Classic problem/riddle
Right JG, it does make you think! A variation I came across many years ago (I think it was in a collection of Saint (Simon Templar) stories by Leslie Charteris. A confidence trickster made his living by making bets with people where it was not intuitively obvious, but the odds were massively in his favour - for example in a room of 50 people at least 2 would have the same birthday. The Saint devised a game involving 3 counters - 1 black both sides, 1 white both sides, and one with 1 side black and the other side white. The counters were shaken up in a bag and one removed and placed face down without revealing the other side. The object was to guess the colour of the hidden side. What would you call if the visible side was black? (assuming the counter edges are all the same colour!)
For the counters, knowing there is a black side means that it could be the double black counte or the white/ black counter.
Of the three sides that you do not know, two of them are black and one of them is white.
Therefore, chose black, that is a 2/3 chance. White has only a 1/3 chance of coming up.
Of the three sides that you do not know, two of them are black and one of them is white.
Therefore, chose black, that is a 2/3 chance. White has only a 1/3 chance of coming up.
Yes. Another way of looking at it is that you will draw out a counter with both sides the same colour in 2 out of every 3 attempts. In the story, the confidence trickster worked out the correct strategy, but failed to take into account the Saint's skill at sleight of hand!
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NileVentures
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Gazuty - I must say that this is one of the best explanations (and I have heard / read a few) of the Monty Hall problem that I have seen.gazuty wrote: You can prove this very quickly.
If at the start you are allowed to pick two boxes what would happen.
Well you could get two carrots.
Or you could get a carrot and a ferrari.
Or you could get a Ferrari and a carrot.
So of the three outcomes, there is a one in three chance of getting two carrots and a two in three chance of getting a Ferrari and a carrot.
By swapping you are choosing two boxes.
Not 50/50.
Good stuff.
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NileVentures
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I like the Birthday Problem - another classic.gazuty wrote:A great explanation of the birthday problem.
http://en.wikipedia.org/wiki/Birthday_problem
I often use it when watching a football match with friends: I offer a beer to whoever can give the best estimate of the probability, out of the 22 players plus the ref, of two of them sharing the same birthday. It gets them every time. But you must be able to the explanation or they will all want a free beer from you.
P(Not same b'day) = (1/365)^23 × (365 × 364 × 363 × ... × 343) = ~49% for 23 people.
Therefore: P(Same b'day) = ~51% for 23 people.
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NileVentures
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PS - the Birthday Problem at a football match does not work when QPR are playing ManU!
The probability of same birthdate for two professional football teams would be higher than for a random selection of the general population because of selection bias of birthdates in the determination of probability in becoming a professional footballer.
What is this bias that you speak of? Are you suggesting that an individual's star sign can influence their chances of becoming a successful footballer?gazuty wrote:The probability of same birthdate for two professional football teams would be higher than for a random selection of the general population because of selection bias of birthdates in the determination of probability in becoming a professional footballer.
The star sign one is funny. The doctor in the delivery suite exerted a greater gravitational force on the newborn than the nearest star.
No, I reference the selection bias that favours older children in children's sport. Eg say the cut offs for u/6 is 1 Jan. To play u/6 I must be not six years old on the 1st of Jan of the relevant year. Therefore, those born in the December will be almost a year older than some in the comp. Being a year older at age of 6 means being 20% older than someone who is 5 and given the rapid development of children at that age, makes one a lot more skilful. Such a child is more likely to be considered a better player, to get into the regional squad and then to the national squad. Getting to the regional or national squad means better training from better coaches and more training than the younger child. By the time the boy is 10 he has had hundreds of additional hours of tuition over his younger also rans. You get the picture of the theory.
Now for the proof. Look at the cut off dates for junior leagues in the relevant country of origin of the relevant player (when they were a junior). The bias will be there. Birth dates of those in the top leagues will predominate to the month(s) pre the cut off.
This is not my idea. I read about it in the Malcolm Gladwell book Outliers. http://www.gladwell.com/outliers/
No, I reference the selection bias that favours older children in children's sport. Eg say the cut offs for u/6 is 1 Jan. To play u/6 I must be not six years old on the 1st of Jan of the relevant year. Therefore, those born in the December will be almost a year older than some in the comp. Being a year older at age of 6 means being 20% older than someone who is 5 and given the rapid development of children at that age, makes one a lot more skilful. Such a child is more likely to be considered a better player, to get into the regional squad and then to the national squad. Getting to the regional or national squad means better training from better coaches and more training than the younger child. By the time the boy is 10 he has had hundreds of additional hours of tuition over his younger also rans. You get the picture of the theory.
