How Soul Eggs and Prophecy Eggs Work in Egg, Inc. - 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. Prophecy Eggs scale exponentially.

Soul Eggs determine the base size of your permanent Earnings Bonus. Eggs of Prophecy repeatedly multiply that bonus through compounding. This is why Soul Eggs dominate early progression, while Prophecy Eggs become increasingly powerful later.

This guide explains the formulas, how prestige gains work, and why strategies such as multistiging are mathematically effective.

TL;DR

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The simplified Earnings Bonus formula is:

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

Where:

• $S$ = number of Soul Eggs
• $P$ = number of Prophecy Eggs
• $F$ = Soul Food Epic Research level, from 0 to 140
• $R$ = Prophecy Bonus Epic Research level, from 0 to 5
• $EB_{\%}$ = the Earnings Bonus percentage displayed by the game

The practical interpretation:

• Doubling your Soul Eggs doubles your Earnings Bonus.
• Each Prophecy Egg multiplies your Earnings Bonus by between $1.05$ and $1.10$ before artifacts and stones.
• Prophecy Egg bonuses compound with one another.
• Soul Egg gains during a prestige have strong diminishing returns.
• Prestiging resets that diminishing-return curve.

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1. What the Earnings Bonus Actually Means

The game displays your permanent boost as a percentage.

For example:

• $100\%$ Earnings Bonus means your income becomes $2\times$ normal.
• $1{,}000\%$ Earnings Bonus means your income becomes $11\times$ normal.
• $10{,}000\%$ Earnings Bonus means your income becomes $101\times$ normal.

The actual cash multiplier is:

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

The extra 1 represents your farm's original earnings before the bonus is applied.

Example

If the game displays:

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

Then your real income multiplier is:

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

So your farm earns 251 times its unboosted income, not 250 times.

At enormous late-game values, this distinction becomes practically insignificant, but it matters when learning how the percentage is interpreted.

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2. The Basic Earnings Bonus Formula

Ignoring artifacts, stones, and special modifiers:

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

Variables

The formula has three major parts:

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

A useful mental model is:

• Soul Eggs = quantity
• Soul Food = value per Soul Egg
• Prophecy Eggs = exponential multiplier applied to all Soul Eggs

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3. Soul Eggs 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 add to the same linear base.

Example

Suppose you have:

$$S=1{,}000{,}000$$

With no other upgrades:

$$EB_{\%} = 1{,}000{,}000\times10 = 10{,}000{,}000\%$$

If you gain another one million Soul Eggs, your total becomes two million:

$$EB_{\%} = 2{,}000{,}000\times10 = 20{,}000{,}000\%$$

Your Soul Egg count doubled, so your Earnings Bonus doubled.

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4. Soul Food Increases the Value of Every Soul Egg

Soul Food is Epic Research that adds one percentage point to the value of every Soul Egg per level.

The value of one Soul Egg is:

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

Where $F$ is your Soul Food level.

At level zero:

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

At the maximum level of 140:

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

Therefore, maxing Soul Food changes the linear Soul Egg component from:

$$10S$$

to:

$$150S$$

That is a permanent multiplier of:

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

So maximum Soul Food makes your Soul Egg contribution 15 times larger than its original value.

Example

With one million Soul Eggs:

Without Soul Food:

$$EB_{\%} = 1{,}000{,}000\times10 = 10{,}000{,}000\%$$

With maximum Soul Food:

$$EB_{\%} = 1{,}000{,}000\times150 = 150{,}000{,}000\%$$

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5. Prophecy Eggs Scale Exponentially

Prophecy Eggs do not add a fixed amount to your Earnings Bonus.

Instead, every Prophecy Egg multiplies the total Soul Egg component:

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

Where:

• $P$ = number of Prophecy Eggs
• $r$ = bonus provided by each Prophecy Egg

Without Prophecy Bonus Epic Research:

$$r=0.05$$

With maximum Prophecy Bonus Epic Research:

$$r=0.10$$

Therefore, the Prophecy multiplier ranges from:

$$1.05^P$$

to:

$$1.10^P$$

Why This Is Compounding

With a $10\%$ Prophecy bonus:

• 1 PE gives $1.10\times$
• 2 PE give $1.10\times1.10=1.21\times$
• 3 PE give $1.10^3=1.331\times$
• 10 PE give $1.10^{10}\approx2.594\times$

The second Prophecy Egg multiplies the result of the first one. The third multiplies the result of both previous eggs, and so on.

