Odds guessing experiment

2008-04-16

in Science, Security

One of the subtle pleasures associated with reading this blog is the occasional opportunity to be experimented upon. Today is such a day.

Instructions:

  1. Read all these instructions before actually completing step two.
  2. Flip a coin.
  3. Please actually flip a coin. People who choose ‘randomly’ in their heads do not actually pick heads and tails equally. If you don’t have a coin use this online tool.
  4. If it landed heads, click here.
  5. If it landed tails, click here.
  6. When you click one of the links above, you will see a description of an event.
  7. Before looking at the comments below, estimate the probability of the event you see described happening in the next year.
  8. Write that as a comment, indicating whether you are answering the heads question or the tails question.

When you are done, you are naturally free to read the other question and the comments left by others.

Even if you don’t normally comment, please do so in this case. I want to get enough responses to permit a statistical comparison.

Report a typo or inaccuracy

{ 86 comments… read them below or add one }

Yuan April 16, 2008 at 8:57 pm

Heads: 60% chance

tristan April 16, 2008 at 8:59 pm

tails.

Didn’t that already happen?

It’s hard for me to estimate probability as a number, so I’m just going to say I wouldn’t be at all surprised if it happened (again?).

Milan April 16, 2008 at 9:05 pm

Two more things:

1) If you cheated and looked at both options before answering, please do not post an answer. Doing so would wreck the experiment.

2) If you want to know the reasoning behind the experiment, click here.

Scott April 16, 2008 at 9:13 pm

Tails- 10%

caity April 16, 2008 at 9:17 pm

heads:

55%

Mike Kushnir April 16, 2008 at 9:18 pm

heads – 5% chance.

Matt T April 16, 2008 at 9:19 pm

Heads: 0.12

My answer is based on my belief that the event is easily possible, but unlikely.

Fourth Dwarf April 16, 2008 at 10:19 pm

Heads: 50%

Including Hurricane caused flooding as a factor.

Sarah April 16, 2008 at 11:10 pm

Heads – 10%, because the figure seems unusually high.

Kerrie April 16, 2008 at 11:21 pm

Heads, 20% probability including the fact that stupid Americans can’t take care of each other and so a high death toll would be more likely in America than in more competent/compassionate countries.

I realize “hateful rant” wasn’t on your instructions, but oh well. ;)

Zandara April 17, 2008 at 1:59 am

Tails:

Not knowing any of the meteorological factors makes it hard for me to estimate this, but I would say… 10%. It’s not really based on any statistics or research.

Mark April 17, 2008 at 4:30 am

Heads – 5%

Paul April 17, 2008 at 6:05 am

Heads

5%

Ben April 17, 2008 at 7:49 am

Heads 0.05

Milan April 17, 2008 at 10:32 am

It’s a bit odd that we got 10 heads in 12 trials. We will need a lot more data if we are going to be able to draw any meaningful conclusions.

One last note: you can express your answer as a proportion (0.1) a percentage (10%) or a fraction (1/10).

Numbers less than one, without percentage signs, will be treated as a proportion. For example, 0.55 = 55%.

Milan April 17, 2008 at 10:35 am

Incidentally, the mean heads estimate is running at 22.7%, compared with 10% for the mean tails estimate.

Milan April 17, 2008 at 10:48 am

This Powerpoint presentation includes results from two experiments similar to the one above. It doesn’t provide any methodology, though it says that the second example was given to ‘forecasting experts.’

Example 1:

* Massive flood somewhere in North America in which more than 1000 people drown (2.2% probable)

* An earthquake in California causing a flood in which more than 1000 people die (3.1% probable)

Example 2:

* A complete suspension of diplomatic relations between USA and USSR sometime in 1983 (0.14%)

* A Russian invasion of Poland and a complete suspension of diplomatic relations between USA and USSR sometime in 1983 (0.47%)

The flood experiment is also mentioned on this page.

Anon April 17, 2008 at 11:05 am

Between 1903 and 2002, there was never a year where 1,000 people died in a flood.

The worst years:
1903: 178
1913: 527
1914: 180
1922: 215
1927: 423
1935: 236
1955: 302
1969: 297
1972: 554
1977: 210
1982: 155
1983: 200
1986: 208

On the basis of these records, the people making estimates for heads are likely seriously overestimating the risk of so many flood deaths.

