# Re: origin of quote about random search?

• From: curt@xxxxxxxx (Curt Welch)
• Date: 12 Apr 2009 21:22:58 GMT

Monica <syntience@xxxxxxxxx> wrote:
On Apr 12, 1:15 pm, N <n.m.ke...@xxxxxxxxxxxxx> wrote:
On 12 Apr, 15:46, YKY (YAN King Yin, =D5=E7=BE=B0=CF=CD)

<generic.intellige...@xxxxxxxxx> wrote:
Who said:

"When the search space is large, the only reasonable search method is
random" or something like that?

Thanks in advance!

there are 3 possible answers to 1 test question.
Only one answer is the correct one. Mr.A can only
make one choice.

Mr.A, picks 1 answer and is shown another without
knowing if either is the correct one.

Your wording is a bit confused there. As was pointed out, this is the
Monty Hall problem from the classic American TV Game show - "Lets Make A
Deal". Money Hall was the game show host.

http://en.wikipedia.org/wiki/Monty_Hall_problem

The contest is trying to find the high value prize behind three closed
doors. He picks one door, the host (who knows the answer) picks one of the
doors which wasn't selected by the contestant (and which he knows is not
the correct answer), and opens it - reveling that the "good" prize is not
behind that door. The contestant can then either stick with his first
pick, or switch, to the remaining closed door.

Mr.A can change his mind if he feels like staying
with his first pick, or chooses either of the other
two.

No, he can choose the other one which hasn't been opened yet. The one that
is open is not out of play because it's obvious the prize is not behind it.

Even if he does change his mind it seems that the
chances are 50/50 that either of these answers is
the correct one perhaps, as the third could also
be right.

for some reason, his chance of choosing the correct
answer, even without understanding the question
increases if he changes his mind.

It's not just "some reason". It's just simple statistics. Though it's not
very intuitive.

The trick is that the game show host has given you a hint which you didn't
have when you made the first choice. He basically said "don't pick this
door or you will lose". Now that you have that hint (extra information),
you can make a better choice than you did the first time.

It's not intuitively obvious, but the better choice after you get the hint
is always to switch.

What it looks like, is that after the hint, you have a 50/50 chance of
picking the right door - but that it would make no difference which you
picked. So that switching, or staying with the first pick would be equally
good. But it's not.

If you stay with your first pick, then you are not using the hint. If you
played the game 3000 times, and always stayed with the first door you
picked, you would win about 1000 times, and loose about 2000 times. That
is clearly not taking advantage of the 50/50 odds he gave you with the
hint. The result in that case, is the same if you get the hint or not.

If, after he gave you the hint, you flipped a coin, and randomly picked one
of the doors (randomly stayed, or switched), your odds of wining would be
50/50, and you would 1500 out of 3000 on average. That would be better
than always staying with the first door, and only winning 1 out of 3 times.

However, if you switch every time, you will end up winning 2000 out of 3000
on average. You will do even better than 50/50 odds.

By switching every time, you are first picking a door, which you know you
will not end up with. 1/3 times, that will be winning door, and you will
lose when you switch. However, if the winning door is one of the other
two, you are guaranteed to get it when you switch. So you end up winning
2/3 times. After the hint, the other door is always the one with the best
odds of winning.

are we more likely to come home with a higher degree
if we change our options on our course? do people who
know less about mathematics but change their minds
more about the answers to questions stand and equal
chance to graduate with the best maths student of that
year?

No, those people flunk out and don't get a degree.

Your question doesn't apply because no one is giving you a hint in your
example like with the Monty Hall problem. It only works win you are given
a hint. The Monty Hall problem is just confusing because it's hard to
grasp how to best make use of the hint.

If you took a multiple choice test, marking all your answers, turned it in,
and then the teacher crossed out one of the answers you didn't pick on each
question, and told you that answer was wrong, and then asked you if you
wanted to change any of your answers, then the problem would be similar.
If you had picked the first answer randomly (because you had no clue what
was right), then it would always be better to switch to one of the other
answers. But if you had some idea of what was more likely to be like, the
decision to switch or stay becomes harder.

The hint would turn a test with 3 answers per question, into a test with 2
answers per question. You are always going to expect to get more right if
you pick randomly from 2 answers than from 3 for each question. In effect,
the teacher made the test easier, and asked if you wanted to take it again.
If you are picking answers randomly, you will do better to take it again.
Because of the special way the test was "made easier", you would want to
change every answer to get the best score. But if you don't understand
math, and probabilities, you wouldn't understand why you should do that! :)

This author is confused about the Monty Hall Paradox, which is also
irrelevant in this context. Go google for it.

--
Curt Welch http://CurtWelch.Com/
curt@xxxxxxxx http://NewsReader.Com/
.

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