7. Probability & Mathematical Guarantees

Fairness is treated as a measurable property derived from on-chain state. The protocol ensures that "winning" always results in a net economic gain.

The Probability Model

Every valid entry in a pool of size N has an equal weight.

  • Single Entry Odds: The probability of one entry winning is 1/N.

  • Multiple Entry Odds: For a user with k entries, the probability is k/N.

The Profitability Threshold (N > 10)

To prevent winners from being "mathematically disadvantaged" by low participation, the protocol enforces a Profitability Threshold. A pool only resolves if it contains at least eleven entries.

The math ensuring the third-place winner is net profitable (Reward > Entry Fee) is derived as follows:

fraction x (N x E) > E

Where:

  • E: Entry Fee

  • N: Total Entries

  • fraction: The fixed reward percentage for 3rd place

If N < 11, no randomness is requested; instead, all entries are automatically carried over to the next pool.

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