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Mesaboogie
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This is probably the most pedantic post of recent months, but I thought I'd post it anyway for the hell of it.

I've been putting together a Bank Night type effect recently for my show and wanted to add some byplay on the probabilites of whether the money will be in a certain envelope. During my research studying various types of this effect I stumbled across Richard Osterlinds version on his MIND MYSTERIES 1 DVD.

In the effect, he has 4 envelopes handed out then proceeds to ask three of the people to open their envelopes. Since he knows where the money is, he can be safe knowing that these envelopes are empty. This leaves his envelope and the one remaining participant's.

He then jokes, that "Your odds have increased from 20% to 50%, but so have mine"

Now I understand this statement, to the laity seems accurate and it's a nice gag at the end too. However, it's incorrect.

From the perspective of the last remaining participant, her odds of having the money have in fact increased from 20% to 80%, whereas Richards remains at 20%.

Since these odds would probably seem a little odd to the majority of the general public, do we still state them, or do we continue, as Richard has, to state what most people would generally think, if anything to get a gag out of it?

I'd actually be interested to know whether Richard was aware of this inaccuracy?

For the record, if the performer is also unaware of where the money is, ie he has placed the money in one of the enevlopes blind, then the odds would be 50/50. But this is not the case here.

Andrew
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ddyment
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Andrew's analysis is incorrect, and is based on the common probability fallacy of assuming that events are somehow "remembered" by the objects at hand. This is why, after a legitimate coin toss has produced "heads" ten times in a row, people will bet heavily on "tails" for the next toss, whereas the probability of "tails" for that toss are exactly what they are for any toss: 50%.

In the case of Richard's bank night, when the end scenario is reached (two envelopes left) the spectator's odds of having the money are 50%, as Richard states. These odds are not affected by what has gone before. Correctly, of course, the odds are 0%, as the game is rigged; if it were fair, though, they would be as stated by Richard.

Topics such as these are discussed in the "Magical Equations" forum, under the "Mind Benders" category.
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Richard Osterlind
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Quote:
On 2008-12-02 04:31, Mesaboogie wrote:
This is probably the most pedantic post of recent months, but I thought I'd post it anyway for the hell of it.

I've been putting together a Bank Night type effect recently for my show and wanted to add some byplay on the probabilites of whether the money will be in a certain envelope. During my research studying various types of this effect I stumbled across Richard Osterlinds version on his MIND MYSTERIES 1 DVD.

In the effect, he has 4 envelopes handed out then proceeds to ask three of the people to open their envelopes. Since he knows where the money is, he can be safe knowing that these envelopes are empty. This leaves his envelope and the one remaining participant's.

He then jokes, that "Your odds have increased from 20% to 50%, but so have mine"

Now I understand this statement, to the laity seems accurate and it's a nice gag at the end too. However, it's incorrect.

From the perspective of the last remaining participant, her odds of having the money have in fact increased from 20% to 80%, whereas Richards remains at 20%.

Since these odds would probably seem a little odd to the majority of the general public, do we still state them, or do we continue, as Richard has, to state what most people would generally think, if anything to get a gag out of it?

I'd actually be interested to know whether Richard was aware of this inaccuracy?

For the record, if the performer is also unaware of where the money is, ie he has placed the money in one of the enevlopes blind, then the odds would be 50/50. But this is not the case here.

Andrew



Andrew,

You are making the same mistake that many gamblers do when playing craps our roulette. The dice (or wheel) has no memory. At the start of each play, everything is new. When I get down to one person and myself, we each have a 50/50 chance of having the money. Nothing before that matters.

Richard
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Sorry, ddyment. I must have posted not seeing yours.
ddyment
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Richard Osterlind wrote
Quote:
:Sorry, ddyment. I must have posted not seeing yours.

No doubt we simply posted simultaneously, but I hit "Submit" first.

And what are the odds of that? Smile
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mindhunter
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Quote:
On 2008-12-02 11:39, ddyment wrote:
Richard Osterlind wrote
Quote:
:Sorry, ddyment. I must have posted not seeing yours.

No doubt we simply posted simultaneously, but I hit "Submit" first.

