# Supplementary Notes

Fairness Analysis: Based on the above process analysis, it is evident that once the serverSeed hash chain is determined, the casino cannot manipulate the sequence of {$serverSeed\_i$} to skew the outcome in their favor before the clientSeed is known.

Once the clientSeed value is determined, ChainVerse has already disclosed $serverSeed\_N$, and it is impossible to change or reset the entire {$serverSeed\_i$} sequence (due to the collision resistance property of hash functions).

At the conclusion of the game, the server discloses the serverSeed used in that round. Users can verify:

· Whether the computed game result matches the announced lottery result based on the serverSeed and clientSeed.

· Since $serverSeed\_{i+1} $ disclosed in the previous round is the hash value of the server seed for the current round, users can verify whether the following formula holds true:

serverSeedi+1=hash(serverSeedi)serverSeed\_{i+1} = \text{hash}(serverSeed\_i) serverSeedi+1​=hash(serverSeedi​)

This verification ensures transparency and fairness in the gaming process, where outcomes are determined by the combined action of the disclosed serverSeed and clientSeed.

<mark style="background-color:red;">hash(serverSeed\_{i}) ==serverSeed\_{i+1}</mark>