Please Help Me Conduct An Experiment. Pick A Number.

[jyl]

To the denizens of the OT Board, I would appreciate your help in conducting an experiment. It involves playing a game.

Pick a real number from 0 to 100, and PM your picked number to me, ALONG with your occupation. DO NOT post your number on this board, please. The winner is the person who picks the number that is closest to 1/2 of the arithmetic average of all numbers picked.

Again, please DO NOT post your picked number here or otherwise try to hint at your number or tell people what your strategy is. (I'll delete your picked number from the experiment.) No problem if you want to discuss the various possible strategies or how stupid this experiment is or why won't jyl just go away or any other topic.

The winner gets . . . err, what does s/he get, anyway . . . how about a custom-printed 8x10 of the image below. You can always use it as a coaster.



The experiment ends when I get enough responses. I'll announce the end, and the winner.

[jyl]

Great, keep the PMs coming!

ronin, I get it now.

Those who sent a number alone, can you please send me PMs with your occupation? (If you don't want to state, you don't have to, but it helps the experiment and I wanted to make sure this part wasn't simply overlooked.)

[djmcmath]

Does "gigolo" count as an occupation, or is that a hobby?

[Overpaid Slacker]

My occupation is in my profile -- lollygagger.

JP

[jyl]

Isn't gigolo is the singular of gigli, which was the title of a bad movie with Ben Affleck and what's her face?

I shall have to create a new category for "lollygagger". Sounds porno somehow.

BTW, trying to skew the results by picking a number outside of the 0 to 100 range doesn't work - the pick gets deleted, ha! - you can try again ("you" know who "you" are).

[island911]

Originally posted by jyl
. . . "lollygagger". Sounds porno somehow.

LOL

[bryanthompson]

If everyone uses the thinking I used, I should have halved my number... or wait, are they thinking that too? Maybe I should have gone 1/4. Damn. I never win these things.

[jyl]

Just 'cause you're paranoid doesn't mean they aren't out to get you :-)

[jyl]

Great response, everyone. I almost have enough, how about ten more and we're done. When the experiment ends, I'll post the anonymized results and explain what all this was about.

[jyl]

What was all that about? The idea of the game is to guess how many steps ahead the other players are operating, and then to think one step ahead of that.

So, to operate “zero steps ahead” is to simply randomly pick a number, without trying to “win”. There is no preferred “pick” since there’s no strategy involved.

“One step ahead” is to pick a number closest to the average of all numbers picked by people operating zero steps ahead. This “pick” would be around 50.

“Two steps ahead” is to pick a number that would be 1/2 of the average of all numbers picked by people operating one step ahead. This pick would be around 25.

“Three steps ahead” is to pick a number that would be 1/2 of the average of all numbers picked by people operating two steps ahead. This pick would be around 12.5.

And so on down, converging on a pick of 0 as one operates an increasing number of steps ahead. It is not necessarily better to operate more steps ahead, as we’ll see.

Based on your estimate as to how the playing population is distributed among zero-step-ahead-ers, one-step-ahead-ers, two-step-ahead-ers, etc, you could formulate a strategy. For example, if you think 40% of OT Board members are operating one step ahead and 60% are two steps ahead, you might pick 17.5 = 1/2 * (0.4 * 50 + 0.6 * 25). As it turns out, that is very close to the actual answer.

The winner is kjb who picked 17. The runner-up is Island 911 who picked 17.45847. Third place goes to Paco Anton who picked 15. These are close enough than I’ll send each of you a print - I will get working on them ASAP.

In total I got 33 entries. The arithmetic average of all the picks was 33.26, implying that the average player was operating about 1.5 steps ahead. The “right” answer was thus 16.63 = 1/2 * 33.26.

Picks were distributed as follows: from 0-10 there were 4, 10-20 were 8, 20-30 were 4, 30-40 were 5, 40-50 were 3, 50-60 were 5, 60-70 were 2, 70-80 were 1, 80-90 were 0, 90-100 were 1. Picks tended to cluster around 50, 33, 25, 17, 12, and 1.

I read about this experiment in an article on behavioural finance. Variants of this game have been played many times by various groups in different professions. The typical numbers of “steps ahead” was about 2. For example, when 20 CEOs played the game, they on average operated 1 step ahead. 32 US high school students who played were operating 1.6 steps ahead. Appx 30 CalTech students were operating appx 2.6 steps ahead. 124 Harvard economics students were operating appx 4.4 steps ahead. 136 game theorists were operating 4.3 steps ahead. Professional investors, in several games of up to 1000 players, were operating 2.3 to 3.2 steps ahead (although in some German games, they were operating <1 step ahead).

