Pricing

Visual Price Curves

mermaid
graph LR
    subgraph "Aggressiveness = 0 (Linear)"
        A1[0 ETH] -->|Constant Price| A2[Target]
    end
    
    subgraph "Aggressiveness = 50 (Moderate)"
        B1[0 ETH] -->|Gradual Increase| B2[Target]
    end
    
    subgraph "Aggressiveness = 100 (Steep)"
        C1[0 ETH] -->|Rapid Increase| C2[Target]
    end

Bonding Curve Model

Mathematical Formula

text
S = S_final × (R / R_target)^exponent

Understanding the Exponent

The aggressiveness factor controls how the exponent affects price progression:

Aggressiveness Factor Impact

Cumulative Token Distribution

See how tokens are distributed throughout the bonding process with different aggressiveness factors.

Example: 10M B3 target, 1.25M total token supply (1M available for bonding, 250K reserved for LP)

Real-World Example: Alice's Purchase

Let's follow Alice, who wants to buy tokens from a new project at launch:

Project Setup:

• Total Supply: 1.25M tokens (1M for bonding + 250K for LP)
• Target: 10M B3 to reach migration
• Aggressiveness: 100 (maximum reward for early buyers)
• Current Progress: 0% (project just launched)

Alice's Purchase: Alice decides to buy 1M B3 worth of tokens right at launch (0% progress).

1. Alice sends: 1M B3 tokens
2. Trading fee (3%): 30K B3 goes to fee recipients
3. Amount for curve: 970K B3 advances the project to ~9.7% progress
4. Tokens received: ~306,000 tokens (calculated from bonding curve)

Comparing Different Entry Points: If Alice waited and bought the same 1M B3 worth at different project stages:

Early Buyer Advantage: Alice gets 6.2x more tokens by buying at launch versus waiting until 90% progress!

Interactive Price Calculator

typescript
// Calculate tokens received for a given trading token amount
function calculateTokensReceived(
  tradingTokenAmount: number,
  currentRaised: number,
  targetAmount: number,
  totalSupply: number,
  aggressiveness: number
): number {
  const exponent = 1 / (1 + aggressiveness / 100);
  
  // Calculate supply at current raised
  const currentSupply = totalSupply * 
    Math.pow(currentRaised / targetAmount, exponent);
  
  // Calculate supply after purchase
  const newRaised = currentRaised + tradingTokenAmount;
  const newSupply = totalSupply * 
    Math.pow(newRaised / targetAmount, exponent);
  
  // Tokens received = difference in supply
  return newSupply - currentSupply;
}

// Example usage
const tokens = calculateTokensReceived(
  1,        // 1 ETH purchase
  5,        // 5 ETH already raised
  10,       // 10 ETH target
  1000000,  // 1M total supply
  50        // 50% aggressiveness
);
console.log(`You'll receive ${tokens.toFixed(0)} tokens`);

Choosing Your Aggressiveness Factor

Decision Framework

Selling Mechanics

When users sell tokens back to the curve:

1. Price Calculation: Uses inverse of buying formula
2. Fee Deduction: 5% fee applied to proceeds
3. Curve Update: Reduces total raised amount
4. Price Impact: Large sells significantly impact price

Sell Price Formula

typescript
// Calculate trading token received for selling tokens
function calculateTradingTokenReceived(
  tokenAmount: number,
  currentSupply: number,
  currentRaised: number,
  targetAmount: number,
  totalSupply: number,
  aggressiveness: number
): number {
  const exponent = 1 / (1 + aggressiveness / 100);
  
  // Calculate new supply after sell
  const newSupply = currentSupply - tokenAmount;
  
  // Calculate corresponding raised amount
  const supplyRatio = newSupply / totalSupply;
  const newRaised = targetEth * 
    Math.pow(supplyRatio, 1 / exponent);
  
  // ETH received (before fees)
  const ethBeforeFees = currentRaised - newRaised;
  
  // Apply 5% fee
  return ethBeforeFees * 0.95;
}

Edge Cases & Limits

Real-World Examples

Case Study: Fair Launch Token

• Aggressiveness: 10
• Target: 50 ETH
• Result: Nearly linear pricing, community appreciated fairness

Case Study: Hype Token

• Aggressiveness: 85
• Target: 100 ETH
• Result: Reached target in 2 hours, early buyers gained 8x

Case Study: Balanced Project

• Aggressiveness: 45
• Target: 25 ETH
• Result: Steady growth over 3 days, 2.5x advantage for early buyers

Next Steps