Idle Incrementation Analysis

Project Overview: Idle Economy & Progression Modeling

• Genre: Idle / Incremental Game Economy
• The Challenge: Designing and balancing a 15-minute (900 seconds) progression simulation with exponentially scaling upgrade costs.
• My Role: Systems & Economy Designer
• Tools Used: Excel (Data Modeling), Python (Algorithmic Testing), Unity (Playable APK and EXE Build)
• Project Files: [Download Playable APK] | [View Excel Simulation Model] | [View Python Scripts]

The Design Problem: Exponential Scaling vs. Time

Idle games are built on a delicate balance between active/passive income and delayed gratification. In this project, I created a rigorous mathematical model to simulate exactly 15 minutes of gameplay.

The core mechanics rely on six tiers of upgrades (from Small Mines to Alchemical Mines), where the cost of each building scales exponentially based on ownership. The formula dictating this inflation is: Cost = BaseCost*1.1^N (Where N is the number of that specific mine type already owned).

The design challenge was to find the absolute "optimal path" to reach the maximum possible gold at turn 901. To solve this, I built a detailed spreadsheet tracking second-by-second income, cumulative costs, and purchasing decisions.

Man vs. Machine: Why Algorithms Fail at Idle Games

To find the perfect progression curve, I didn't rely solely on manual playtesting. I developed Python algorithms to calculate the highest possible yield and attempted to use Excel Solver. However, the results revealed a fascinating reality about game design: Human intuition consistently outperformed the algorithms.

Both my own manual playthroughs and the playtest data from other players yielded significantly higher final gold counts than the Python scripts. Here is the systemic breakdown of why this happens:

• The "Local Optima" Trap: Most standard optimization algorithms (like Greedy algorithms) evaluate the immediate Return on Investment (ROI). If a Small Mine offers the best cost-to-income ratio at second 45, the algorithm buys it. However, it gets stuck in "local optima," constantly buying cheap upgrades and delaying massive power spikes.
• Combinatorial Explosion: The sheer volume of possibilities across 900 seconds with 6 variable upgrade paths creates a mathematical web too vast for simple solvers (like Excel Solver) to compute brute-force.
• The Power of Delayed Gratification: Human players naturally understand macro-strategy. A human can look at the board and decide, "I will buy absolutely nothing for the next 40 seconds to save up for a Huge Mine." Humans willingly accept a mathematically "sub-optimal" period of low income because they intuitively understand that the massive exponential spike later will eclipse short-term losses.

Design Takeaway

This experiment proved that a well-designed idle game cannot be balanced purely by running automated scripts. True progression design requires understanding the player's psychological willingness to "wait for the big reward." The APK provided here is the playable manifestation of this very economic model, allowing players to test their own delayed gratification against the math.