Rules for a fair lottery

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firehairlives

Guest
This is an example of what i belive by the rules of probability would be a fair lottery for item drops.


Not taking into account the number of people from one guild that were there. It could be taken to rediculous levels but i think this is what i would call fairer than what i have seen today. no offence ment to anyone there btw =)

Example

5 guilds went on a hunt and 5 items were droped.
All guild are given a number.

guild a is given 0-19, guild b 20-39, guild c 40-59, guild d 60-79, guild e 80-99.

A mob is picked and killed. The copper drop is taken as the way to choose which guild is given item number 1. Copper drops are random and in the region of 0 to 99. This means each guild has an equal chance at receiveing item number 1 which would be the "best item" available (the one that most would wish to have).

88 Copper is dropped so item number 1 goes to guild e.

Guild e, who got the drop is then removed from the rest of the lottery so they can only have 1 item.

We are now down to 4 items and 4 guilds.
guild a 0-24 guild b 25-49 guild c 50-74 guild d 75 -99
once again the probability dictates from a ramdom copper drop on the "next best item" all have an equal chance at getting the item apart from guild e who have now got an item thus are no longer in for another one.

I hope to see more of this sort of fair sharing of item in the future and also any responces to this posting example lottery.


Firehairlive/Softouch
 
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old.Ebeneezer

Guest
Beat me to it :)

First let me explain that I am a professional mathematician with a PhD working in the field of probability, so I know how to handle a fair lottery.

Second, what I write here is not a witch-hunt or me accusing people of cheating. I simply want to point out that with the wrong method of lottery it is open to exploitation by sharp and astute people.

I want to focus on todays Legion drop lottery. The rules were:

- each guild present chooses a number between 0 and 99

- somebody kills a mob and tells number of copper dropped

- guild nearest to amount selects item and drops out of lottery

So today this is the list of numbers chosen in order of speech:

Odins 50 (but decided to pull out to have seals only)
Red Guard 33
Aesirs 42
Realm Defenders 17
Cradle 20
Blizzard 47
Dragons 75
Cutting Edge 12
Nolby 27
Diva 60
Badgers 78
White Rose 80

(see screenies below for proof)

Rearranged this gives

Cutting Edge 12
Realm Defenders 17
Cradle 20
Nolby 27
Red Guard 33
Aesirs 42
Blizzard 47
Diva 60
Dragons 75
Badgers 78
White Rose 80

Ok now in practice this means the following numbers win for each guild:

Cutting Edge numbers 0 to 14 -> 15 numbers = 15 % chance win
RD numbers 15 - 18 -> 4 numbers = 4% chance
Cradle 19 - 23 = 5%
Nolby 24 - 29 = 6%
Red Guard 31 - 37 = 7%
Aesirs 38 - 44 = 7%
Blizz 45 - 53 = 9%
Diva 54 - 67 = 14%
Dragons 68 - 76 = 9% chance
Badgers 77 - 78 = 2% chance
WR 80 - 99 = 20%

The numbers 30 and 79 would have to been rerolled as 2 guilds are closest to each one.

So clearly this cannot be fair. Three guilds have over a 10% chance of winning.

Some additional points to raise. Suppose after CE choose that one guild chooses 13 and another 11, that means CE only wins on exactly 12...a 1% chance!!! You can really stitch someone up on this!

Also, it pays to go as late as possible. Had CE chose last, I would have chosen 79, meaning I get 79-99 = 21% chance.

Also, we need to more people to party to kill mobs to verify the coin drop. I don't think this has happened yet, but people can make up numbers. NOTE I am not saying this happened today.

From my screenies you can see what I wanted to do...that's give everyone an equal number of numbers each (as Fire has said before me). So 11 guilds could be split like:

Cutting Edge numbers 1 to 9
RD 10 -18
Cradle 19 - 27
Nolby 28 - 36
Red Guard 37 - 45
Aesirs 46 - 54
Blizz 55 - 63
Diva 64 - 72
Dragons 73 - 81
Badgers 82 - 90
WR 90 - 98

with reroll on 0 and 99. Each guild has an even 9 numbers each then. What's fairer than that?