Only three hurricanes have ever caused more than 1,000 total deaths (all causes, not just flooding):

1900 – Galveston, Texas – 8,000 deaths
1928 – Lake Okeechobee, Florida – 2,500 deaths
2005 – Katrina – 1,800 deaths

AT April 17, 2008 at 12:30 pm

Heads: 5%

Hilary April 17, 2008 at 1:13 pm

Tails: 55%

zoom April 17, 2008 at 2:22 pm

Heads.
.00005

R.K. April 17, 2008 at 4:04 pm

The highest ‘heads’ estimate is 12,000 times the lowest one.

Also, I wonder whether the very last ‘heads’ estimate inappropriately took into consideration the two comments above with actual flood and hurricane data.

R.K. April 17, 2008 at 4:05 pm

(I am not posting a response of my own because I cheated and looked at the other answer, before coming up with an honest guess of my own.)

Emily April 17, 2008 at 7:39 pm

Heads: 4% chance

Emily April 17, 2008 at 7:41 pm

(I am not sure what good my input is though, considering that I don’t know a thing about flooding trends in North America. It’s more of a gut-response.)

Brett Banks April 17, 2008 at 10:15 pm

Heads 5%

zoom April 18, 2008 at 9:04 am

RK – No, I followed the rules and did not read the comments until after I guessed. (My prediction did take into account the time variable – ie, that the event would take place in the next year. I suspect others may have overlooked that.)

Milan April 18, 2008 at 10:32 am

Running tally:

Heads (n=13)
– Mean: 18.2%
– Median: 5%
– Standard deviation: 0.2165

Tails (n=3)
– Mean: 25%
Median: 10%
– SD: 0.2598

The small number of tails responses remains a mystery

Mark April 18, 2008 at 3:45 pm

Probability of at least 13 heads in 16 trails = 1 in 94
So, not fantastically unlikely.

Neal April 19, 2008 at 8:10 pm

Tails: 5%

Neal April 19, 2008 at 10:10 pm

After posting that, I realize that I have fallen victim to this phenomenon. I doubt if I had the heads question, I would have picked a number above 5%.

zoom April 20, 2008 at 8:30 am

Do you still need more responses Milan? If so, I could post something on my blog to point a few more people in this direction.

Nora April 20, 2008 at 9:44 am

Heads question – pretty improbable. Small number.

Milan April 22, 2008 at 9:48 am

zoom,

The responses above are quite varied and not really sufficient to draw conclusions from. Perhaps more data would help.

Jackie April 22, 2008 at 1:13 pm

Tails.

1 in 50.

Deb April 22, 2008 at 1:27 pm

Heads 1%

Bonnie April 22, 2008 at 1:35 pm

tails
5%

cdn_skylark April 22, 2008 at 1:36 pm

Tails.

5%

Elizabeth April 22, 2008 at 1:51 pm

70% chance (Tails)

Dave April 22, 2008 at 1:57 pm

Heads, 10 % .

Milan April 22, 2008 at 2:11 pm

Running tally:

Heads (n=15)
– Mean: 16.5%
– Median: 5%
– Standard deviation: 0.2060

Tails (n=8)
– Mean: 20.2%
Median: 7.5%
– SD: 0.2652

Milan April 22, 2008 at 2:13 pm

The distribution of guesses is extreme on both sides:

Heads: 60% v.0 005%
Tails: 5% v. 70%

Gabriel... April 22, 2008 at 2:14 pm

Heads: 0.5%

XUP April 22, 2008 at 2:23 pm

Heads – 2% and only because I’m not sure what flooding would include – more than 1,000 died during Katrina, but that was flooding and a bunch of other stuff related to the reason for the flooding and the aftermath of the flooding.

Jenna April 22, 2008 at 2:25 pm

Heads – 50%

Megan Butcher April 22, 2008 at 2:31 pm

tails & 70%

It’s a guess, but a (speciously) reasoned one:

“Well. 100%. Of course that’s going to happen. It’s *Florida*. And the end times are coming so the hurricanes are getting worse. New Orleans. Wait. 1000 people is a lot of people. Generally not many people die in hurricanes. Maybe one or two? How many died in Katrina? 3000? No, that was 9/11. Hmm. 1000 is a lot. Not 100%. But the end times still makes it higher than 50%.”

Soire April 22, 2008 at 2:51 pm

Tails: 75% or better

mud mama April 22, 2008 at 3:11 pm

Heads – less than 1% chance. Thats a pretty high death toll if it was 200 ppl I’d say 50%

Manon Charpentier April 22, 2008 at 3:19 pm

Tails. 0% probability of happening.

Jenny April 22, 2008 at 3:20 pm

Heads – 20% chance, probably involving an earthquake.

