	—
3	1.2	4	—
4	1.3	4	—
5	1.3	4	—
6	1.4	4	—
7	1.4	4	yes
8	1.5	4	yes
9–10	1.5	5	yes

Final Energy

Everything required for the normal energy formula has now been established. For an ordinary recipe, where R = 1, this reduces to:

E_{\mathrm{final}} = \left\lfloor S \times V \times R \times Q\right\rfloor

It should be noted that only a single floor is applied, and it comes at the very end. The game does not floor S × V first and multiply by Q afterward, a subtlety that turns out to be another common source of one-energy discrepancies for anyone reverse-engineering the formula.

A Floating-Point Caveat

Something of note is how the game exposes ordinary IEEE-754 binary64 behavior, which is the representation Luau numbers use internally. In other words, a value that ought to be a clean integer on paper can, in memory, sit fractionally below that integer.

Brown Mushroom, Green Apple, Raw Bear Meat, and Raw Bird Meat together demonstrate this rather neatly. At cooking level 1, their contributions sum to S = 100, and four distinct identities give V = 1.15. On paper, then, one would expect:

100 \times 1.15 = 115

Binary64, however, evaluates this expression to a value just below 115; the final floor therefore produces 114, which is precisely what the game displays in practice.

Moreover, it is to be noted that there is no epsilon correction applied anywhere in this model, and values that appear "almost" integer should not be nudged into place. Ordinary floating-point arithmetic, combined with a plain floor, reproduces the game's behavior exactly as observed.

Recipe Exceptions

As mentioned, most recipes are governed by the normal energy policy described above; a handful invoke a different one instead, and depending on which recipe has been resolved, the game may force full cooked contributions, introduce an additional multiplier, enforce a minimum value, or forgo the calculation altogether in favor of a fixed return value.

Full-Potential Recipes

Bread, Baguette, Spaghetti, the tested Spaghetti variants, and Breadsticks with Sauce all skip positive interpolation entirely; every ingredient instead receives its full cooked contribution:

C_i = \left\lfloor E_iM_i\right\rfloor

The ordinary variety multiplier still applies afterward, unchanged, and this energy behavior has been confirmed for the named Spaghetti variants specifically. However, it is to be noted that the exact conditions under which several of them resolve still require further testing.

The Burger Family

Burgers and Burger Buffet behave identically to the full-potential recipes above, but with an additional 2.25× recipe multiplier layered on top:

E_{\mathrm{Burger}} = \left\lfloor S_{\mathrm{full}} \times V \times 2.25 \times Q\right\rfloor

This is solved for the ordinary four-ingredient case, and all three named variants have been confirmed to follow it. Note, however, that the fifth ingredient slot and the seasoning slot have not been tested thoroughly enough to state a concrete behavior for either; whether a Burger cooked with five ingredients or with seasoning still follows this formula, or invokes some other policy entirely, remains untested and is left for a future revision of this page.

Smoothies

A valid Smoothie reverts, somewhat curiously, to the normal interpolation formula rather than the full-potential one. Samerian Ice contributes zero energy in this context, yet still counts as an identity when placed in slots 1–4. The recipe then applies R = 1.5 and guarantees a minimum of 5 energy:

E_{\mathrm{Smoothie}} = \max\left(5,\left\lfloor S \times V \times 1.5 \times Q\right\rfloor\right)

Note that this minimum belongs to Smoothies alone and is not a general rule of the formula. Mistake and Disgusting Smoothie are simpler still, in that they always return exactly 5 energy, with no calculation involved at all.

Single-Ingredient Recipes

A meal consisting of a single ingredient does not, on its own, imply full cooked potential. The ingredient must first resolve into a valid solo recipe in its own right; the cases currently established are Pumpkin, Wheat, Festive Cookie Dough, and fish.

Most other ingredients instead require a valid multi-ingredient recipe to resolve at all, and it is therefore not sufficient merely to check whether the ingredient list has a length of one.

Status Tiers, Slot 5, and Duration

Status tiers are a matter entirely separate from energy, and Balanced Meal tests indicate that each ingredient supplies its own tier independently; adding either a duplicate fruit or another, distinct common fruit was not observed to increase the tier already supplied by a different ingredient.

Slot 5 proves somewhat unusual here as well: an ingredient placed in that slot loses its primary Recovery or Energizing contribution, yet retains its secondary effect regardless.

Orange Swiftcap, Cursed Mushroom, and Raw Krystoros Meat each demonstrated exactly this. In slot 5, they retained Featherfall III, Insanity III, and Poisoned IV respectively, while losing their primary Energizing or Recovery contribution; moving the very same ingredient back to slot 4 restored both effects in full.

For a meal with N distinct status effects, each individual effect receives a duration of

D_{\mathrm{each}} = \frac{6.5\,E_{\mathrm{final}}\,Q}{N}

The game divides the total duration budget evenly among the distinct effects present, then floors each resulting displayed duration down to whole seconds.

One further point of note is that E_final already incorporates cooking quality, and yet the duration formula applies Q a second time regardless. A Perfect meal therefore receives 6.5 × 1.5 = 9.75 seconds of total status-duration budget per point of displayed energy. Seasoning has not been observed to alter this calculation in any way.

Summary

Putting all of the above together, the normal recipe formula may be stated in full as

\begin{aligned} U &= \left|\left\{\text{identities in slots 1--4}\right\}\right|, \\ \alpha &= \frac{U-1}{3}, \\ C_i &= \begin{cases} \left\lfloor E_i\left(1+\alpha(M_i-1)\right)\right\rfloor, & M_i\geq1,\\ \left\lfloor E_iM_i\right\rfloor, & M_i<1, \end{cases}\\ S &= \sum_i C_i, \\ V &= 1+0.05(U-1), \\ E_{\mathrm{final}} &= \left\lfloor S\times V\times R\times Q\right\rfloor. \end{aligned}

Under ordinary circumstances R = 1; Burgers use R = 2.25; Smoothies use R = 1.5 and additionally enforce a minimum of 5. Full-potential recipes, meanwhile, replace the positive-interpolation branch entirely with $\lfloor E_iM_i\rfloor$ .

Finally, it should be noted that any verified ingredient-specific behavior takes priority over the general formula whenever the two disagree; Tuna remains the clearest known example of this. The game, in the end, is complicated enough without our having to pretend that every ingredient behaves perfectly within a single tidy equation.