Egg, Inc. Soul Eggs & Prophecy Eggs: The Math Explained

Mystical Eggs are the foundation of long-term progression in Egg, Inc., but the game does not clearly explain the mathematics behind them.

The most important distinction is simple:

Soul Eggs scale linearly. Eggs of Prophecy scale exponentially.

Soul Eggs determine the base size of your permanent Earnings Bonus. Eggs of Prophecy - commonly called Prophecy Eggs or PE - repeatedly multiply that base through compounding.

That is why Soul Eggs dominate early progression, while Prophecy Eggs become increasingly important later.

This guide explains:

• How the Earnings Bonus formula works
• Why Soul Eggs and Prophecy Eggs scale differently
• How Soul Food, artifacts, and stones affect the formula
• Why prestige gains have strong diminishing returns
• Why prestige events outperform equivalent earnings events
• Why multistiging can produce more Soul Eggs per boost session

Accuracy note: Auxbrain confirms the general mechanics, while several detailed formulas are community-documented. Exact values may change after game updates. The prestige calculations using an exponent of 0.21 are late-game approximations, not universal results for every player.

TL;DR

View

Ignoring artifacts and stones, the simplified Earnings Bonus formula is:

$$\boxed{ EB_{\%}=S(10+F)(1.05+0.01R)^P }$$

Where:

The practical interpretation:

• Doubling your Soul Eggs doubles your Earnings Bonus.
• Soul Food increases the value of every Soul Egg.
• Each Prophecy Egg multiplies your current Earnings Bonus by roughly 1.05× to 1.10× before artifact modifiers.
• Prophecy Egg multipliers compound with one another.
• Soul Egg gains during one prestige have strong diminishing returns.
• Prestiging resets that diminishing-return curve.
• Multistiging is useful only when the extra gains outweigh rebuilding time.

---

1. What the Earnings Bonus Actually Means

The game displays your permanent earnings boost as a percentage, not as the final cash multiplier.

For example:

The actual cash multiplier is:

$$M_{\text{cash}}=1+\frac{EB_{\%}}{100}$$

The extra 1 represents your farm's original unboosted earnings.

Example

If the game displays:

$$EB_{\%}=25{,}000\%$$

Then:

$$M_{\text{cash}} =1+\frac{25{,}000}{100} =251$$

Your farm earns 251× its unboosted income, not 250×.

At enormous late-game values, the difference becomes practically irrelevant, but it matters when interpreting the formula correctly.

---

2. The Earnings Bonus Formula

Ignoring artifacts, stones, and special modifiers:

$$\boxed{ EB_{\%}=S(10+F)(1.05+0.01R)^P }$$

The formula has three components:

$$\underbrace{S}_{\text{Soul Egg count}} \times \underbrace{(10+F)}_{\text{value per Soul Egg}} \times \underbrace{(1.05+0.01R)^P}_{\text{Prophecy compounding}}$$

A useful mental model is:

• Soul Eggs: quantity
• Soul Food: value per Soul Egg
• Prophecy Eggs: compounding multiplier applied to the entire Soul Egg base

Complete example

Suppose a player has:

• $S=1{,}000$ Soul Eggs
• $P=10$ Prophecy Eggs
• Soul Food level $F=0$
• Maximum Prophecy Bonus level $R=5$

Substitute the values:

$$EB_{\%} =1{,}000(10)(1.10)^{10}$$

Since:

$$1.10^{10}\approx2.593742$$

Then:

$$\boxed{ EB_{\%}\approx25{,}937.42\% }$$

The actual income multiplier is:

$$M_{\text{cash}} =1+\frac{25{,}937.42}{100} \approx260.37$$

So the farm earns approximately:

$$\boxed{260.37\times}$$

With maximum Soul Food, set $F=140$:

$$EB_{\%} =1{,}000(150)(1.10)^{10} \approx389{,}061.37\%$$

Therefore:

$$\boxed{M_{\text{cash}}\approx3{,}891.61\times}$$

Maximum Soul Food creates a 15× improvement because the value of each Soul Egg rises from 10% to 150%.