And what are the odds of that? Smile


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OTTOEMEZZO
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I have to agree with Andrew. If Richard knows which envelope has the cash and he wants to eliminate all but one envelope, that spectator's chance rises to 80%.
Here's a quick scenario. Let's assume that the cash is always in envelope number 1. In this scenario, there's an 80 percent chance that one of the 4 spectators will choose envelope number 1. Here are the possibilites of which envelopes the spectators will choose:
1 2 3 4
1 2 3 5
1 2 4 5
1 3 4 5
2 3 4 5

As you can see, spectators will have the envelope with the number 1 on it and Richard eliminates the other three, that spectator has an 80% chance of holding cash. Here are the eliminations for the previous 5 cases (keep in mind that Richard cannot eliminate the cash enevelope on this turn):
2 3 4 are eliminated
2 3 5
2 4 5
3 4 5
and 3 4 5 (this is the only scenario where Richard has the number 1 (WINNING) enevelope in his hand.

His chances after the eleminations are 20% while the spectator's are 80%.
Of course, as Andrew correctly stated, this only applies if Richard knows which envelope holds the cash and that he eliminates the 3 spectators without the cash. If it were random, then yes, the chances would be 50/50.

With all this said, I believe Richard's presentation is correct! You don't want to confuse the spectators' with complicated math and even mathmaticians will have a hard time recognizing that Richard made a technical mistake.

This problem is one of the oldest and most argued ones by mathematicians. There are numerous top mathematicians who still do not understand why the percentages change like that. For more info on this puzzle, take a look at "Tricks of the Mind" by Derren Brown. That's one excellent book. Cheers.
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Caliban
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I also agree with Andrew. Assuming that there are 5 envelopes at the start, 4 random ones are selected leaving Richard with the 5th, and Richard (who knows where the bill is) always chooses envelopes he knows to be empty as the ones to be opened. At the end there will always be an 80% chance of the bill being in the spectator's envelope and a 20% chance of it being in Richard's.

It's nothing to do with chance having no memory because there is no chance involved (other than the the original 20% chance of the bill starting with Richard). Which envelopes get opened is not decided by chance - it's decided by Richard - who DOES have a memory and deliberately chooses empty envelopes to be opened.
Mesaboogie
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Thanks Vlad and Caliban for clearing this up, which saved me a lot of typing. I didn't realise my initial claim would produce doubt, as I was only stating whether it right to tell the audience what most people would think. For me, I'd find it hard having a degree in Maths stating an incorrect probabilty to an audience even though most will question it, as some have already here - call it pride ! Smile

Doug, out of interest you stated "These odds are not affected by what has gone before" - this is correct, as the odds of the envelope being "in the audience" will never change, it's 80%, even when three of them have been opened (since they are handpicked by Richard and ALWAYS empty)

So, Richard, will you change your patter now Smile

Regards
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ddyment
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Yes, I stand corrected, assuming that the effect is as described by Andrew, and Richard is the one eliminating the (known to him) empty envelopes. I had incorrectly assumed that it was a classic Bank Night effect, where the participants were selecting and opening envelopes.

But as stated, this is the classic "Three Prisoners Problem" (also, and more popularly, called the "Monte Hall Problem"), well-known to mathematicians (and decidedly counterintuitive to others).
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Richard Osterlind
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This is all well and good, but you are completely forgetting about the fact that I deliberately direct each spectator to choose number 2 and that is the person, besides mine, whose envelope I leave unopened. Since I have stated that it was number 2 that contained the money in the last 7 shows I did that means you have figure what are the odds that I would direct the person towards the right envelope again and what odds are at work that misdirect attention away from the envelope that really contains the $100. The formula for that is X/2e + 72.5w. When you divide all that by the fact that I offer to switch my envelope for theirs and they do that about one time in 46, you arrive at the 50/50 percentile!






JUST SAY THE LINE AND GET THE LAUGH!!!!! Smile

Richard
Chris K
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Yes, Richard's last sentence is key.

For those more interested, this is known as the Monty Hall paradox (http://en.wikipedia.org/wiki/Monty_Hall_problem). It is especially dangerous to those who consider themselves knowledgable about statistics because this is a situation in which everything does not "Start new".

The probability that one of the four passed out objects contains the money is 80% (4/5), all other steps are known as DEPENDENT steps (80% of the time A happens, 20% B happens). This is why statistical problems always stress independence.

I had to do the proof with a statistics professor who didn't believe me once, then he went to his department meeting to make sure I wasn't messing with him. I had less success in an MBA class where the Ops Management professor got... um... personal until I whipped out the peer reviewed papers.

In the end, you get vehement denials of the probability (look at Doug's or Richard's posts), but the denials mean just as much as anything else on the board here, nothing. I absolutely love problems that make experts completely wrong. For the record, here is one that works on 90% of math teachers even though it is a common problem.

