Fair Lottery aims to be a decentralized application (dApp) that implements the lottery game in a "fair" way. A user can bet any amount of money and choose the probability of winning. The maximum possible win is calculated on the basis of the bet amount and the chosen probability. After about a minute from purchasing the ticket, it is possible to determine whether it is a winner or not, getting the reward. No third-party entity can control or manipulate the lottery by rigging the tickets or removing funds belonging to the lottery itself. The lottery code itself is written on the blockchain and it's immutable. Once deployed no one can change it.

You buy a ticket of value X Ethereum and select a P in ]0,1[ probability that the ticket will be a winning ticket. If you bought a winning ticket you will get back X/P - fee Ethereum. Where the fees are a total of 0.002*(X/P-X). More on fees later. Example:

1. I buy a 1 Ethereum ticket with a winning probability of 10%. If it's a winning ticket i can redeem it and get back 1/0.1 - 0.002*(1/0.1 - 1) = 9.98 Ethereum to my account. If i lose i get back nothing. On average 1 times out of 10 i will win.
2. I buy a 10 Ethereum ticket with a winning probability of 99%. If it's a winning ticket i can redeem it and get back 10/0.99 - 0.002*(10/0.99 - 10) = 10,100808 Ethereum to my account. If i lose i get back nothing. On average 99 times out of 100 i will win.

You can redeem the ticket after at least 5 blocks of its purchase. You must redeem the ticket within 255 blocks of its purchase otherwise you can no longer collect the reward. This is because the contract has a limited view of 256 blocks behind and the random function is based on the blocks hash.

True randomness in a deterministic environment is not possible. However, this system guarantees a generation of random numbers that cannot be tampered by anyone. The randomness is generated in a distributed ways by the miners. Until there isn't a miner that control 51% of the block generation the randomness is guaranteed.

The random function is implemented as follows:

function random(uint256 i, address ticketOwner, uint256 ticketIndex) private view returns (uint256) {
	bytes32 ticketId = keccak256(abi.encode(ticketOwner, ticketIndex));
	bytes32 seed = blockhash(i) ^ blockhash(i + 1) ^ blockhash(i + 2) ^ blockhash(i + 3) ^ blockhash(i + 4) ^ ticketId;
	return uint256(seed);
}

Where i is the index of the block in which the ticket was bought, ticketOwner is the owner address, ticketIndex is the index of the ticket referred to the owner. It is possible to find out if the ticket is a winner only after 5 blocks from the purchase. In this way the miners competing to find the next block increase the entropy of the random function.

Basing the random function on n blocks means that to compromise it, a miner must be able to find n blocks in a row. Furthermore, to have a guaranteed win, the malicious miner should include the purchase transaction of the ticket in the i-n block and be able to mine n further blocks and publish them all together. In fact, if the malicious miner publishes the blocks as he mines them, he would risk that another miner will insert a block that is out of his control. So the malicious miner has a very high profit loss. In this case n = 5 and this means that even if a malicious miner controlled 49% of the hashing power he would have about 2.8% chance of finding 5 blocks in a row to have a guaranteed win. But that means he would lose 97.2% of the profit that comes from the minig. This would still be a possible attack if a lot of Ethereum could be won from the lottery. This is where the safety factor comes into play.

The net winnings must be less than the P/SafetyFactor. Where P is the lottery liquidity reserve. The net win is the total win minus the ticket price. In this way it is guaranteed that in order to empty the liquidity reserve, SafetyFactor tickets at the winning limit must win at the same time. For now SafetyFactor = 10.

Scenario 1: pool da sola cerca di vincere il 100% dei ticket, ovvero, gioca solo ticket vincenti Scenario 2: la pool decide di influenzare soltanto l'ultimo blocco, decidendo se scartarlo o meno. Scenario 3: si svuota la pool e qualcuno perde anche se vince.

The lottery owner is the one that deploy the smart contract in the blockchain and the whom that puts the funds for the ethereum pool. The owner gets 0.1% of the potential win as a fee for each bet. The pool also gets 0.1% of the potential win as a fee for each bet. The owner can't manipulate the fairness of the lottery. The owner can only change the safety factor of the pool.

Edoardo Barbieri Emanuele Pansici