Common Sense Statistics Problem

I recently read a statistic that seems counterintuitive to some people but shouldn't be to those who can think straight. When I quizzed others at my poker table only one player got it about right. Though the question isn't about poker I believe good poker players should be able to deduce the approximate answer.


At what age is an American even money to die within one year? In other words if you are told that a randomly picked person is x years old and you have no other information, you can predict the chances that the person in question will live more than a year from that point. (eg 62 might be 98%) How old does that person have to be before his chances drop to 50%?


Please reply only with a number and nothing else, for the time being. It spoils things if you include an explanation.

91

86

nm

68

68

Let's analyze your answer. You say that, at any age, Americans have a 50% chance of dying within one year. Thus, according to your theory, in the first year of life, half of the "newborn" population will die. In the second year of life, another 50% of that "generation" will kick the bucket. By the 5th year, nearly 97% will have perished [do the math: 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/32 = 0.03125 = 3.125% of the population remains]. Five more years, and the "generation" is virtually extinct (0.097656% remain, for those of you keeping score at home).


Common sense tells us that the human survival rate is much greater than that in America, and even in Afghanistan for that matter. I'll stand by my answer (posted below) of age "zero." Taking into account infant mortality, stillbirth, accidents, and illness, the (actual) birth day is a precarious point in the human lifecycle.


Also, DS provided a clue when he said the answer was "counterintuitive." People, naturally, would assume the answer to be a big number, so, countrary to common sense, I picked a small one. [Btw: Your answer is counterintuitive as well, and you deserve points for that. However, based on the above calculations, I still believe it to be wrong.]


I also think that DS was bluffing when he wrote: "players should be able to deduce the approximate answer." By using the word "approximate," he's trying to coax us into guessing a large, awkward number.


Come on, Mr. Sklansky, don't leave us hanging!

im pretty sure

He would say it depends on the genetics and lifestyle of the person.

I don't see how age zero can be correct. The question was explicitly stated to only refer to Americans. Half of the babies born in America are not dead within a year. Not even close.

about 112. I will let others elaborate.

I was going to guess 109, I swear.

What the hell is the answer to the pocket 55 question?

It's late, I've been out all day, and the sheer volume of posts on my favorite forums is starting to stress me out (since my obsessive nature makes me want to read them all) so much I'm only a 50% favorite to live another year.


Anyway, I'd guess about 97 or so.


Regards,


Rick

My thought was that you either will die within a year or you won't. 50/50. I've obviously missed something if the answer is 112! Could you explain?

I obviously have no idea about longevity.


But it is also obvious that anyone up to, like, 100, has at least a 50% chance of continuing to live, just because I know a couple old people.


So, the main thing I was left to go on was,


"When I quizzed others at my poker table only one player got it about right."


For some reason this stuck in my mind as "only one player got it near right." So I pictured players calling out "80" and "90," and Sklansky shaking his head, and then one player blurting out "110!"


So I figured, in the distribution of guesses, 110 had to be "near" right, but I assumed this had to mean just in terms of having the "right" idea, and also being measured relative to other people's ridiculous guesses of, like, 75.


Finally, I balanced this probable distribution of answers on the side beneath the correct answer with Jimbo's strategy of picking the highest answer + 1. After all, if it could be 115, it could very easily be 160, people very rarely live to be that old, and who knows what type of assumptions an actuary might choose to extrapolate at that point on the curve, or how they change each year (as the oldest person on Earth doesn't die, and a zillion new people are added to the over-100 population).


My first guess was 105, then 120, then 125, then 130, then 200, so I figured I'd back off to 130.


I had this same problem in football pools, before I knew how hard football betting was. I strangely assumed everybody else would get the point spreads right (!?), and so I picked a high over-under, figuring my only chance was to differentiate myself and get lucky.


