Financial Model Expert and Strategy Consultant
The Polytopia Calculator helps players determine the optimal number of turns required to recoup an initial star investment based on subsequent per-turn production and consumption rates. Use this tool to compare different strategic expansion options quickly.
Polytopia Calculator
Polytopia Calculator Formula:
$$T = \frac{I}{P – C}$$
Formula Source: The Battle of Polytopia Economy GuideVariables:
- I (Initial Investment): The one-time star cost of an expansion, such as settling a city or upgrading a resource.
- P (Production): The total stars earned per turn from all cities and income sources after the investment is made.
- C (Consumption): The total stars spent per turn on unit maintenance and ongoing costs.
- T (Turns until Profitability): The number of turns required for the net star gain ($$P-C$$) to equal the Initial Investment (I).
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What is Polytopia Calculator?
The Polytopia Calculator is an essential strategic tool designed for competitive players of The Battle of Polytopia. It shifts focus from immediate unit power to long-term economic efficiency by determining how quickly a strategic expenditure pays for itself in star currency. By understanding the “Turns until Profitability” (T) for different expansion or construction decisions, players can ensure their limited star resources are deployed for maximum efficiency, accelerating their economic engine.
Economic advantage is often the deciding factor in Polytopia matches. Making the right investment—be it a new city, a monument, or an advanced tech—requires knowing the break-even point. This calculator provides that critical metric, allowing players to compare a low-cost, low-yield option against a high-cost, high-yield one. The result helps inform decisions on when to prioritize development over immediate military action, offering a significant edge in resource management.
How to Calculate Polytopia Calculator (Example):
- Identify the Investment (I): Suppose you spend 30 Stars to buy a Super Unit (I=30) which immediately increases your Star production by 5 Stars/Turn.
- Determine Net Production ($$P-C$$): If your Production (P) is 25 Stars/Turn and your Consumption (C) is 15 Stars/Turn (due to unit maintenance), your Net Gain per turn is $$25 – 15 = 10$$ Stars/Turn.
- Apply the Formula: Divide the Initial Investment (I) by the Net Gain per turn ($$P-C$$): $$T = \frac{30}{10}$$
- Get the Result: The Turns until Profitability (T) is 3. This means it will take 3 turns for the initial 30 Star investment to be fully recouped from the net star income.
Frequently Asked Questions (FAQ):
Production (P) is the total stars earned from all cities and resource tiles each turn. Consumption (C) is the total star cost incurred from unit maintenance each turn. The difference ($$P-C$$) is your net star gain, which determines profitability speed.
What happens if Production (P) is less than Consumption (C)?If $$P < C$$, your Net Gain is negative, meaning you are losing stars each turn. In this case, the calculator will flag an error, as you will never reach profitability. The strategy requires reducing unit maintenance or increasing city level/resources.
Can I use this for non-star investments?No, this specific calculator is designed for Star currency profitability. For movement or damage efficiency, you would need a different model.
What is the consistency check used for?If you enter values for all four variables (I, P, C, and T), the calculator checks if the relationship $$T = \frac{I}{P – C}$$ holds true. If the difference is outside a small tolerance, it warns that the inputs are inconsistent.