This 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.

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6. A Complete Earnings Bonus Example

Suppose a player has:

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

The formula is:

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

Substitute the values:

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

Since:

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

We get:

$$EB_{\%} \approx 1{,}000\times10\times2.593742$$ $$\boxed{ EB_{\%}\approx25{,}937.42\% }$$

The actual income multiplier is:

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

The Same Example With Maximum Soul Food

Set $F=140$:

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

The actual income multiplier becomes:

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

Maximum Soul Food produced a $15\times$ improvement because the value of each Soul Egg increased from $10\%$ to $150\%$.

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7. How Valuable Is One Additional Prophecy Egg?

An additional Prophecy Egg 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:

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

Because Soul Eggs scale linearly, one new Prophecy Egg is immediately equivalent to increasing your Soul Egg count by the same percentage.

At $5\%$:

$$\Delta S_{\text{equivalent}} = 0.05S$$

At $10\%$:

$$\Delta S_{\text{equivalent}} = 0.10S$$

Example

Suppose you have:

$$S=1\text{ quadrillion Soul Eggs}$$

One additional Prophecy Egg at $10\%$ power gives the same immediate Earnings Bonus increase as adding:

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

However, the Prophecy Egg is even more valuable long-term because it also multiplies every Soul Egg you earn in the future.

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8. Adding Artifacts and Stones

Artifacts can modify both major parts of the formula.

A practical extended form is:

$$EB_{\%} = S(10+F+A_S) \left( 1.05+0.01R+\frac{A_P+A_B}{100} \right)^P$$

Where:

• $A_S$ = additional percentage points per Soul Egg from Soul Stones
• $A_P$ = additional Prophecy percentage points from Prophecy Stones
• $A_B$ = additional Prophecy percentage points from the Book of Basan

The exact values depend on artifact rarity, tier, stones, and equipped loadout.

Why Prophecy Improvements Become So Powerful

Suppose an artifact changes the Prophecy base from:

$$1.10^P$$

to:

$$1.11^P$$

At 10 Prophecy Eggs, the relative improvement is:

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

That is roughly a $9.5\%$ improvement.

At 200 Prophecy Eggs:

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

The same one-percentage-point change now produces approximately 6.12 times more Earnings Bonus.

That is why Books of Basan and Prophecy Stones become increasingly valuable as a player's Prophecy Egg count grows.

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9. How Soul Eggs Are Earned During a Prestige

Your pending Soul Eggs are primarily determined by the amount of prestige earnings accumulated since your previous prestige.

In practical terms, you earn more pending Soul Eggs by earning more money.

The following factors increase Soul Egg gains indirectly because they increase income:

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

The game does not simply award Soul Eggs at a constant rate. Each additional Soul Egg becomes progressively more expensive in terms of prestige earnings.

Auxbrain describes this directly: the prestige counter does not grow consistently, and each additional Soul Egg becomes increasingly difficult to earn during the same prestige cycle.

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10. The Soul Egg Gain Curve

The community-documented Soul Egg gain formula is piecewise, using several power-law regions.

A compact representation is:

$$G = B_{\text{research}} B_{\text{event}} \sum_{i=0}^{6} \max \left( 0, (10^{-6}\min(x,U_i))^{a_i} - L_i^{a_i} \right)$$

Where:

• $G$ = pending Soul Eggs
• $x$ = modified prestige earnings
• $B_{\text{research}}$ = Prestige Bonus Epic Research multiplier
• $B_{\text{event}}$ = prestige event multiplier
• $a_i$ = exponent used in each earnings region
• $L_i$ and $U_i$ = lower and upper bounds of each region

The documented exponents are:

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

The important practical behavior is not the exact piecewise implementation. It is that all of these exponents are far below $1$.

A power function with exponent below $1$ has diminishing returns.

