What's a boy to do?

When you first picked, you had a one in three chance of being right.

Right.

With one board removed, your pick 'still' has a one in three (33 1/3 %)
chance of being right.

John, care to respond to my question, posted above?

vince

"Wolfgang" wrote in message
...

The question.......what should you do?

The easiest way to convince yourself of the correct answer (since it's
non-intuitive) is to play the game with someone. After a short while,
you'll realize that the only way you can get it right if you don't switch is
if you picked it right from the beginning - in other words, 1 chance in 3.

jeffc wrote:
"Wolfgang" wrote in message
...

The question.......what should you do?

The easiest way to convince yourself of the correct answer (since it's
non-intuitive) is to play the game with someone. After a short while,
you'll realize that the only way you can get it right if you don't switch is
if you picked it right from the beginning - in other words, 1 chance in 3.

Sure, first they take all yer shiny new nickels.......

Hey, I've only got just so many five dollar bills, ya know!

Anyway, that's right.....so long as we stress the "convince" part, as
opposed to learn. Unless and until you become familiar with the
correct solution to the Monty Hall problem (whether it's explained to
you or you work the logic out for yourself) intuition can lead you down
a long and, if it's presented as a betting game, ruinous road.

Wolfgang
who wouldn't bet any of his few remaining shiny new nickels on the
prospect of selling these revolutionary analyses to the folks who run
vegas.

"jeffc" wrote in message
.. .

"Wolfgang" wrote in message
...

The question.......what should you do?

The easiest way to convince yourself of the correct answer (since it's
non-intuitive) is to play the game with someone. After a short while,
you'll realize that the only way you can get it right if you don't switch
is if you picked it right from the beginning - in other words, 1 chance in
3.


Or just play by yourself:
http://math.ucsd.edu/~crypto/Monty/monty.html

This puzzle right smack dab in the center of my realm, as its a regular
component of one of my classes. I can take you all to school on the solution
on several levels, but I'm not working today so you're off the hook.

MEANWHILE: how about this cherry;

You toss three darts at a target. Dart A misses the target, then Dart B
misses by even more. What is the probability that Dart C will miss by more
than Dart A?

--riverman

"riverman" wrote in message ...

Or just play by yourself:
http://math.ucsd.edu/~crypto/Monty/monty.html
--riverman

I got it right, 3 out of 5 times, by changing my selection each timed.

Op

"Opus McDopus" wrote in message
...

"riverman" wrote in message
...

Or just play by yourself:
http://math.ucsd.edu/~crypto/Monty/monty.html
--riverman

I got it right, 3 out of 5 times, by changing my selection each timed.

Op

Yep. A better way to convince yourself that changing doors is the best
strategy is to make a spinner out of a paper clip and a piece of paper. Draw
a circle divided in thirds, and unbend the paper clip so it works as a
pointer, and hold it in the center with the pencil when you spin it. Agree
beforehand that the prize is in a given section, and decide that you will
always switch. After about three spins, it becomes abundantly obvious how it
all works.

--riverman

On Sun, 29 Oct 2006 11:02:22 +0800, "riverman"
wrote:



Or just play by yourself:
http://math.ucsd.edu/~crypto/Monty/monty.html

This puzzle right smack dab in the center of my realm, as its a regular
component of one of my classes. I can take you all to school on the solution
on several levels, but I'm not working today so you're off the hook.

Unfortunately, the first 4 or 5 times I tried it with not changing, I
was right every time. Then the odds started to work out, but I had
those early successes to work out of my mind.

--
Antiquis temporibus, nati tibi similes in rupibus
ventosissimis exponebantur ad necem.

http://www.visi.com/~cyli

On Oct 27, 12:40 pm, "Wolfgang" wrote:
An interesting problem was recently brought to my attention.

Let us say that you and I are standing next to a table on which I have
placed three boards identical in every respect except that each has a
different number painted on it.....1, 2, and 3, respectively.

I say to you that if you turn your back I will place a five dollar bill
under one of the boards and a slip of paper that says "you lose" under each
of the others. You then turn back to face the table and point to or name
the board you think has the five dollar bill under it. If you're right, you
win the five bucks.

We proceed. You pick, say, board number one. I say, "O.k., tell you what,
I like you so I'm going to make this easier for you," and I remove board
number three to show you that it has a "you lose" tag under it. Obviously,
the five dollars must be under one of the other two. "So," I say, "would
you like to stick with your original pick, or change your mind?"

It is a given that the game is not rigged in any way and you are not being
fooled by anything ambiguous or otherwise misleading in the description.

The question.......what should you do?

Wolfgang

It don't matter. Play the game 300 times and you win 100 no matter how
you do it.
Initially your chances are 1/3.
With the give away the chances are expressed (1/2)*(2/3), which is
1/3 same as above. Again if you play 300 times you win 100.
If I remember correctly Poission figured all this out working for a
wealthy French nobelman who loved to gamble.

Wolfgang wrote:
RE Obviously, the five dollars must be under one of the other two.

The way you stated this, you removed what at one time looked like
a one in three chance. But, the way you stated this, you took away
one of the three choices, and the one you took away was known
to be false.

So there are now two choices left, one of which is guaranteed
to be correct. And you have no evidence to indicate one choice
over the other.

The current 50-50 condition is unrelated to a previous condition,
when three chances were involved. And it doesn't matter how many times
to you do it (if you follow the sequence of events you specified).

If you restate the problem, and say you now remove one of three
choices, leaving two that might be false, or two choices that
contain at most one true, then it is a different problem.

Jesus, forget mathematicians. When you need answers to difficult
problems,
always ask a sliver digger (a carpenter).

salmobytes wrote:
Wolfgang wrote:
RE Obviously, the five dollars must be under one of the other two.

The way you stated this, you removed what at one time looked like
a one in three chance. But, the way you stated this, you took away
one of the three choices, and the one you took away was known
to be false.

So there are now two choices left, one of which is guaranteed
to be correct. And you have no evidence to indicate one choice
over the other.

The current 50-50 condition is unrelated to a previous condition,
when three chances were involved. And it doesn't matter how many times
to you do it (if you follow the sequence of events you specified).

If you restate the problem, and say you now remove one of three
choices, leaving two that might be false, or two choices that
contain at most one true, then it is a different problem.

Jesus, forget mathematicians. When you need answers to difficult
problems,
always ask a sliver digger (a carpenter).

I won't speak for anyone else, but when I need the answer to a
difficult question (or even what may turn out to be a not so difficult
question, for that matter) I think I'll ask someone who can at least
make his or her position on a previous question (not to mention an
explication thereof) clear.

Thanks, anyway.

Wolfgang
still, the venture was not entirely without profit.......we have at
least learned something about the origins of old expression, "to a man
with a hammer......."