Lottery backed by funds from the DAO, with profits going to the DAO. Proposal to be submitted.
DAO Lottery brainstorming
Ticket for .1 ETH? About $1USD at current prices, it's low enough that pretty much anybody can do it and also low enough that it'll take a lot to get any significant amount tied up in the Jackpot.
Weekly payouts? Monthly? Allows for an accumulation of tickets over time, with each ticket getting a random number to determine the payout, if any. Can't get higher payouts and lower payouts on the same ticket.
Cumulative ratio of odds must be lower than payout at that level. This will leave a small amount of profit for the DAO, while still giving good odds (significantly better than Powerball, apparently).
Example (actual payouts up for debate, I'm taking suggestions (should we have each higher payout have lower odds than the previous payout?)):
- 2x - 15% - cumulative 48% plus jackpot odds (less than 1/2)
- 3x - 9% - cumulative 33% plus jackpot odds (less than 1/3)
- 4x - 12% - cumulative 24% plus jackpot odds (less than 1/4)
- 8x - 3% - cumulative 12% plus jackpot odds (less than 1/8)
- 10x - 9% - cumulative 9% plus jackpot odds (less than 1/10)
Jackpot - 50% of the ticket sales goes to the jackpot pool. On a jackpot win, that pool gets distributed to the winners evenly. There can be multiple winners, just like in Powerball.
- The odds of the Jackpot need to be set very carefully. There needs to be a very, very low probability of a large amount of ETH getting stuck in the jackpot at any time. I'll be working on the math for this myself, and I'll get a simulation running to double check. If the Jackpot ever ends up with too large of a chunk, we will have the ability to change the price of a ticket. We will lower the price of a ticket, and hopefully that will sort things out quickly.
On that note, we need to be careful building this thing. It's going to be difficult to change the code after it's submitted, so everything that can possibly be a variable must be a variable. Everything. Payouts and odds will probably be in a variable-size list, so we can add or delete things at will.
Most of the lottery will be automated, but it will be editable by a multisig of trusted people, likely the devs and maybe a few other well-known and trustworthy DAO members. Not the DAO directly, even though that's where the profits will go, since that would mean reaction times would be way too large.
Alright, so, Jackpot odds:
- 1/x = the odds of winning the jackpot
- n = the number of tickets sold
- m = the odds the jackpot doesn't get hit
So...
- 1-1/x = the odds of not winning the jackpot
- (1-1/x)^n = the odds that none of the tickets sold win the jackpot
- m = (1-1/x)^n
We're looking for appropriate odds for the jackpot, so we're going to solve for x and assign values to m and n
- nth root of m is rendered by m^(1/n)
- m^(1/n) = 1-1/x
- m^(1/n)-1 = -1/x
- 1-m^(1/n) = 1/x
- 1/(1-m^(1/n)) = x
Current ETH in existance is a little over 80 million, so I'm going to take a wild baseless guess and say the total ETH in the future will be 100 million. Things can be changed as this changes, but I'm going to base these numbers on this.
Let's say I want to have a very good chance that the jackpot never holds more than 10% of the ETH in existance, so as to not influence the price of ETH as much as possible. We're going to use nines notation for this.
- If I have 6 9's of certainty, then m = .000001
- Assuming a market cap of 100 million and a ticket price of .1, 10% of ETH would be n = 100,000,000 tickets
- x = 1/(1-m^(1/n))
- x = 7,238,241.8654
So jackpot odds of a little worse than 1 in 7 million.
If I want 9 9's of certainty,
- m = .000000001
- n = 100,000,000
- x = 1/(1-m^(1/n))
- x = 4,825,494.7424
So jackpot odds of a little better than 1 in 5 million.
A quick look at those odds suggests obvious averages for when the jackpot will be hit, and it's in high hundreds of thousands of ETH. However, knowing statistics over large numbers tends to be finicky and weird, I'll come back later with some math of actual averages. Also, coded simulations, possibly in python because I don't really want to launch eclipse every time I want to run or update this thing.
I ran the numbers a couple weeks ago, just now uploading them cause I just got time. Turns out my initial numbers were bad, they ended up giving an EV of over 1. The new calculated numbers are below.
- multiplier - odds - cumulative odds used in the code
- 2x - 10% - 19.1% plus jackpot odds
- 3x - 5% - 9.1% plus jackpot odds
- 5x - 3% - 4.1% plus jackpot odds
- 10x - 1% - 1.1% plus jackpot odds
- 100x - .1% - .1% plus jackpot odds
Which gives us 2(.1)+3(.05)+5(.03)+10(.01)+100(.001)=.7 EV, just from the set payouts. It should be noted that the cumulative odds of a Powerball win, a very popular lottery, is 1 in 24ish, which is just better than 4%. The EV is also quite small. I forget the exact number there, but it's fairly easily calculable if you go to their site.
Putting in a jackpot of .25 of every ticket, that leaves .05, or 5%, for the DAO.
Jackpot numbers again, this time using a ticket price of .1 Eth (again) and the jackpot gets .025 Eth/ticket, so
- m = .000000001
- n = 400,000,000
- x = 19,301,977.4735
So jackpot odds of 1 in 19 million at max.
Brainstorming on random number generation, we're not in a particular hurry here. We could probably set the random number to be the hash of the 6 or whatever consecutive bitcoin blocks after the end of the lottery's current segment. So, weekly drawings, and it takes an hour-ish to generate the random numbers. That doesn't seem like a big deal. In this scenario, I'm not envisioning numbers like Powerball's number drawings. I'm thinking a random number per ticket, with the given odds above. So, hashes of consecutive bitcoin blocks to get a large stream of random numbers. Split that up into a seed per ticket, and generate the random number of each ticket from those seeds. Consecutive bitcoin blocks makes it significantly harder to game the system. After that, each ticket has a certain chance of getting the jackpot or a payout, or nothing. There can be multiple jackpot winners.
Now, there are pros and cons to this build. A con is you can't buy multiple tickets with the same set of numbers, as you can in Powerball. So you can't bet more than the ticket price on a given random number. The pro exchange for that is pretty big though. It allows us to be nearly guaranteed to pay out the rewards. If you could bet a large amount on a single random number and win big with that number, you could easily clean the house and still put the lottery into debt. That's not a thing we can handle, and this eliminates that possibility.
Again, everything possible in variables, so having the method of random number generation be a variable means we could change that later without going through a huge contract update. I'd like to have the Lottery contract run by a multisig, as it requires a faster reaction time than the DAO is capable of. Say, a multisig of people who designed the lottery mixed with some trusted members of the DAO. With the DAO being given the ability to remove people from the multisig, and maybe add them. Maybe give the DAO the sole ability to do that? Idk. Needs discussion.