I just read the New Jersey Pick 3 lottery rules over. They have a simple system:
1) 50% of the ticket sales go to the prize pool
2) (they have a bunch of ways to win, but I'll unitize them all to a number of 'Wins')
They calculate Ticket intake * .5 / # Wins => Prize Share
3) Each Winning bet gets a prize share.
To compare, the powerball system
A) seeds the jackpot with an amount, ($10mm), advertises twice that as the 'annuitized jackpot', and proceeds as follows:
B) 50% of the ticket sales go to prizes.
C) Roughly 58% of the prizes go to the jackpot, won maybe once a month. The other 42% are for the smaller prizes.
As noted by the powerball website, powerball is designed for people who are motivated by a big jackpot. Presumably Pick 3 is designed for people who are motivated by a small, frequent (it runs twice a day) payout.
So, either of these seem like fine setups -- hard-headed expected-value-discounted-cashflow-type people only play powerball when the advertised annuity is up in the $250MM+ range, and everyone else plays when they like the sound of the jackpot size. No math people play Pick 3, I'm sure.
I was considering a much simpler 'winner takes it all' setup, as taabl doesn't take absolutely nothing from the lotteries. But that may change, I could make it sponsor a server eventually, in which case a seeded pick 3 with a set prize could be interesting... I'll read over the rules and try to make sense of it
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My takeaways:
I) I think your lottery needs to choose a personality: is it going to be a big prize, monthly-ish win type situation, or a frequent small-scale wins one? I don't mean monthly drawings, just likely 'big' wins at once a month.
II) You probably should have a minimum pot for jackpot winners: this ensures people want to play more often. You would fund this out of your own funds to start, and then whatever you decide your rake should be, eventually.
III) An out of the box idea I had is that you could write some sort of rules algorithm and allow anyone to run their own lottery; you'd take, say 10% off the top, and lotto designers could choose their own payouts, jackpot rollovers, etc. Natural selection will tell you the most successful lottery designs quite quickly, I imagine.
I) Not yet, right? We're still playing with possibilities
II) That's what the side pot would be in my latest plan
III) That's actually a great idea! Once the system is stable and running on its own (and on a real server) I'll certainly take a stab at that!
As a sample 'powerball'-esque lottery: if you had a jackpot minimum prize of 10 BTC and two drawings a week, 100 people playing per drawing, odds of winning say 1 in 1000, then you'd see the following:
Week 1, Drawing 1
20 BTC goes in: 10 covers the jackpot: 10 BTC goes to rake
80 BTC goes in: 40 goes to rake, jackpot is now 50.
Week 1, Drawing 2: Jackpot 50
100 BTC goes in: Jackpot is now 100 (no winner)
Week 2, Drawing 1: Jackpot 100
Odds of nobody winning so far: (900 / 1000 ) ^2 = 81%
More people get interested: 150 buy. Nobody wins.
Week 2, Drawing 2: Jackpot 175.
Odds of nobody winning so far: 69%
I don't know if this would be appealing to people or not. I bet if the jackpot were 1,000 BTC, odds of winning say 1 in 5,000 to start then it would be appealing. The simplest way to keep math-oriented speculators out is to keep the expected value down, except in rare circumstances.
It's gotten too late for me to add more to the conversation, so I'll summarize a TL;DR -- Copy some successful lotteries! Use the rake to provide a guaranteed pool! (Possibly: let people use your software to host their own lotteries).
I copied the local state lottery, but they do two things differently:
- keep 40% of the prize pool for themselves
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- Have millions of bets every week
It's very easy to perceive value when you look at a million euro first prize, even though the chances are 13,983,816 to 1, with bet repetitions allowed. But they do prime the lotteries with a big first prize, and only the others are number of bets dependent.