There was no way I ever would have picked 112. It was either 105, or 130. I figured, if they could make the 105+ stretch, the laws of physics would change, causing numbers on the line to become closer together.


eLROY

Yes, there are only two possible outcomes, but that does not imply that the probabilities of them occuring are equal. For example, in the last Super Bowl, someone betting the Rams would have had to lay 11:1, far from an even money prop.


Think of it another way. If each year you have a 50% chance of dying, then the odds of your living for 5 years from today are (.50)^5 = 1/32. That would be a depressing prognosis indeed.

gist was that if spontaneous abortion rate was 50% (i think it really is about 30%, most all of that within first 2 weeks), then conception could be a correct answer.


brad

The key to understanding this is that at a 50% mortality rate, the population distrubution looks like exponential decay. Surely, if the subject lives through one year, the next year he's not going to be better than 50/50 to live again.


Since people do occasionally live to 110 or more, if you put x at 90 then the population of 90 year olds would have to be 2^20. Clearly, it's not. Is the population of 100 year olds 2^10? Nope. So it's much later than that. The answer's going to occur when there are only a handful of people alive at that age.

LIFE EXPECTANCY STATISTICS


How long can I expect to live? Here's the answer:


PRESENT AGE/ AVERAGE YEARS REMAINING/ YEAR OF DEATH


0 75.7 years 2071


25 52.2 2048


30 47.5 2043


35 42.8 2038


40 38.2 2034


45 33.7 2029


50 29.3 2025


55 25.1 2021


60 21.1 2017


65 17.5 2013


70 14.1 2010


75 11.1 2007


80 8.4 2004


85 6.3 2002


Data are derived from the National Center for Health Statistics as

reported in: International Journal of Bio-Medical Computing 39: 209-217

1995

LIFE EXPECTANCY STATISTICS



How long can I expect to live? Here's the answer:



PRESENT AGE/ AVERAGE YEARS REMAINING/ YEAR OF DEATH

<PRE>

0 75.7 years 2071

25 52.2 2048

30 47.5 2043

35 42.8 2038

40 38.2 2034

45 33.7 2029

50 29.3 2025

55 25.1 2021

60 21.1 2017

65 17.5 2013

70 14.1 2010

75 11.1 2007

80 8.4 2004

85 6.3 2002

</PRE>

Data are derived from the National Center for Health Statistics as

reported in: International Journal of Bio-Medical Computing 39: 209-217

1995

I doubt that there are enough statistical samples to give a definitive answer on this. In this case, your safest bet should be to to pick the age of the oldest American alive: You're looking for a point from which on the population curve is either zero or falls steeper than C*(1/2)^(-n). The later case is probably meaningless (chances are there are no Americans of the age of exactly 111 or 113) and the answer would soley depend on the interpolation method used.


cu


Ignatius

"If each year you have a 50% chance of dying, then the odds of your living for 5 years from today are (.50)^5 = 1/32. That would be a depressing prognosis indeed."


Hell, I'm not concerned about 5 years from today. I'm worried about 5 minutes from now. After all, I'll either be dead or alive one minute from now.

And I was going to pick the winning numbers for last week's Powerball, so I'm entitled to the prize money. I swear.

An interesting but obviously old chart. It would be quite a feat indeed for an 85 year old to live 6.3 more years and then die this year.

yeah, at the bottom it says it was published in 1995 but looks like it uses 1996 as the current year.


also i cut and pasted from google so im not 100% sure of it, but it does have a footnote at the bottom so theoretically at least it can be verified.


brad

Sklansky better stop jerking us around and tell us how he reached that answer. Enough of this know it all crap....

if you extrapolate from the chart it would be about 95 to have a life expectancy of .5 years.


but that doesnt really mean anything.


brad

it makes a tremendous difference which population(s) youre talking about.


original post didnt specify so i think most of us assumed (modern day) americans.


brad

I'll elaborate in more common sense terms, since I don't have a statistical background.