You are making a trip that is exactly 60 miles. You drive the first 30 miles at 30 MPH (or KPH). How fast must you drive the last half of the trip to have an average speed of 60 MPH (or KPH)?

I know this strictly belongs in equations section, but I am merely adding to the thread.

Lem
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On the one hand, this thread is really funny. To worry about the exact mathematics when you are talking about doing mentalism or performing magic in general is like worrying about whether you should call an effect, telepathy, clairvoyance or whatever. To most people, you are a mindreader. Some of Koran’s greatest publicity came from “reading Ed Sullivan’s mind” when, in fact, everything he did on the show was a type of prediction.

What counts is if you are entertaining.

But look, if you want to split hairs, even if it is right about the final outcome being 80% to 20%, you are completely overlooking the fact that this is a game of wits between the performer and the spectator and the performer is allowed to say whatever he wants to make the outcome come out right.

Let’s see, I have been doing this routine since about 1978. I don’t know how many thousands of times I have said that line and experimented on just how to deliver it. Sometimes it would get a bigger laugh, sometimes not. Then I would think about it and how to improve it. Now, finally, I think I got it right!

More important than worrying about whether the line about the odds of the game are correct, I worry more about my odds of doing a great show and getting rebooked by the company!

Richard
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John riggs has an excellent little line (which I obviously cannot share) on his last Gods with Feet of Clay dvd...i've pinched that on many occassions...sorry mr. riggs..

I've wondered if the bizarrists ever do a death warrant version? where you get left with the only signed death warrant out of five?

I suppose you could do a cheeky one, and you get left with a tax bill, the rest get a refund...

I love effects where you can easily adapt the premise to suit particular audiences...
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Quote:
On 2008-12-02 15:37, Richard Osterlind wrote:
even if it is right about the final outcome being 80% to 20%, you are completely overlooking the fact that this is a game of wits between the performer and the spectator


But you would have known I would realize that, so I can clearly not choose the envelope closest to you.

;)
Every problem contains the seeds of its own solution. Unfortunately every problem also contains the seeds of an infinite number of non-solutions, so that first part really isn't super helpful.
Mesaboogie
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Quote:
On 2008-12-02 14:51, Richard Osterlind wrote:
This is all well and good, but you are completely forgetting about the fact that I deliberately direct each spectator to choose number 2 and that is the person, besides mine, whose envelope I leave unopened.


It doesn't matter how much you try and direct a spectator to choose enevlope 2, the probablity remains the same.

Richard, I think you are getting a little flustered here. If you reread my initial post you'll notice the main point I was trying to make was NOT about who was right or wrong about the odds, but whether we should be interested in being correct and possibly confusing the audience or forget what odds are right or wrong and just entertain.

As it happens, I completely agree that entertainment is what it's all about, and hence why I've decided not to mention the probablities, right or wrong, at the end point. I'll find another line to get the laugh Smile

I did say it was a pedantic post !! lol !!

Andrew
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Chris K
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Since Mr. Osterlind posted before me and then right after my post, I must assume he is referring to my post, because nothing else had changed on the thread. Here's what I love about the Café:

I very clearly stated the following things (the first two things in my post):

Quote:
Yes, Richard's last sentence is key.

For those more interested, this is known as the Monty Hall paradox


Yet Mr. Osterlind feels this was me worrying. He's wrong and, furthermore, I don't even know why he would think that.

As STATED, I think it's an obscure point. However, I also provided information that was geared exactly towards, and I quote, "For those more interested". Yet, as usual on the Café, Mr. Osterlind feels obligated to defend his excellent but factually incorrect line. Fine, he must have skipped the first two sentences in my post, whatever. This "worry" that he seems attributed to people seems a bit odd too and, for the life of me, I can't figure out where he is coming from, can anybody help me? Never said I was worried, never implied it, agreed with his basic premise, just pointed out that he was factually incorrect (which he is/was).

I hate feeling attacked merely because I am stating facts. I hate even more when people put words in my mouth ("worried").

Finally, I don't even think Richard's line is good, to be honest. Sure, it works for some people but I just don't like it (and it has nothing to do with the factual inaccuracy).

Why is it that 1.) people feel obligated to jump on here when they have incorrect information (Doug and Mr. Osterlind here), then, when it is pointed out that they are completely inaccurate, do they then shift attacks, sometimes going so far as to make things up? I am not singling them out, except that they are the ones who did it here.