Perhaps one reason this game gets played mostly in financial circles may be that this is not a very common sort of problem. In many cases, we don’t need to “get ahead” of anyone – e.g. the proverbial “rocket scientist” has a difficult job, but at least the rocket isn’t alive and trying to outwit him. I speculate – this is purely speculation – that for an engineer, operating too many steps ahead might be a bad thing, as it might distract from solving the immediate critical problem.

In the situations where we are trying to get the drop on someone, we usually have a specific opponent – e.g. Kim Jong Il, the opposing chess player, the racing driver ahead of us. So here we have to think ahead of a human opponent, but at least we have a particular opponent to analyze.

But this sort of problem does come up in the financial markets, where everyone is trying to outwit everyone else but nobody has a specific individual opponent. For example, suppose you invest in the sort of things that might be affected if China floats its currency. Do you wait until China actually does float the yuan to see what happened and then make a decision? Do you try to anticipate the float and take a position in the yuan? Do you invest in things that will be affected by a change in the yuan’s value, e.g. Chinese real estate and wages? Do you invest in things that will be affected by those things, e.g. go short Chinese manufacturers and long Vietnamese and Indian manufacturers? Etc etc.

Anyway, I’ve always wanted to play this game, and so thanks to everyone for helping. Hope this is interesting! If anyone plays this game again, I'd be interested to hear the results.

[tswaney]

John, did you find anything interesting with the "occupation" component of your experiment?

[AFJuvat]

Aside from the fact that I can't read and thought he wrote "pick a number from 0 - 1000 rather than 100.....

AFJuvat

[jyl]

Originally posted by tswaney
John, did you find anything interesting with the "occupation" component of your experiment?

Here's the distribution of occupations:
Engineer (engineer, machinist, mechanic, etc) 5
Info Tech (programmer, tech services, IT manager, etc) 6
Attorney 2
Student 2
Business (sales, consulting, small business, etc) 8
Retired 3
Education 1
Other 3
Did Not State 2

The three lowest picks (1, 1 and 4) were by persons in the "retired" category, which includes self-described ner'do'wells as well as actual retirees; perhaps these folks have too much time on their hands and/or are particularly Machiavellian thinkers.

Of the four picks closest to the correct answer, three were by engineers and one from a consultant.

There were seven picks of numbers exceeding 50, although under no circumstances could the correct answer be above 50. There was no pattern of occupations among these picks.

An interesting thing about this game is that, if we played it again and again, I suspect the picks would get lower and lower - assuming we knew and remembered the results of each previous game. When I look at some of the cyclical stock sectors, I notice that investors seem to be getting more and more anticipatory with each cycle. Perhaps these are related.

[billwagnon]

The whole thing reminded me of the sign at the roller rink:

THE MAXIMUM SPEED OF ANY SKATER SHALL NOT EXCEED THE AVERAGE SPEED OF ALL THE SKATERS!!!

[350HP930]

Damn, I didn't see the part about picking 1/2 of the average so I gave what I thought the skewed average would be. For that reason I submitted 47 but certainly would have been shooting for closer to the real answer if I hadn't missed that critical part of the problem.

[nostatic]

I guessed orange. Do I win?

[Leland Pate]

Well, looks like you guys slept at a Holiday Inn Express last night...

I have no idea what 'yall are talking about.

[Paco Anton]

jyl,

No need to send a package overseas to Spain. I'll just enjoy being in the top three.

[island911]

Originally posted by jyl
What was all that about? The idea of the game is to guess how many steps ahead the other players are operating, and then to think one step ahead of that.

. .. .The winner is kjb who picked 17. The runner-up is Island 911 who picked 17.45847. Third place goes to Paco Anton who picked 15. These are close enough than I’ll send each of you a print - I will get working on them ASAP.

Doh .. . so close. Did ya wait for on-ramp to submit a number? . . .I coulda had it.

interesting game. . . no need for a print.

[CamB]

I was going to pick 1, on the basis that everyone would pick very low in anticipation of trying to game the outcome.

Job = investment banker. Really I should have known better.