How many.......?

[tikay]

Was mightily impressed with Mully & Tighty yesterday, especially on those "number" questions.

I could make a reasonable guess at the capacity of a football stadium owned by a successful club - if we said 50,000, we can't be THAT far out, but some of the other questions seemed impossible.

Then Team Clever Clogs - Mully, aided & abetted by Posh Alex - introduced us to  the wonders of "Fermi Problem".

https://en.m.wikipedia.org/wiki/Fermi_problem


For those who cba to read tall the gumf, here's the example on wiki......


The classic Fermi problem, generally attributed to Fermi, is "How many piano tuners are there in Chicago?" A typical solution to this problem involves multiplying a series of estimates that yield the correct answer if the estimates are correct. For example, we might make the following assumptions:

1.There are approximately 9,000,000 people living in Chicago.

2.On average, there are two persons in each household in Chicago.

3.Roughly one household in twenty has a piano that is tuned regularly.

4.Pianos that are tuned regularly are tuned on average about once per year.

5.It takes a piano tuner about two hours to tune a piano, including travel time.

6.Each piano tuner works eight hours in a day, five days in a week, and 50 weeks in a year.

From these assumptions, we can compute that the number of piano tunings in a single year in Chicago is
(9,000,000 persons in Chicago) / (2 persons/household) × (1 piano/20 households) × (1 piano tuning per piano per year) = 225,000 piano tunings per year in Chicago.

We can similarly calculate that the average piano tuner performs
(50 weeks/year)×(5 days/week)×(8 hours/day)/(2 hours to tune a piano) = 1000 piano tunings per year per piano tuner.

Dividing gives
(225,000 piano tunings per year in Chicago) / (1000 piano tunings per year per piano tuner) = 225 piano tuners in Chicago.

The actual number of piano tuners in Chicago is about 290


 

[tikay]

So let's test it.

Here's your question.

How many female poker players who live in London will play online poker tonight? (Thursday 30th September).


I'll give it a bash, let's see if anyone else dare make the same fools of themselves as I am about to.

 

[celtic]

317

[buzzharvey22]

The population of London is somewhere around 8.8 million.

50%ish of these are women, 4.4m

80% of these are over 18 years old and legally allowed to gamble in the uk, 3.6m

1% of women play poker, 36,000

50% of poker players play online. 18,000

People will play 2 nights per week online, 2/7 x 100 = 28.5% chance of playing on a random night.

28.5% of 18000 = 5130

My guess is 5130 women will play poker online in London tonight.

[TightEnd]

do you have the answer to this?

ideally you want there to be an actual provable answer.....


anyway london has 8.5m people, roughly

lets say 4.25m are women

lets also say that london is younger than the rest of the country, on average

now we have to make an estimate of

a) how many of london's women play poker online

and b) of that number how many would be playing tonight

i remember a piece of work a few years ago that said there were 250,000 or so uk online poker players

most of them are male?

lets say 25% are female 60-70,000

of that 60-70,000...london is 8.5/64m of the uk population = 13% of total

13% of 65,000 say is 5,000

how many of those 5000 would be playing tonight

impossible to say but lets say its sub 50%.

i'll fermi 2,000 as the answer

but the question isn't a great example

[tikay]

How many female poker players who live in London will play online poker tonight? (Thursday 30th September).


I'm not entirely sure if it is critical to get all the "reducers" in the correct order, but anyway, off we go.

These are all "my best guess", no google referencing.

12 million people live in London.

20% are under age, 20% are too old, 10% are unwell, hospitalised or in prison, 20% don't have internet or a computer at home.

So we are down to 30% of 12 milly which = 3.6 million.

How many of them play online poker? 1 in 100 seems too many, 1 in 200 seems not enough. Call it 1 in 150. So divide 3.6 milly by 150 & we get 24,000.

Female poker players equal around 5% of the total poker playing population. So, 24,000 x 5% = 1,200.

The average recreational poker player plays Online 2.5 times per week. (That's a rough industry standard).  They'll play less on Monday (MNF) or when CL is on telly (Tues & Weds), but more at weekends.  Let's leave it at 2.5 times per week.

So they will play every 2.8 days. So from that there is a 36% chance they will play on Thursday.  (I think....).

1,200 x 36% = 429.

So, that's the answer, 429.  Which is patently, obviously & clearly wrong.