Most people who are say, 50, would consider their chances of living to 100 very remote. Thus, the answer being so high is counterintuitive to them, as you said in your original post. However, what they are failing to consider is that once you've hit 90, your chances of living to 100 have gone way up, and once you've hit 99, living to 100 is more likely than not. Thus, the answer being more than 100 does not surprise me.


The poker analogy might be, your chances of making a straight flush are extremely remote before any cards are dealt. But once you get dealt suited connectors, the chances have gone way up, and when you flop the straight flush draw, they go way up again.

i rang my old Gran up and told her the good news that she had a greater than 50/50 chance of living until her next birthday


you would've thought she'd have been more pleased to hear it, wouldn't you?

I wasn't able to get a lot of data to hand, but vague recollections along these lines make me think David's answer is sensible:


- Life insurance premiums should provide some starting point. All I remember about term life insurance is that Mutual of Omaha was willing to sell term life insurance to 95-year-olds and, if I recall correctly, annual premiums were less than the death benefit, so MofA thought 95-year-olds were enough less than 50-50 to die within a year to cover the rake.


- If you got your hands on census data, then you could trace down to the first year where the number of people aged (N+1) or more is half or less the number of people aged (N). That wouldn't quite be right (population growing over time, maybe influenza/war/etc. killed people unevenly, etc.) but it's probably close.


- Think about the length of time that the "world's oldest person" holds on to the title. I looked on the web and found four articles where "such and so, the documented world's oldest person, died". Those people were between 115 and 122 and each held the title for about a year, some more some less. So you'd think the answer would be somewhere around there.

You would think so, particularly if it's next week and she has a big party planned.

Even if you know the average age of people and know the "standard deviation" there may be no right answer since it reasonably possible that most 120 year olds get to be 121 and so on. Or it could be that if the oldest person EVER was say 143 that the anwer would be 142.


The "right" answer, I believe, is -8.5 months. These people have less than 50:50 chance of surviving through birth.


- Louie

According to http://www.ssa.gov/OACT/STATS/table4c6.html

qx (probability of dying within 1 year) for an American male at 106 is 0.488163 and

at 107 is 0.512571. For female 108 0.496428, and 109 .526214. This didn't specifically say the population were Americans, but it was Social Security data, so I assume that's the case.


So the answer is between 106 and 107 for American males, and between 108 and 109 from American females, or about 108 overall. Needless to say, the sample size when the ages get that high is pretty small.


People that get the answer wrong by undershooting it by a large amount are probably not understanding what the question actually is, likely confusing it with what one's life expectancy is. Either that or not understanding to what a great extent a population would have to had degredated for qx to be that high.


BTW, older actuarial tables only went up to 100, at which point a person was dead (even if they were alive), and the insurance policy would be paid off. So the answer in that case would be 99 years old.

im suprised there arent more actuaries here, but here goes a fairly legitimate answer...


the soa (society of actuaries, these are the people that collect mortality data and such) has some data on their website and the answer to skalansky's question is that it depends. it depends on the year of your birth, your sex, where you life, your race, if you have life insurance, if you have an annuity, etc.. for the combined american population, the answer seems to be around 108 for males and 109 for females (according to the latest data soa has on their website soa.org). if david has a different source, i would be interested in hearing where his answer comes from.

I will put my fingers in here again.


I can't see how you can deduce age probabilities from an average age.


I thought maybe you could assume a normal distribution, but you have to have an underlying single distribution first, and the "percentage dying each year" changes with age. eg if you have 100 35 year olds, then next year you will probably have 99 (at least), but if you have 100 70 year olds, then it's different, next year you will probably only have say 95 71 year olds.


Because the distribution changes with age, I don't think you can read a normal distribution. Rather, the distribution would be squarish, with a sharp drop near the end.

But where would that sharp drop be. I can not see how the average age will tell you.


So please David, I need to be enlightened once again.

It's a pointless exercise. You could probably get the answer for this from someone who works for a life insurance company.


What does this have to do with poker.