I ask because an admin (PM me and I will name names and forward PMs if they deny it) has told me, point blank, that well-reasoned arguments come off as bullying and do not promote the atmosphere the Café is trying to promote. I wonder what that atmosphere is? Say things that are wrong then redirect when people point it out?

I am serious here. I disagree with Osterlind as I don't think this whole thing is funny (although people pretending to be experts and getting it wrong does strike me as personally amusing). It's an issue with the Café as a whole and, as of today, I have a prime example that it is as much the professionals as the amateurs.

Mr. Osterlind, feel free to read any or all of my posts, if you find factual information funny, you'll be rolling out of your chair.

Outta here,
Lem
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Quote:
On 2008-12-02 17:29, Mesaboogie wrote:
Quote:
On 2008-12-02 14:51, Richard Osterlind wrote:
This is all well and good, but you are completely forgetting about the fact that I deliberately direct each spectator to choose number 2 and that is the person, besides mine, whose envelope I leave unopened.


It doesn't matter how much you try and direct a spectator to choose enevlope 2, the probablity remains the same.

Richard, I think you are getting a little flustered here. If you reread my initial post you'll notice the main point I was trying to make was NOT about who was right or wrong about the odds, but whether we should be interested in being correct and possibly confusing the audience or forget what odds are right or wrong and just entertain.

As it happens, I completely agree that entertainment is what it's all about, and hence why I've decided not to mention the probablities, right or wrong, at the end point. I'll find another line to get the laugh Smile

I did say it was a pedantic post !! lol !!

Andrew



Andrew,

No, no, no I am not becoming flusstered here nor am I taking any offense with anything you said. Frankly, I had never even thought of the legitimacy of the line. It's just a line! I was joking about it all in my second post.

What I was trying to point out is that magic doesn't not have to be completely logical or accurate to be effective. Lines like the one I use in my bank nite come and go so quickly no one is analyzing them. They are just having fun.

And finally what I was trying to point out is that often you will do a routine over and over and find little nuances and bits and pieces that fall into place and just work. Often they don't really make sense, but they work. And the bottom line is, if it works, you keep it.

So no, I am not at all flusttered or upset with anything you said.

All my best,
Richard
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Quote:
On 2008-12-02 17:54, Lemniscate wrote:
Since Mr. Osterlind posted before me and then right after my post, I must assume he is referring to my post, because nothing else had changed on the thread. Here's what I love about the Café:

I very clearly stated the following things (the first two things in my post):

Quote:
Yes, Richard's last sentence is key.

For those more interested, this is known as the Monty Hall paradox


Yet Mr. Osterlind feels this was me worrying. He's wrong and, furthermore, I don't even know why he would think that.

As STATED, I think it's an obscure point. However, I also provided information that was geared exactly towards, and I quote, "For those more interested". Yet, as usual on the Café, Mr. Osterlind feels obligated to defend his excellent but factually incorrect line. Fine, he must have skipped the first two sentences in my post, whatever. This "worry" that he seems attributed to people seems a bit odd too and, for the life of me, I can't figure out where he is coming from, can anybody help me? Never said I was worried, never implied it, agreed with his basic premise, just pointed out that he was factually incorrect (which he is/was).

I hate feeling attacked merely because I am stating facts. I hate even more when people put words in my mouth ("worried").

Finally, I don't even think Richard's line is good, to be honest. Sure, it works for some people but I just don't like it (and it has nothing to do with the factual inaccuracy).

Why is it that 1.) people feel obligated to jump on here when they have incorrect information (Doug and Mr. Osterlind here), then, when it is pointed out that they are completely inaccurate, do they then shift attacks, sometimes going so far as to make things up? I am not singling them out, except that they are the ones who did it here.

I ask because an admin (PM me and I will name names and forward PMs if they deny it) has told me, point blank, that well-reasoned arguments come off as bullying and do not promote the atmosphere the Café is trying to promote. I wonder what that atmosphere is? Say things that are wrong then redirect when people point it out?

I am serious here. I disagree with Osterlind as I don't think this whole thing is funny (although people pretending to be experts and getting it wrong does strike me as personally amusing). It's an issue with the Café as a whole and, as of today, I have a prime example that it is as much the professionals as the amateurs.

Mr. Osterlind, feel free to read any or all of my posts, if you find factual information funny, you'll be rolling out of your chair.

Outta here,
Lem


I don't have to say anything to answer your post, Lem. It clearly speaks for itself.
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Is typing "flusttered" a sign that I am flustered???
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