[tikay]

do you have the answer to this?

ideally you want there to be an actual provable answer.....


anyway london has 8.5m people, roughly

lets say 4.25m are women

lets also say that london is younger than the rest of the country, on average

now we have to make an estimate of

a) how many of london's women play poker online

and b) of that number how many would be playing tonight

i remember a piece of work a few years ago that said there were 250,000 or so uk online poker players

most of them are male?

lets say 25% are female 60-70,000

of that 60-70,000...london is 8.5/64m of the uk population = 13% of total

13% of 65,000 say is 5,000

how many of those 5000 would be playing tonight

impossible to say but lets say its sub 50%.

i'll fermi 2,000 as the answer

but the question isn't a great example

No, I don't have a prove-able answer. If I did, I'd probably make the numbers "backfit".

In your example, which uses much different baselines to mine, 25% of poker players are female jumps off the page. Surely far, far less than 25%? If you made that 5% (five times less) your final number would be similar to mine. (That's called backfitting I suppose).

Think I'd best stick to NFL Last Longers.

[TightEnd]

yes we get similar answers if 5% of poker players are female. your estimate feels more right than mine on that.

[mulhuzz]

Ironically you want to minimise the steps you take. Which seems counter intuitive because you think x% too much here is roughly cancelled by y% too little there, etc.

There's a good explanation for maths heads (multiply guesses is the same as adding their logarithms).

One way to think about it is it's like the bookie and his overround. The most teams (guesses) in your acca (fermi steps) the more money the bookie steals.

I think about 200 seems to be the answer. On a weekend it might be 800. Although tonight is a football night which surely has some effect.

[tikay]

Ironically you want to minimise the steps you take. Which seems counter intuitive because you think x% too much here is roughly cancelled by y% too little there, etc.

There's a good explanation for maths heads (multiply guesses is the same as adding their logarithms).

One way to think about it is it's like the bookie and his overround. The most teams (guesses) in your acca (fermi steps) the more money the bookie steals.

I think about 200 seems to be the answer. On a weekend it might be 800. Although tonight is a football night which surely has some effect.

Appreciate the explanation.

If you are between 200 & 800, my 429 does not look quite so bad. I might have got there incorrectly though. My teacher called them the "workings outs".

[tikay]

Ok, lets do an easier one. We can (reasonably) get a prove-able answer to this.

How many people in Great Britain own a mobile phone?

Or....


How many people in Great Britain own a motor car?

[atdc21]

Tis like a technical version of ' What Johnny Lodden thinks. imo '

[mulhuzz]

Ok, lets do an easier one. We can (reasonably) get a prove-able answer to this.

How many people in Great Britain own a mobile phone?

Or....


How many people in Great Britain own a motor car?

If the question is 'at least one mobile' (not the total number of of mobiles) then I'll go for a pretty simple two step approach:

60m people in Britain.
Mobile phone penetration something like 75%
45m mobile phone owners in Britain.

Fermi problems are useful to test dimensional analysis. They might not give you the correct answer but they are a quick way to test another answe, roughly. Eg for piano tuners you could think 2 or 20 or 200 or 2000 or 20000 piano tuners (or more!)

For mobile phones in Britain fermi isn't really 'useful' as an error catcher because you're never going to be an order of magnitude out (eg 200 not 2000, 450k not 4.5m) because mobiles (and cars) are so widespread.

[mulhuzz]

The point of all of that being, if we predict that now there are 45m mobile phone owners in Britain and then launch a serious study and spent loads of money and it tells us 55m, we still don't know if we are right.

Where as if Fermi tells us there should be 225 piano tuners and we scientifically measure 4000 of them then something is wrong. There's a bias or something unaccounted for in either number and we can't use either with any great confidence.

Now that might sound silly for piano tuners in Chicago (surely we just count them rather than spend loads of money on a science experiment ) but for stuff like 'what's the tensile strength of this bit of metal' where finding out can be costly and expensive, it's good to be able to roughly 'sanity check' the number you get out.

[TightEnd]

How many people in Great Britain own a motor car?

UK Population is 65m

Population over 17 is about 55m (a bit less?)

how many people per household, on average? 4 sound about right?

55/4= lets say 14

average uk household 2 cars?

14*2=28m cars?


then google

"this is the list of summary results from the DVLA publication: “ At the end of 2012 there were 34.5 million vehicles licensed for use on the roads in Great Britain, of which 28.7 million (83 per cent) were cars.12 Apr 2013"





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