💰︱Bet Settlement

The PlayLand protocol is committed to ensuring the integrity and stability of its betting environment. To achieve this, we implement a mathematical model that determines the maximum safe bet size based on the liquidity available in the betting pool.

This model takes into account not only the total liquidity but also potential payouts, ensuring the financial stability of the platform.

Mathematical Model for Determining Safe Bet Size

To calculate the maximum safe bet size, we consider several factors including the total liquidity, current committed funds, house rake, and the maximum potential payout multiplier.

Formula:

$𝐵=𝐿−𝐶(𝑋+𝑅)×𝑀B=(X+R)×ML−C​$

Where:

• $𝐵B$ = Maximum safe bet size

• $𝐿L$ = Total liquidity in the betting pool

• $𝐶C$ = Total current committed funds in unresolved bets across all games

• $𝑅R$ = House rake for the specific game as a decimal

• $𝑀M$ = Maximum potential payout multiplier for the game

• $𝑋X$ = Safety factor, a precautionary buffer to manage unexpected fluctuations

Implementation and On-Chain Settlements

All betting operations, including the application of this formula, are conducted on-chain to ensure transparency and security. The PlayLand blockchain explorer provides public access to records of all transactions, allowing users and auditors to verify the authenticity and fairness of the game outcomes.

Example Application of the Formula

Scenario Setup:

• Total Liquidity (L): $100,000

• Total Committed Funds (C): $25,000

• House Rake (R): 5% (0.05)

• Maximum Payout Multiplier (M): 10

• Safety Factor (X): 10

Calculation:

Substituting these values into the formula gives:

$𝐵=100,000−25,000(10+0.05)×10B=(10+0.05)×10100,000−25,000​$ $𝐵=75,000100.5B=100.575,000​$ $𝐵=746.27B=746.27$

This calculation tells us that the maximum safe bet that can be placed, considering the house rake and the possibility of a payout being 10 times the bet amount, is approximately $746.27.

Safety and Liquidity Considerations

This bet size ensures that even if the player wins the maximum payout, the liquidity of the betting pool remains adequate to cover this and other outstanding bets. The use of a safety factor (X) and inclusiveness of the house rake (R) in the calculation further enhances the robustness of this model, guarding against potential liquidity crises.

By meticulously managing bet sizes through this mathematical model, our platform upholds a responsible gaming environment and ensures operational continuity, protecting both the interests of the players and the platform's financial health.