Now for the proof. Look at the cut off dates for junior leagues in the relevant country of origin of the relevant player (when they were a junior). The bias will be there. Birth dates of those in the top leagues will predominate to the month(s) pre the cut off.
This is not my idea. I read about it in the Malcolm Gladwell book Outliers. http://www.gladwell.com/outliers/
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Will Sharpe
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That's a good example but I think you stumbled on the details. Anyone born in Jan will in a better position if Jan 1 is the cutoff date. Same example would apply to children in school right? If they are grouped based on year of birth the ones born early are ahead of the ones born late in the year statistically speaking.gazuty wrote:The star sign one is funny. The doctor in the delivery suite exerted a greater gravitational force on the newborn than the nearest star.
No, I reference the selection bias that favours older children in children's sport. Eg say the cut offs for u/6 is 1 Jan. To play u/6 I must be not six years old on the 1st of Jan of the relevant year. Therefore, those born in the December will be almost a year older than some in the comp. Being a year older at age of 6 means being 20% older than someone who is 5 and given the rapid development of children at that age, makes one a lot more skilful. Such a child is more likely to be considered a better player, to get into the regional squad and then to the national squad. Getting to the regional or national squad means better training from better coaches and more training than the younger child. By the time the boy is 10 he has had hundreds of additional hours of tuition over his younger also rans. You get the picture of the theory.
Now for the proof. Look at the cut off dates for junior leagues in the relevant country of origin of the relevant player (when they were a junior). The bias will be there. Birth dates of those in the top leagues will predominate to the month(s) pre the cut off.
This is not my idea. I read about it in the Malcolm Gladwell book Outliers. http://www.gladwell.com/outliers/
Will Sharpe wrote:
That's a good example but I think you stumbled on the details.
Story of my life and a weakness in myself that I recognise. Almost perfect but never 100%. Still it hasn't stopped me being very successful.
My weaknesses are perhaps shown up best in mathematics. In each exam I was simply unable to check my work, my brain would just say "yep, yep, yep" and would not pick up silly errors, usually in basic arithmetic. So my whole undergrad degree is full of close runs. At University, I never got less than 90% in any maths subject but I max out at 97%. Never got the magic 100.
Wish I knew what others do to develop thoroughness, but my brain just isn't wired that way. Still, I'm glad about the way it is wired. No point not being able to get past 50% of the concepts even if very thorough. I was lucky enough that while my friends were tuning out or saying "why" as each new mathematical concept was explained my brain said "of course".
Hi
Just reopening this post..
Has anybody thought how to apply this in real trading situations..
Ie if something appears to 50:50..but isn't?
I would have thought that 3 selection markets would suit ie (ie football, Home, away and draw perhaps?)
Something to think about of you cant get to sleep at night!
Regards
Peter
Just reopening this post..
Has anybody thought how to apply this in real trading situations..
Ie if something appears to 50:50..but isn't?
I would have thought that 3 selection markets would suit ie (ie football, Home, away and draw perhaps?)
Something to think about of you cant get to sleep at night!
Regards
Peter
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NileVentures
- Posts: 79
- Joined: Mon Oct 22, 2012 9:13 pm
Hi Peter,
There are a number of web-sites dedicated to the Monty Hall Problem:
- http://montyhallproblem.com/
- http://lifehacker.com/5950569/know-how- ... -decisions
The generalisation is that you need to be in a situation where you make a decision at certain odds and then you have new information arrives that informs you that your initial decision is not wrong and eliminates one of the options. You should then change your mind.
The only applications I can see would be in fixed odds arcade or casino games.
You should turn your thinking around: try to invent an arcade game based on the Monty Hall Problem in the knowledge that, given new information, most men will stick with their original decision and most women will change their mind!
There are a number of web-sites dedicated to the Monty Hall Problem:
- http://montyhallproblem.com/
- http://lifehacker.com/5950569/know-how- ... -decisions
The generalisation is that you need to be in a situation where you make a decision at certain odds and then you have new information arrives that informs you that your initial decision is not wrong and eliminates one of the options. You should then change your mind.
The only applications I can see would be in fixed odds arcade or casino games.
You should turn your thinking around: try to invent an arcade game based on the Monty Hall Problem in the knowledge that, given new information, most men will stick with their original decision and most women will change their mind!