
Post by shekki on May 16, 2016 17:15:15 GMT
This is my idea of lottery.  Lottery draw will be at Sunday 12:00 server time.
 Tickets can be bought until Sunday 11:00 server time. At same time next week lottery draw tickets can be bought.
 A ticket costs 1,000,000 gold and you can buy 100 tickets.
 Ticket purchase gold will be added to pot.
 You also can donate other funds in pot, that will get spread like gold% does.
 10% of total pot will carry over next week pot, rest 90% is shared via winnings.
 All left overs carry to next week pot as well.
 Lottery is 6 digits, range of 115. Means 1:5,005 chance. So pot will grow around 5b gold before there should/might be a winner.
Winnings:  6 numbers right 80% pot.
 5 numbers right 15% pot
 4 numbers right 5% pot
 Every tie % pot will be divided between all ties.



Post by shekki on May 16, 2016 21:18:09 GMT
added few replies from old thread: *wipes mouth after finishing tuna* While I really do like having something added to the game, so that we have something else to do, I'd like to point out a couple of things. If a T1 player buys 1M gold worth of tickets, and someone like Althus dumps 999M gold, and that the lucky winner gets ALL of the gold, then we can safely say that Althus has a 99.9% chance of winning, and gaining a tiny bit of gold, while the T1 player has a .1% chance of walking away with a fortune. No problems there, right? But if we were to set aside 20% of the pot for the next time we have a lottery, of that 1B gold, 200M is removed from it. No problem there right? Look a bit further, if 20% of the pot were to be removed, then effectively 20% of your ticket gold is lost from you. So Althus loses 199.8M gold and the T1 player loses 200,000 gold. And the chances still remain the same. This means that richer players are at a disadvantage if we have a carryover. This is not a problem in the winner takes all scenario.  Unless we do real life tickets, like 00000000 on 115 range. so althus need get 50k tickets to have 100% and that costs 50b gold. So 1b gold tickets doesn't gurantee a win, you need do it week after week..  This lottery sounds fantastic. There should be a equal chance for everyone to win in my opinion. Each individual can only buy 1 ticket for a x price. Any additional tickets would be counted as a bonus to the overall pot. The reason there should be a limit to the amount of purchasable tickets is so higher level players don't have an advantage over newer players since they have a much higher income in comparison. It could be made where as individual can buy up to an x amount of tickets where they are given a slightly higher chance of winning rather than 1/x people participating. In terms of frequency I think about 23 times a week should be fine. By having it occur various times during the week, you can make it where one lottery is low stakes with a minor buyin whereas the one later in the week can be for higher stakes.