One final thought. How can we be certain that the mob drop is drops every number equally between 0 and 99 ? I know in a following patch that Mythic has put in a true random number generator for this very reason.

I suggest going forward that guilds participating in lotteries in future agree a set of numbers like I show above beforehand and publish them on the forums. Then a party is formed to kill mobs so that there are witnesses. When the random numbers come in we use those instead of mob kills.

BTW : despite 15% CE came last :rolleyes:

---------------------------------------------------------------------------------

The screenshots backing me up are here:

http://homepage.ntlworld.com/brian.hunton/Lottery1.jpg

http://homepage.ntlworld.com/brian.hunton/Lottery2.jpg

http://homepage.ntlworld.com/brian.hunton/Lottery3.jpg

http://homepage.ntlworld.com/brian.hunton/Lottery4.jpg
 
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old.Ebeneezer

Guest
Yes BTW Fire is correct. Numbers must be redistributed after guilds pull out to make sure that each guild has the same number of numbers each.
 
M

MunchkinCE

Guest
Well it just so happens I was working on this when we were discussing the raid lottery.

First of all check this out: http://www.btinternet.com/~adam.j.howson/LootLottery.htm

Its very simple to use, thus:

1. Print out the sheet above.
2. Total the amount of guilds in the lottery and find that number on the left hand side.
3. Allocate each guild a number range.
4. Kill a mob.
5. The amount of copper it drops is compared to the ranges allocated in 3.
6. The winning guild picks an item and drops out.
7. All other guilds are dropped down one line on the sheet.
8. Go and kill another mob.
9. Repeat from 6 until all loot gone or guilds are finished.

Obviously if it drops 0 copper, you kill another one.
Also, if the mob drops over the highest range amount of copper, you kill another one.

If there are more items than guilds, then you keep the same order and start again (there goes another tree :) )

If you are being really organised, you could fill this in and publish it in advance so people can follow it themselves.

Also the mob killer needs to have representatives from the other guilds in his/her group to verify the amount of copper dropped.
Edit: You also need to check that the mob CAN drop up to 99 copper :)

Hopefully this will sort out loot distribution forever :)
 
T

Thorarin

Guest
I agree, though personally I'd whip out some d20 system dice to speed up the process ;-)
 
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old.Foldroll

Guest
Pardon my naiveté, but is there no random number generator in DAoC?

And while I wasn't involved in the raid in question, I don't think my guild was invited, surely if there is enough trust to give the drops to one person to distribute, there should be enough trust to draw off-line lots or something?

Otherwise what is the point hunting with people you expect to try to screw you over?

I know that a guild mate of mine recently organised a hunt, and was in charge of handling the lottery, using the "kill a green mob and count the copper" method. And apparently our guild finished up with nothing.

I guess that proves we are all really unlucky, but fair...
 
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old.casiraghi

Guest
Pardon my naiveté, but is there no random number generator in DAoC?
Click to expand...

Will be in 1.51

And good post ebe and fire, lets hope all future lotteries will be held like this. Realm Defenders was lucky this time and got 1st drop, even though odds were against us:)

At first Legion lottery i was one of the last to choose and did calculate the way to increase my odds just like u described, alltough we only got 4th in that draw :)
 
G

Garnet

Guest
OOOOPsie :D

I forgot to put a guild number into the lottery resulting in no item but really doesnt matter :)

I wont forget next time hehe
 
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old.casiraghi

Guest
oops, wasn't there in person just was told we got the first drop :)
 
M

MunchkinCE

Guest
Perhaps we should set up a group to run lotteries?

I would be happy to do it, as long as we dont call it Camelot...... ;)
 
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