Equal Opportunity Game is now over 3 years old and ...

... and I have only these recorded answers below ... I also have the ones mentioned in the text, which most often favor outcome shown on the graphics in the oldest post below on this page.

Obviously, I have not attracted much attention to this address. If you find this little problem interesting, please, direct some of your friends here.

Below are the comments (except of the spam) which came in the 30 months or so since this address was set up. I also ask people to send a comment to ladreview@gmail.com if they prefer that for some reason. That address is only for the "vote" on this "game".
And today I also add a new summary of the game.

The Game:
We get 20 thousand ten-cent coins (only $2000 in the game) and collect a group of thousand people who want to play. Each person gets twenty coins.
---
Now the game starts. It has very simple rules: the players meet person to person, each pair puts all their money together and divide them in any equal opportunity way, for example by using dice, playing cards, small games, or just any guessing-game. Anything goes, as far as it does not favour the stronger, the weaker, the more beautiful or those with social problems: simply equal opportunity, indeed just. The only thing which is not recommended is to agree that "just" is fifty-fifty – then nobody can gain in the game.
After a while: we look at the "wealth distribution". How many people have zero to four coins,
how many have 5 to 9 coins, and so on, up to 20 to 24, .... 30 to 34, etc.
What will the distribution be? Other people have answered before you, here are some suggestions:
(A) On average people still have 20 coins each, some a little bit less, some a little bit more.
(B) Any reasonable amount is roughly equally probable
(C) most will become "poor", there is some middle class, and few rich
These three most often given answers are summarized in the sketch
(drawn as usual in newspapers)


Which is your answer? (A) (B) or (C) - or another suggestion?
Please use "Comments" or mail to ladreview@gmail.com to tell us about your guess

The author said...

An answer came to ladreview@gmail.com
from Simone:
-----
In your game, I also would expect a Gaussian distribution as long as people meet randomly. I reality, I would expect that people that accidently gained some money start to hang out with people that also have a lot of money in order to minimise losses. Those who feel to have most money will probably hide somewhere, so they do not have to participate in the game anymore. Those who feel poor might start a revolution than, which will result in some redistribution of money, and than everything can start again...
-----
Simone (biologist ..., German)

The author said...

Here is the first ever online answer.
I managed to find it in my mail.

I expect the average mount of the whole will migrate to a greater average amount for a smaller sample. Those that have none, drop from the sample because they are not balanced by those that have it all. The trend over time is for average amount of increasing WEALTH to to be shared by an increasingly smaller group. This is life.
DW

--
Posted by Anonymous to Equal Opportunity Game at 1/05/2006 01:37:20 PM

the author said...

Another answer came from Anna, particle physicist. Her idea came from seeing a similarity with clustering in galaxies in early Universe astrophysics, or perhaps cosmology. She just thinks that in any such distributions there will be some clusters, it means a bunch of rather rich gamers with many coins left and another group who would have not so many coins.

I hope I have recorded this well enough.

Anonymous said...

Hei Ladi, I am junbai, I think the answer of your game may is a multinormal distribution. But when the rounds of your game goes to infinitive then it closes to gaussian distribution.

Anonymous said...

.. well.. i dont think the bar chart reflects the nearest case that might happen coz maybe some little ppl will get rich and the other will get poor and no one will stay in between !!

franko (united kingdom)

(and Franco also added some advertising - or somebody did)

A team of successful entrepreneurs credited for...... SelectWealthSystem......
A new home-based-business marketing system that provides the strategic high ground for internet marketing.
Pro Team Marketing uses an automated marketing system that is currently promoting a cutting-edge young company, entering the early growth stage, that targets the largest consumer base in the United States with their financial educational products.

the author said...

The last comment is sort of interesting. It is a promoting link for some service, i.e. close to SPAM, but it also contains a sort of legitimate "answer".

So we allow it to stay here.

Equal Opportunity Game soon 3 years

The game is not a real game, you can not win anything here. You can go straight here to see all the comments and add your solution http://equal-opportunity-game.blogspot.com/2006/02/equal-opportunity-game_01.html

The idea of this "game" is soon three years old as a general public question. The story has been used by me for years (perhaps since 1995) in my physics teaching. The answers at this "blogsite" are few, even the spam traffic is very weak. We just need to enter more entries, probably.