View

---

3. Soul Eggs and Soul Food Scale Linearly

Without Soul Food research or Prophecy Eggs:

$$EB_{\%}=10S$$

Every Soul Egg contributes a base bonus of 10%.

The important mathematical property is:

$$EB(2S)=2EB(S)$$

Therefore:

• Increasing Soul Eggs by 10% increases Earnings Bonus by 10%.
• Doubling Soul Eggs doubles Earnings Bonus.
• Multiplying Soul Eggs by ten multiplies Earnings Bonus by ten.

Soul Eggs do not compound with one another. They enlarge the same linear base.

How Soul Food changes the base

Soul Food adds one percentage point to the value of every Soul Egg per research level:

$$V_{\text{SE}}=10+F$$

At level zero:

$$V_{\text{SE}}=10\%$$

At the maximum level of 140:

$$V_{\text{SE}}=10+140=150\%$$

The Soul Egg component therefore changes from:

$$10S$$

to:

$$150S$$

That is a permanent improvement of:

$$\frac{150}{10}=15\times$$

Soul Food is still linear, but it multiplies the value of your entire existing and future Soul Egg collection.

---

4. Prophecy Eggs Scale Exponentially

Prophecy Eggs do not add a fixed amount to your Earnings Bonus. Every PE multiplies the entire Soul Egg component:

$$M_{\text{PE}}=(1+r)^P$$

Where:

• $P$ is the number of Prophecy Eggs.
• $r$ is the bonus provided by each Prophecy Egg.

Without Prophecy Bonus Epic Research:

$$r=0.05$$

With maximum Prophecy Bonus Epic Research:

$$r=0.10$$

The Prophecy multiplier therefore ranges from:

$$1.05^P$$

to:

$$1.10^P$$

Why this is compounding

At a 10% Prophecy rate:

• 1 PE gives $1.10\times$
• 2 PE give $1.10^2=1.21\times$
• 3 PE give $1.10^3=1.331\times$
• 10 PE give $1.10^{10}\approx2.594\times$

Each new PE multiplies the result created by all previous PE. That repeated multiplication is exponential growth.

Prophecy Egg multiplier table

This is why Prophecy Eggs appear modest early in the game but become extraordinarily powerful at high counts.

How valuable is one additional Prophecy Egg?

One additional PE changes your Earnings Bonus from:

$$EB_{\text{old}}$$

to:

$$EB_{\text{new}}=EB_{\text{old}}(1+r)$$

At the base 5% rate:

$$EB_{\text{new}}=1.05EB_{\text{old}}$$

At the maximum 10% rate:

$$EB_{\text{new}}=1.10EB_{\text{old}}$$

The relative improvement from one PE remains 5% to 10% before artifact modifiers. However, the absolute Earnings Bonus gained becomes larger because that percentage is applied to an increasingly large base.

With the rest of the loadout fixed, one PE is immediately equivalent to increasing the Soul Egg count by the same percentage:

$$\Delta S_{\text{equivalent}}=rS$$

For example, with one quadrillion Soul Eggs and a 10% PE rate:

$$0.10\times1\text{ quadrillion} =100\text{ trillion Soul Eggs}$$

That PE also multiplies every Soul Egg earned in the future, which makes it permanently valuable.

---

5. Adding Artifacts and Stones

Artifacts can modify both major parts of the Earnings Bonus system.

A safe general representation is:

$$\boxed{ EB_{\%}=S\,V_{\text{SE}}\,Q^P }$$

Where:

• $V_{\text{SE}}$ is the effective value of each Soul Egg after Soul Food and Soul Stone modifiers.
• $Q$ is the effective multiplier applied by each Prophecy Egg after Prophecy Bonus, Prophecy Stones, the Book of Basan, and relevant stacking rules.

This form avoids pretending that every artifact effect is simply additive. Exact values depend on artifact tier, rarity, socketed stones, equipped loadout, stacking rules, and in-game rounding.

