# Math formula

## Mathematical Model for Conversion

Validated by ChatGPT. [*Read details here*](https://chatgpt.com/canvas/shared/67b597e341b0819185fc82f3d490e79d)*.*

> <mark style="background-color:green;">**For max trading volume for 100% of oMAIGA unlocks, 10,000,000 BNB trading volume on whitelisted DEX LP is calculated (appr. $8b based on $800/BNB).**</mark>

<figure><img src="/files/WUtkqpVZWee8u3xAMkMf" alt=""><figcaption></figcaption></figure>

### **Monte Carlo simulation for market variability**

To model **uncertainty and randomness in market behavior**, we introduce a **stochastic noise factor.** This ensures **random market fluctuations** are factored into the unlock model, preventing overly rigid outcomes.

<figure><img src="/files/Rsa8jqMxhgDm0kVfIEoa" alt=""><figcaption></figcaption></figure>

### **Final oMAIGA conversion calculation**

Bringing all components together, the **final unlock formula** is:

<figure><img src="/files/rlFKyJEti7ccPYwrLtwF" alt=""><figcaption></figcaption></figure>

This ensures that:&#x20;

✅ Unlocks **scale with trading volume**

✅ Buy-side demand **boosts unlock rates**

✅ Manipulative behaviors **reduce unlock amounts**

✅ Market fluctuations **introduce realistic unpredictability**

We believe by using this novel approach of a new type of token model is akin to taking a long-term approach involves addressing the cold-start problem by gradually increasing depth and liquidity in the market.

{% hint style="success" %}
💡 As depth and liquidity improve, more traders are attracted to the market, resulting in increased trading volume over time, thus, improving the bullishness and sentiment for MAIGA token and Maiga ecosystem.
{% endhint %}

## Key Features of the PoT token model

✅ **Bullish Momentum Rewards**

* Strong Buy Volume (Buy Ratio > 0.75) & Surging Volume (+1m/day) → 1.4x unlock boost
* Moderate Buy Volume (Buy Ratio 0.6-0.75) & Uptrend (+500k/day) → 1.2x unlock boost
* Impact: Encourages traders to drive sustained bullish momentum.

✅ **Bearish Protection Against Dumping**

* Weak Buy Volume (Buy Ratio < 0.45) & Declining Volume (-50k/day) → 0.8x unlock slowdown
* Extreme Sell-Off (Buy Ratio < 0.35 & Volume Collapse -100k/day) → 0.5x severe unlock reduction
* Impact: Prevents large-scale sell pressure by discouraging exits during crashes.

✅ **Scenario-Specific Adjustments for Manipulation Prevention**

* Flash Loan Attacks → 0.3x unlock penalty
* Wash Trading Detection → 0.6x unlock penalty
* Liquidity Sniping → 0.75x unlock penalty
* Bot-Driven Momentum Trading → 1.3x unlock boost (to encourage algorithmic liquidity)
* Impact: Protects from fake volume tricks while rewarding legitimate long-term liquidity strategies.

## Real world market behavior

<table data-header-hidden><thead><tr><th width="262">Market Scenario</th><th width="246">Dynamic Unlock Adjustments</th><th>Impact</th></tr></thead><tbody><tr><td><strong>Market Scenario</strong></td><td><strong>Dynamic Unlock Adjustments</strong></td><td><strong>Impact</strong></td></tr><tr><td>Bull Market (Strong Buying)</td><td>1.4x unlocks when buy ratio > 0.75</td><td>Encourages sustained FOMO</td></tr><tr><td>Healthy Uptrend</td><td>1.2x unlocks when buy ratio > 0.6</td><td>Promotes stable growth</td></tr><tr><td>Sideways Market</td><td>1.0x unlocks remain unchanged</td><td>No forced incentives</td></tr><tr><td>Mild Bear Market</td><td>0.8x unlocks when buy ratio &#x3C; 0.45</td><td>Prevents exit dumps</td></tr><tr><td>Severe Bear Market</td><td>0.5x unlocks when buy ratio &#x3C; 0.35</td><td>Locks down selling pressure</td></tr><tr><td>Flash Loan Attack</td><td>0.3x unlocks</td><td>Blocks instant liquidity abuse</td></tr><tr><td>Wash Trading</td><td>0.6x unlocks</td><td>Removes fake trading benefits</td></tr><tr><td>Liquidity Sniping</td><td>0.75x unlocks</td><td>Prevents thin liquidity targeting</td></tr><tr><td>Bot Momentum Trading</td><td>1.3x unlocks</td><td>Rewards consistent volume creation</td></tr></tbody></table>

### Formula to prevent wash trading at CEX

> <mark style="background-color:yellow;">**Initially on TGE, 100% of whitelisted DEX LP volume is used for calculation to prevent wash trading on CEXs and DEXs LPs with little liquidity**</mark>

Instead of using raw volume, apply a weighted formula that prioritises organic liquidity sources using **Volume-Weighted & Liquidity-Adjusted Data**. This method reduces influence from low-trust exchanges.

**Example:**

* Binance (W=1.0), Coinbase (W=0.9), OKX (W=0.8), KuCoin (W=0.6), Suspicious Exchange (W=0.2)
* If reported volume is 100M, 50M, 30M, 20M, and 40M, then:

<figure><img src="/files/K1FnYBjsZ8nsM8MWS0LD" alt=""><figcaption></figcaption></figure>

### **Buy/Sell ratio normalization formula**

Since buy/sell volume ratios impact unlocks, they must be weighted & smoothed. This prevents **sudden manipulation attempts** from spiking buy ratios.

<figure><img src="/files/iEzSamg8gsvjeUk2wViI" alt=""><figcaption></figcaption></figure>

## **Monte Carlo Simulation (100 Runs)**

To validate the model, a Monte Carlo simulation was performed with 100 runs, incorporating:

1. Randomised Buy Volume & Trading Volume. Each run sampled buy/sell ratios from real-world crypto datasets.
2. Scenario-Specific Modification. Each run randomly introduced flash loan attacks, wash trading cycles, and whale movements to test the model’s robustness.
3. Standard Deviation Calculations. The unlock trajectories were analyzed to identify expected unlock ranges and extreme market deviations.

<figure><img src="/files/Z9JKWD3JaXlQ0UihhZEC" alt=""><figcaption></figcaption></figure>

✅ Bullish Market Conditions → Unlocks increase up to 1.4x due to high buy pressure.

✅ Bearish Market Conditions → Unlocks reduce up to 50% to prevent dumping.

✅ Wash Trading & Flash Loans Are Penalized → Unlocks are slashed by 40-70% in manipulation scenarios.

✅ Monte Carlo Confidence Intervals Show Stable Outcomes → Despite market noise, the model remains predictable and robust.


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