At high earnings, the behavior can be approximated as:

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

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11. What the $0.21$ Exponent Means

If prestige earnings increase by a factor of $m$, pending Soul Eggs increase by approximately:

$$m^{0.21}$$

This explains why a huge earnings multiplier does not create an equally huge Soul Egg multiplier.

Example: A 500x Soul Beacon

A simplified late-game approximation is:

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

So multiplying the relevant prestige earnings by 500 increases pending Soul Eggs by approximately $3.69\times$, not $500\times$.

The exact result depends on the full boost combination, timing, artifacts, and which region of the piecewise formula the player occupies.

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12. How Much More Income Is Needed to Double Soul Egg Gains?

To find the earnings increase required to double pending Soul Eggs, solve:

$$m^{0.21}=2$$

Raise both sides to the power of $\frac{1}{0.21}$:

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

You need approximately 27 times more prestige earnings to receive twice as many Soul Eggs in the same high-level prestige run.

This is why the Soul Egg counter moves rapidly at first and then appears to slow down.

The game is not malfunctioning. You are moving along a diminishing-return curve.

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13. Why Prestige Events Are Stronger Than Earnings Events

Consider two different events:

1. A $2\times$ earnings event
2. A $2\times$ prestige event

A $2\times$ earnings event affects the input to the power function:

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

So it produces approximately $15.7\%$ more pending Soul Eggs in the late-game approximation.

A $2\times$ prestige event multiplies the resulting Soul Egg reward directly:

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

Therefore:

This is why Saturday prestige events are so important for building Soul Eggs.

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14. Why Multistiging Works

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

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

Suppose the simplified Soul Egg function is:

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

One long 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:

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

Compare the two outcomes:

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

Ignoring rebuild time and other practical constraints, two equal prestige runs can produce approximately 72.9% more Soul Eggs than putting the same total prestige earnings into one continuous run.

The Practical Tradeoff

The mathematical advantage does not automatically mean that more prestiges are always better.

A multistige also costs time:

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

The best strategy maximizes:

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

A player should add another prestige to the boost session only while the extra reset creates more Soul Eggs than the lost rebuilding time costs.

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15. Soul Eggs vs. Prophecy Eggs

The two resources solve different progression problems.

Soul Eggs

Soul Eggs are farmed repeatedly through prestige.

Their contribution is linear:

$$EB\propto S$$

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

Prophecy Eggs

Prophecy Eggs are limited and usually obtained through:

• Contracts
• The monthly gift calendar
• Trophies
• Certain special rewards

Their contribution is exponential:

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

Each new Prophecy Egg becomes more valuable as your existing Prophecy Egg count and Soul Egg count increase.

Comparison

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16. Practical Conclusions

For Early-Game Players

Focus primarily on:

• Reaching higher-value eggs
• Increasing your chicken population
• Buying useful Epic Research
• Prestiging whenever progress becomes inefficient
• Collecting every available Prophecy Egg

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

For Mid-Game Players

Start optimizing:

• Prestige boost combinations
• Saturday prestige events
• Earnings artifacts
• Soul Food
• Prophecy Bonus
• Contract completion

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

For Late-Game Players

The most important optimizations increasingly involve:

• Prophecy Eggs
• Books of Basan
• Prophecy Stones
• High-efficiency prestige loadouts
• Multistiging
• Soul Eggs earned per minute rather than per individual prestige

At high Prophecy Egg counts, tiny improvements to the Prophecy multiplier can outperform very large-looking additive bonuses elsewhere.

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Final Mental Model

The complete system can be understood as:

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

And prestige progression can be understood as:

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

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 the diminishing-return curve.
7. Multistiging exploits that reset several times in one boost session.

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

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Sources and Further Reading

The game developer confirms the general relationship between Soul Eggs, Prophecy Eggs, Earnings Bonus, and prestige progression. The detailed formulas are primarily community-documented and may change if the game is updated.

• Auxbrain Support - General Egg, Inc. FAQs
• Auxbrain - Mystical Eggs Deep Dive
• Egg, Inc. Wiki - Earnings Bonus
• Egg, Inc. Wiki - Soul Eggs
• Egg, Inc. Wiki - Eggs of Prophecy
• Egg, Inc. Wiki - Prestige