Equal Opportunity Game - more guesses? ...the distribution of rich and poor?

The game is not a real game, you can not win anything here. You can go straight here to see all the comments and add your solution http://equal-opportunity-game.blogspot.com/2006/02/equal-opportunity-game_01.html

(The original page of this blog has somehow been lost. This is a new copy of a blog set up a month ago. The original posting has got three comments. One person disagreed strongly with the suggestion of the final distribution below. That comment suggested that there will be few "rich" and many "poor", describing also why. That has been lost, but fortunately I found the posting in my mail. It is added as a comment (No.2.) by me now)

.... each pair puts all their money together and divide them in any equal opportunity way, for example by using dice, playing cards,.....
What will be the distribution of rich and poor?

Please note: those who lose everything are not out of the game: in the next negotiation such person can regain a lot. The number of players does not change. One thousand start, one thousand are counted at the end.
Please, leave your guess in the COMMENTS here (click on COMMENTS) or send a mail to ladreview@gmail.com. Thanks!
Please, indicate your country and leave some indication of your background (science, culture, business, whatever)
The text below has been recovered from Google Cache. Please be patient with our layout. I will try to improve it!

Equal Opportunity Game

Here I describe a very simple game, where everybody has equal opportunity to win.
Please answer the question below, either here as a comment on the blog, or send an electronic mail to a special address
ladreview at gmail.com. You will not win, but you take part in a little experiment.

The Game:
We get 20 thousand ten-cent coins (only $2000 in the game) and collect a group of thousand people who want to play. Each person gets twenty coins.

Now the game starts. It has very simple rules: the players meet person to person, each pair puts all their money together and divide them in any equal opportunity way, for example by using dice, playing cards, small games, or just any guessing-game. Anything goes, as far as it does not favour the stronger, the weaker, the more beautiful or those with social problems: simply equal opportunity, indeed just. The only thing which is not recommended is to agree that "just" is fifty-fifty – then nobody can gain in the game.

So as we start, John and Jane each have 20, they draw cards, Jane leaves with 35 and John now has only five. Jane engages Peter in the game, he already had 30, she 35, they used dice and their calculators on their cellphones, and now Jane has only 5, Peter leaves with 60.
Leave Jane, she has too little, follow Peter. He meets Joan, she had 17, Peter had 60, they used again dice and calculators, but now Peter leaves with nothing, Joan has now 77 coins. Let us follow the poor Peter: he meets Mary who still had 22, they use cards, and now by chance, Peter leaves with 11 and Mary also keeps eleven coins.

After 5 hours or so the game ends and everybody can now keep the coins they have left or they won.

The question is: what will be the wealth distribution in this equal opportunity game?

At the start, there were thousand people in the property group 20 to 24, all had twenty.

Many people answered that since the chances to win and loose are the same, the distribution of the coins should look something like this table

Wealth How many people Before the game
0-4 6 0
5-9 32 0
10-14 106 0
15-19 217 0
20-24 277 1000
25-29 217 0
30-34 106 0
35-39 32 0
40-44 6 0
45-49 1 0

Sum 1000 1000

(This is called a normal or Gauss distribution, and is shown in the diagram below)


What do you think?

If you are writing a comment here or sending mail to the game's address

ladreview AT gmail.com

please, indicate your country and something general about your profession
or education history.

The email account is set up simply for collecting the answers. Your address will not be used for anything and not given to anybody.

More about the (science) game: Equal Opportunity Game

(copied from the lost pages)

It is not a real game, it is about a game. And it has to do with science. I use the story about this game in my teaching to illustrate one very important natural law.

And the game can be put into a computer. Here is the simulation expressed in everyday words

take 1000 boxes
put 20 coins in each box
repeat until you are stopped
( choose two random numbers K and L (up to 1000)
on the table put money from Kth box and Lth box
take some (random) money from table to Kth box
put the rest of the money to the Lth box
)
done
in each box
( count money
write the ammount on the paper
)
count how many amounts are
( from 0 to 4
from 5 to 9
from 10 to 14
from 15 to 20 ...
...
from 45 to 49
...
)
show the table.

In the old days I could have given you a code in Qbasic or GWBasic and you could run it on any PC.
But here we want to guess, so see how lucky we are that windows do not come with BASIC any more!