Why small Prophecy improvements become powerful

Suppose a loadout changes the effective Prophecy base from:

$$1.10^P$$

to:

$$1.11^P$$

At 10 PE, the relative improvement is:

$$\left(\frac{1.11}{1.10}\right)^{10} \approx1.095$$

That is approximately a 9.5% improvement.

At 200 PE:

$$\left(\frac{1.11}{1.10}\right)^{200} \approx6.12$$

The same one-percentage-point change now produces approximately 6.12× as much Earnings Bonus.

This is why Books of Basan and Prophecy Stones become much more valuable as a player's PE count grows.

---

6. How Soul Eggs Are Earned During a Prestige

Pending Soul Eggs are primarily determined by the amount of prestige earnings accumulated since the previous prestige.

In practical terms, more income produces more pending Soul Eggs. Relevant factors include:

• A higher-value egg
• A larger chicken population
• Higher egg-laying rate
• Sufficient shipping capacity
• Earnings boosts
• Running Chicken Bonus
• Earnings artifacts
• A stronger permanent Earnings Bonus

However, the game does not award Soul Eggs at a constant rate. Each additional pending Soul Egg becomes progressively more expensive during the same prestige cycle.

That is why the counter rises quickly at first and then appears to slow down. It is not frozen - you are moving along a diminishing-return curve.

The piecewise Soul Egg gain curve

The community-documented prestige formula uses several power-law regions with exponents:

$$[0.15,\ 0.16,\ 0.17,\ 0.18,\ 0.19,\ 0.20,\ 0.21]$$

The exact region boundaries are implementation details. The important behavior is that every exponent is below 1, which guarantees diminishing returns.

At sufficiently high prestige earnings, the local behavior is commonly approximated as:

$$\boxed{G\propto x^{0.21}}$$

Where:

• $G$ is the number of pending Soul Eggs.
• $x$ is the relevant modified prestige-earnings input.

Late-game approximation: The calculations below use the final 0.21 region. Exact results differ in earlier regions and when an earnings increase crosses a region boundary.

View

What the 0.21 exponent means

If the relevant prestige-earnings input increases by a factor of $m$, pending Soul Eggs increase by approximately:

$$m^{0.21}$$

A huge earnings multiplier therefore does not create an equally huge Soul Egg multiplier.

Example: a 500× Soul Beacon

In the simplified late-game model, treating the 500× effect as multiplying the relevant prestige-earnings input gives:

$$500^{0.21}\approx3.688$$

That means approximately 3.69× as many pending Soul Eggs - not 500×.

The exact in-game result depends on your full boost combination, timing, artifacts, earnings region, and how the active modifiers are applied.

How much more income is needed to double Soul Egg gains?

Solve:

$$m^{0.21}=2$$

Therefore:

$$m=2^{1/0.21}\approx27.13$$

In the late-game approximation, you need roughly 27× more prestige earnings to receive twice as many Soul Eggs during the same prestige run.

---

7. Why Prestige Events Beat Equivalent Earnings Events

Consider two events:

1. A 2× earnings event
2. A 2× prestige event

A 2× earnings event changes the input to the late-game power function:

$$2^{0.21}\approx1.157$$

So it produces approximately 15.7% more pending Soul Eggs, assuming the same high-level region and all other factors remain equal.

A 2× prestige event multiplies the resulting Soul Egg reward directly:

$$G_{\text{event}}=2G$$

This is why 2× and 3× prestige events are especially valuable for building Soul Eggs.

The event multiplier may already be reflected in the displayed prestige counter, so do not expect an additional multiplier after prestiging.

---

8. Why Multistiging Works

A multistige uses one boost session to prestige and rebuild multiple times.

Its mathematical advantage comes from repeatedly resetting the diminishing-return curve.

Idealized two-leg example

Assume the simplified function:

$$f(x)=x^{0.21}$$

One continuous prestige with total earnings of $2x$ produces:

$$f(2x) =(2x)^{0.21} =2^{0.21}x^{0.21}$$

Two separate prestiges, each earning $x$, produce:

$$f(x)+f(x)=2x^{0.21}$$

The ratio is:

$$\frac{2x^{0.21}}{2^{0.21}x^{0.21}} =\frac{2}{2^{0.21}} \approx1.729$$

Under these idealized assumptions, two equal runs produce approximately 72.9% more Soul Eggs than placing the same total prestige earnings into one continuous run.

