Math

Exprmnt0 or LLL (Limited Loss Lotry) employs a bonding curve model to dynamically determine the price of its native token based on supply and liquidity conditions. This section outlines the mathematical foundation governing token pricing, trading logic, and tax mechanisms.

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Key Variables

Variable	Description	Example Value
Virtual Tokens	Simulated tokens used for curve initialization	66,666,666.67
Virtual $LOTRY	Simulated $LOTRY used for curve initialization	13,333,333,333.33
Initial Supply	Tokens initially deposited in the contract	1,000,000,000
Tax	Buy and sell transaction tax	11%
$LOTRY	This token is deployed through clanker	100,000,000,000 is the max supply from clanker

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Token Pricing Formula

The price of the token is determined by the ratio of total $LOTRY to total tokens held in the curve:

$$\text{Token Price} = \frac{(\text{Virtual \$LOTRY} + \text{\$LOTRY in Contract})}{(\text{Virtual Tokens} + \text{Tokens in Contract})}$$

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Market Capitalization

The market cap represents the total circulating token value:

$$\text{Market Cap} = \text{Token Price} \times (\text{Virtual Tokens} + \text{Tokens in Circulation})$$

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Bonding Curve (Constant Product Equation)

LLL follows a constant product invariant, ensuring that the product of total $LOTRY and total tokens remains constant during trades:

$$(\text{Virtual \$LOTRY} + \text{\$LOTRY in Contract}) \times (\text{Virtual Tokens} + \text{Tokens in Contract}) = K$$

Here, ( $K$ ) is the constant product that defines the curve’s balance.

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Buy Transaction

When a user buys tokens with $LOTRY:

1. A 11% tax is deducted and sent to the tax pool.

2. The remaining 89% of $LOTRY contributes to the bonding curve.

$$\text{\$LOTRYtoCurve} = (1 - 0.11) \times \text{\$LOTRYreceived}$$

The number of tokens given to the buyer is computed as:

$$\text{Tokens Given} = (\text{Virtual Tokens} + \text{Tokens in Contract}) - \frac{K}{(\text{Virtual \$LOTRY} + \text{\$LOTRY in Contract} + \text{\$LOTRYtoCurve})}$$

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Sell Transaction

When a user sells tokens:

1. The system calculates the $LOTRY returned from the curve.

2. A 11**% tax** is applied on the $LOTRY before sending it to the seller.

$$\text{\$LOTRYfromCurve} = (\text{Virtual \$LOTRY} + \text{\$LOTRY in Contract}) - \frac{K}{(\text{Virtual Tokens} + \text{Tokens in Contract} + \text{TokensToCurve})}$$

$$\text{NetLOTRYsent} = (1 - 0.11) \times \text{\$LOTRYfromCurve}$$

The deducted 11% from NetLotrysend is routed to the tax pool.