We integrate a weighted probability distribution to allocate rewards based on multipliers, inspired by principles from the risk-neutral probability measure used in the Black-Scholes/Merton model. We incorporate insights from behavioral economics, rewarding actions that align with the long-term health of our token economy. Instead of small, stretched-out rewards, we introduce frequent, gamified airdrop rewards. This method will select random holders under specific parameters, maximizing the number of participants each time, and grant them a reward in $ETH or tokens - an amount with tangible value.

This approach is supported by allocating 1% of taxes from each $PAI transaction and all revenue generated within our ecosystem such as our custom AI bot creating services and betting platform into a weekly buyback fund specifically for these gamified active airdrop rewards. This ensures that the rewards are substantial and the events, exciting.

The distribution algorithm will factor in the duration for which tokens are held, the quantity, and multipliers that enhance the probability of receiving airdrops. These multipliers will be judiciously calculated to maintain balance and fairness.

• This is our simplified formula for you to understand the backbone of this model:

  • R is the reward multiplier for a holder, defined as follows:

    • R = H • T • B • S • L

  • Where:

    • H represents the holding time multiplier.

    • T is the tokens held multiplier.

    • B accounts for buying behavior, rewarding large, one-time purchases.

    • S decreases the chances of swing traders receiving rewards to promote stability.

    • L increases the chances if $PAI is within the top 3 holdings in a wallet.

  • Definition of each multiplier:

    1. H = log(1 + Time held in days)

    2. T = √(Tokens held)

    3. B = (Number of buys)^(-1); (Rewarding fewer, larger buys)

    4. S = e^(−Number of sells in the last 30 days); (Disincentivizing frequent selling)

    5. L = 1.5 if $PAI is in top 3 holdings, 1 otherwise

  • This formula considers holding duration, the amount held, purchase behavior, and loyalty to $PAI. We will continuously adapt and monitor for fairness and impact. The multipliers and parameters will be continuously adjusted to ensure that no single strategy disproportionately dominates the reward system.

This formula considers holding duration, the amount held, purchase behavior, and loyalty to $PAI. We will continuously adapt and monitor for fairness and impact. The multipliers and parameters will be continuously adjusted to ensure that no single strategy disproportionately dominates the reward system.