More generally, splitting the same total earnings into $n$ equal legs gives an idealized advantage of:

$$n^{1-0.21}=n^{0.79}$$

The real tradeoff

The 72.9% result is not a guaranteed in-game improvement. It assumes:

• Both legs earn exactly the same amount.
• Both remain in the same 0.21 region.
• Returning to the target egg takes no time.
• Rebuilding habitats and common research takes no time.
• Population refills instantly.
• Boost duration is not wasted.
• Changes to Earnings Bonus after the first prestige are ignored.

Real multistiging costs time through:

• Returning to the target egg
• Rebuilding habitats
• Buying common research
• Refilling population
• Restoring the Running Chicken Bonus

The actual goal is to maximize:

$$\frac{\text{Soul Eggs earned}}{\text{time spent}}$$

Add another prestige leg only while the gain from resetting the curve exceeds the cost of rebuilding.

---

9. Soul Eggs vs. Prophecy Eggs

The two resources solve different progression problems.

Soul Eggs

Soul Eggs are repeatedly farmed through prestige:

$$EB\propto S$$

They provide the largest immediate progression jumps for most early- and mid-game players.

Prophecy Eggs

Prophecy Eggs are limited and usually obtained through contracts, the gift calendar, trophies, and special rewards:

$$EB\propto(1+r)^P$$

Every PE provides the same relative multiplier for a fixed loadout. Its absolute contribution grows because it multiplies a larger existing Earnings Bonus, and it continues multiplying all future Soul Eggs.

---

10. Practical Strategy by Progression Stage

View

Early game

Prioritize:

• Reaching higher-value eggs
• Increasing chicken population
• Buying high-impact Epic Research
• Prestiging when progress becomes inefficient
• Collecting every available Prophecy Egg

A moderate increase in Soul Eggs can transform early progression because your total is still relatively easy to multiply.

Mid game

Start optimizing:

• Prestige boost combinations
• 2× and 3× prestige events
• Earnings artifacts
• Soul Food
• Prophecy Bonus
• Contract completion

At this stage, both Soul Egg farming and PE collection matter significantly.

Late game

Optimization increasingly revolves around:

• Prophecy Eggs
• Books of Basan
• Prophecy Stones
• High-efficiency prestige loadouts
• Multistiging
• Soul Eggs earned per minute, not merely per prestige

At high PE counts, small improvements to the effective Prophecy multiplier can outperform much larger-looking additive bonuses elsewhere.

---

Final Mental Model

The permanent Earnings Bonus system is:

$$\boxed{ \text{Earnings Bonus} = \text{Soul Egg count} \times \text{value per Soul Egg} \times \text{Prophecy compounding} }$$

Prestige progression is:

$$\boxed{ \text{New Soul Eggs} \propto (\text{prestige earnings})^{\text{an exponent below }1} }$$

In plain English:

1. Soul Eggs build the base.
2. Soul Food makes every Soul Egg stronger.
3. Prophecy Eggs repeatedly multiply the entire base.
4. Earning more money creates pending Soul Eggs.
5. Pending Soul Egg growth slows during a prestige because of diminishing returns.
6. Prestiging resets that diminishing-return curve.
7. Multistiging exploits that reset when rebuilding is fast enough.

That is the mathematical engine behind long-term progression in Egg, Inc.

---

Sources and Further Reading

The developer confirms the general relationship between Soul Eggs, Eggs of Prophecy, Earnings Bonus, boosts, and prestige progression. Detailed formulas are primarily community-documented and may change after game updates.

Community references

• Egg, Inc. Wiki - Earnings Bonus
• Egg, Inc. Wiki - Soul Eggs
• Egg, Inc. Wiki - Eggs of Prophecy
• Egg, Inc. Wiki - Prestige