Dan April 22, 2008 at 3:25 pm

5% – just flat out guessing.

Milan April 22, 2008 at 3:30 pm

Dan,

Is that for heads or tails?

Milan April 22, 2008 at 3:32 pm

Heads

n: 21
Mean: 0.155002381

SD: 0.198693797

1st quartile: 0.04
Min 0.00005
Median: 0.05
Max 0.6
3rd quartile: 0.2

IQR: 0.16

Tails

n: 10
Mean: 0.279090909

SD: 0.318761809

1st quartile: 0.05
Min 0.02
Median: 0.1
Max 0.75
3rd quartile: 0.625

IQR: 0.575

Dan April 22, 2008 at 3:35 pm

Heads, my bad.

Milan April 22, 2008 at 3:52 pm

Here is a boxplot based on the first 32 guesses:

Heads / Tails boxplot

Rhiannon April 22, 2008 at 4:17 pm

Heads; 15.4%

Katherine April 22, 2008 at 4:23 pm

1 %; heads

Sharon April 22, 2008 at 4:29 pm

Heads….10%

Laura April 22, 2008 at 4:45 pm

tails: 20%

Lissa April 22, 2008 at 5:45 pm

Heads: 32%!

Woodsy April 22, 2008 at 5:56 pm

heads

Well, it will happen or it won’t… I don’t like being quizzed… but I am trying to be a good sport… so here’s a number that popped into my head:

69.9%

Heather G. April 22, 2008 at 6:14 pm

Tails: 45%

molly April 22, 2008 at 7:20 pm

heads – 90%

greencolander April 22, 2008 at 7:52 pm

2% – I got the heads question.

Jill April 22, 2008 at 8:04 pm

Tails question: 30%

Malva April 22, 2008 at 8:38 pm

Tails :30% I guess.

Wendy April 22, 2008 at 9:15 pm

Heads – 40% but it’s a total guess

Jay April 22, 2008 at 9:18 pm

Tails: 6%

Aggie April 22, 2008 at 10:55 pm

Tails: 20%

Linda April 23, 2008 at 12:41 am

Heads… 1%

Anna April 23, 2008 at 1:17 am

Tails: one percent.

Anna April 23, 2008 at 1:18 am

Tails: one percent.

Antonia April 23, 2008 at 6:11 am

Heads
5% chance of the exact circumstances. Hard to say as it is very specific.
It the numerical value given in the event description are not a rigourously adhered to criterion, then I think the chances are 25% or greater.

Susan Den Herder April 23, 2008 at 11:40 am

tails 1/1000

Susan Den Herder April 23, 2008 at 11:56 am

I did not cheat, but when I looked at your reasoning, I just wanted to say that I am a person who works with numbers a lot, and I actually worked with flooding/storm statistics in a former job. Totally random, but wanted to let you know. It is a pretty rare storm event that will affect never mind kill 1000 people in the world, never mind one state.

Tiana April 23, 2008 at 3:06 pm

Tails

Odds; 1:100

Melinda April 24, 2008 at 1:07 am

Heads – 50%

(Zoom “sent” me btw)

Jenny April 24, 2008 at 8:13 pm

tails – how about 40%?
Not that I know much about hurricanes or Florida..

elaine April 25, 2008 at 9:13 am

Heads – less than 10% chance.

I’m in the UK, so I don’t know if you’d include my response or not, given that our news coverage is more concerned with our own country I may have a slewed attitude towards this.

Milan April 25, 2008 at 9:52 am

Thank you all for your answers. I am going to use the ones collected so far to write up the results.

Milan April 25, 2008 at 2:47 pm

The results of this experiment will be posted here as of 7:00pm on April 25th.

Kimberly Jones April 25, 2008 at 5:34 pm

The chances of a flood in the U.S. leading to 1,000 deaths happening in the next year are 90%. This was the heads question.

Manitowaning April 26, 2008 at 10:46 am

I got tails and think it has a 33% chance of occuring

Anne-Marie May 1, 2008 at 6:59 am

Heads

20%

mranda June 8, 2008 at 2:48 pm

Tails :

Extremely unlikely, something like 0.05 % or even less.

. November 3, 2011 at 5:38 pm

In one experiment described by Mr Kahneman, participants asked to imagine that they have been given £50 behave differently depending on whether they are then told they can “keep” £20 or must “lose” £30—though the outcomes are identical. He also shows that it is more threatening to say that a disease kills “1,286 in every 10,000 people”, than to say it kills “24.14% of the population”, even though the second mention is twice as deadly. Vivid language often overrides basic arithmetic.

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