Post by mathcat on May 17, 2016 17:02:42 GMT
Narrator: And here you can see a MathCat in its natural habitat, solving math problems on the internet while munching tuna....
*EDIT: Did not read reformatted post about planned lottery format; will do that tomorrow and react, after my face gets intimate with the pillow and everything with the blanket*
*munches tuna*
Alright, let's get started, first let's break a lottery down into its components and see how they work, then pick what kind of lottery we should use.
First off, there are two kinds of lotteries, fixed state lotteries and nstate lotteries, we'll examine the nstate lottery system first.
Nstate lottery
The Nstate lottery is a lottery where the number of possible states changes depending on the input. For example, on an N=Σx, if A B and C buy a ticket each, there are a total of 3 tickets, then there a total of 3 states. If we were to pick at random between the three, then there would be a definite winner. But that's only because N=Σx, and there's no coefficient to the summation (more on that later).
Fixed State lottery
The Fixed State lottery is what most people are used to, for example the 15151515 solution proposed by Shekki. While you can go ahead and pick numbers, the total number of possible combinations (states) is equivalent to 15^4, which is 50625 states. This system makes it so that no matter how many tickets you buy, the fixed number of states means that your chances won't change if someone buys more tickets than you.
MathCat's observations on probability
While nstate and fixed state lotteries vary on the number of states they have, there are a couple of derivations (like win percentage, carry over amongst other things) that we can use to figure out the more indepth differences of both.
The most important number we pay attention to is the payout factor, which is a very good determinant of success for a game of probability. This is taken by getting win chance and multiplying by payout rate.
Now, how does that help us? Let's say that you have a game where you have a 10% chance of winning, and if you do, you 20x your money. That's a payout factor of 2, which is good because it's greater than 1. Anything less than 1 means that you are not in a position to gain that much money by playing.
Now, before the mathematically inclined go on and talk about how "Payout factor is derived by getting the nonwin percentage and raise it to the quantity of payout divided by the input cost, then subtracting that from 1.", this is a oneroll lottery. The combinatoricsummation approach with the tree diagram is the correct way of doing it, but remember that we have the end chance figured out already, which maps out the end of the tree diagram.
The beauty of Nstate (N=Σx) lotteries is that no matter how many tickets are played, there will be ALWAYS someone who wins. If I buy out half the tickets (50% chance of victory), that means that the amount of tickets that I didn't buy is worth an equal amount of gold to mine. This gives us a payout of 2x, ((1/2)*(2)) is equal to one, so Nstate lotteries are fair for everyone.
Now, let's say that for a fixed state lottery, with 50,000 states and 1,000,000 gold per ticket, it would take me 50 billion gold to buy out all the tickets and guarantee to win the entire jackpot. If there was some carryover / donations / ticket gold from other players, then we add those to the payout. So if all the donations and ticket payments by the other players amounted to 50 million, we add in my 50 billion gold for ticket payment. That means I walk out with a jackpot of 100 billion gold. I bought all the tickets, 100% chance. Payout was 2x as big, so that means I had a 100% chance to double my money. That's not a lottery.
If we were to point out the main flaws of the problem, get the winrate and the payout, you get a payout factor of 2. That's greater than 1. But remember that the only way to guarantee a winrate of 100% is to spend 50 billion gold, that's pretty hard to get. But if I'm ridiculously rich, I can do that. That means that ridiculously rich players have the ability to game the system. In fact, if the payout factor is greater than 1, then rich players are already at an advantage.
As for what happens with a payout factor of below 1, I'll use my old example to summarize:
But if we were to set aside 20% of the pot for the next time we have a lottery, of that 1B gold, 200M is removed from it. No problem there right? Look a bit further, if 20% of the pot were to be removed, then effectively 20% of your ticket gold is lost from you. So Althus loses 199.8M gold and the T1 player loses 200,000 gold. And the chances still remain the same. This means that richer players are at a disadvantage if we have a carryover. This is not a problem in the winner takes all scenario.
The payout factor in that example is 0.8, since the payout is reduced by 20%. Poor players gain an advantage over rich players with payout factors of less than 1. Rich players are advantaged by payout factors greater than 1. Everybody is on equal footing at a payout factor of 1, and that's only achievable by an Nstate lottery with N=Σx.
MathCat has been awake for 96 hours by the time of writing. He's not good at explaining to people when he's like that. Heck, nobody is.



Post by mathcat on May 18, 2016 16:02:44 GMT
TL;DR  Mathcat thinks this is a bad lottery format.
First of all, allow me to point out that 15^6 is equivalent to 11390625. That's 11 million states. Now, assuming 100 players draw 100 tickets each time you run the lottery, you have:
Chance of player winning: 100/11390625 Number of people: 100
Total chance that someone gets 6 numbers: (1((1(100/11390625))^100))*100
Which means that each time the lottery is performed, you have a 0.087% chance that someone gets the jackpot. That's bad. And remember we're doing a total of 10000 tickets here, that's 10 billion gold.
Note to Mathinclined: the model there accounts for ticket overlap, which is why it uses an exponential form for 1%, instead of Σtickets/N as %.
10 billion gold, very unlikely someone gets the 80%
Now, what about 4 numbers?
Model: (1(((1(100/(15^4)))^100)^(6C4)))*100
Which gives us 94.84% chance that at least one person gets 4 numbers right.



Post by bluewhale on May 19, 2016 12:22:45 GMT
You have an in built assumption here that people will keep playing this week after week, which I don't think is realistic at all, MathCat. The first few lotteries might be a bit crazy, but you're better off bringing the cost of a ticket down and then new players can actually have a chance of playing the lottery. In total, you're going to require a dynamical calculation based off of the number of tickets bought, which means you certainly can't just allow someone to pick the numbers they want on their ticket like you would in r/l, and I'm not sure people would want to if they buy lots of tickets. Much better off having some random assignment with no clashes.
Also if a player has 50bn gold.. what do they need to play the lottery for? Sure maybe, once or twice, but that novelty is going to run off very quickly, or those people that don't see a return very quickly are going to realise that it's a waste of their gold. Hence, I'm not a fan of this idea at all.
Finally, I highly doubt stabby will build this without there being a gold sink involved (maybe 510% or something like that).

