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The Magic Cafe Forum Index » » Magical equations » » Two doors to freedom! (2 Likes) Printer Friendly Version

Andy Moss
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The 'Monty Hall Paradox' is a fine one but perhaps not easily incorporated iinto a solid magical effect since the odds are only 66.66% in our favour after all.

I recently came across 'The two doors to freedom paradox'. This works for us 100% of the time and may be more user friendly for us.

One idea is to use three half walnut shells and three small marbles. Two of the marbles are white and the third is black. The three walnut shells represent three caves in which live two benevolent elves who will feed you and give you shelter and one malicious ogre who will kill you and eat you if he can. The ogre is represented by the black marble and the elves by the white marbles.

The spectator may place the ogre under any one of the three shells and place the remaining white marbles under the other two whilst your back is turned. You state that the elves because they are pure in spirit will always speak the truth to any question that is addressed to them. In contrast the ogre is by nature deceitful and may either lie or answer truthfully as he so chooses in order to best deceive.

Then the fun begins! You may address any one of the caves by pointing at it and the spectator is then obliged to take on the respective role of either the elf or the ogre depending upon the inhabitant/colour of marble that only they know lies hidden within this cave.

You can then address each cave in any order (it does not matter) asking the following question.

"Am I safe to enter this cave?"

You simply have to remember to focus your attention on the two caves that do not contain the unknown inhabitant who is currently addressing you. If you receive a positive answer on the first of these two remaining caves then this cave certainly contains an elf. If you receive a negative answer then switch to the other cave of the two. This will likewise always contain an elf.

This presentation can be presented as if you have a one in three chance of being eaten by the ogre. The specctator will believe this to be logically the case. However you may repeat this endlessly until they are baffled by your perfect luck/intuition!

Enjoy. Andy.
MC Mirak
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Florida by Phill Smith is an interesting take on the hidden 66% odds in our favor kind of approach. Similar to Doug Dyment's Penney's from Heaven, these kinds of approaches benefit from being repeated.

I prefer these mathematical odds types effects more than logic puzzles because, when I've asked people, that is exactly what they think happened, a logic puzzle. The one exception I've found to this is Tequila Hustler (I use the truth-lie follow-up) so maybe it's just me now that I think about it... Smile Smile

Thanks for sharing the above, was just thinking out loud.
Andy Moss
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You're welcome.Yes,the above effect should be presented in such a way that it does not seem like a logic puzzle.

For example we might keep things as simple as possible and dispense completely with the story presentation. Simply phrase the question as "Is the black marble under this shell?" The spectator answers yes or no.

Remember in their mind the spectator will be thinking down the following route of false logic...

1) There is no way that the mentalist can know for certain if I am telling the truth or not when I answer. The mentalist is not psychic.

2) This is logically the case since there is no way that the mentalist saw which shell I put the black marble under.I also got to mix up all the walnut shells as well. Therefore there was utter randomness in the set up.

3) There is certainly a one in three chance that the mentalist is going to fail since there are three shells and one loser marble.

4) Therefore I will try my best to confuse and misled the mentalist when I have the opportunity to do so by changing the tone of my voice or perhaps I will adopt a poker face throughout."

So since the above is true in the spectator's mind it is best to present this as a psychological test whereby you are reading the spectator's body language and listening to their voice for clues.

What I like about this particular three variable effect is that things are kept so pure and simple. The order of the selection of the shells each time can also be made to seem completely random with no methodology discernable.
Pit Boss
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Very interesting. I'm sure it's just me, but I'm not following the 3 questions and how that tips the info to you. Could you elaborate a bit?

Thanks, JD
ddyment
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It's explained in the OP, but not very clearly. Asking the questions is a two-step process: first, you point to one of the shells (this is what directs the participant to either tell the truth or optionally lie (because only the participant knows the nature of the creature hiding beneath that particular shell)); second, you ask the question(s).

If you're still lost, look up a description of the "two doors to freedom" problem. Here is a good one.

Andy has cleverly enhanced the original by (apparently) giving it another layer.
"Calculated Thoughts" now at The Deceptionary :: Elegant, Literate, Contemporary Mentalism ... and More
Andy Moss
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Thank you Doug for offering everyone the link to the paradox. This web page is the relevant one and the one that inspired my own take.
a brown 1968
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Thanks Andy for bring to my attention

When I combine it with the Tequila Hustle principle , I can start with 6 index cards .
One is marked secretly by a spectator and you eliminate the 5 blank ones leaving the marked card as the last one

With 100% accuracy

Andy
Andy Moss
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That is a wonderful idea Andy! The two principles should fuse together perfectly since they both involve the same sort of truth/lie approach to the questioning. Therefore there would certainly be consistancy in the patter and flavour of the presentation from start to end. Body language reading and discernment of voice tone would work well as the red herring for any such presentation.

We might ask the questions in a seemingly random fashion as per the 'Two doors of freedom' methodology until we get down to the two variables in the line that we have not eliminated in our mind and then we might apply Mark's approach to get to the final one. No need to physically eliminate the cards one by one from the row. Just need to remember the positions that can not logically relate to the secretly marked index card as we go along. Then I would (as a red herring) undertake one or two more questions elsewhere in the line afterwards to throw everything completely off the scent. Thus from six cards the target is found with 100% success!

We could of course achieve this by using an alternative methodology such as binary coding for the six variables. We could also have them merely think of any object out of six in the row rather than have them mark the underside of a card but then there is no proof of identity at the end.

If I understand it correctly, I think that your own hybrid approach has the potential to be superior to the use of binary coding. I will have to experiment.
Andy Moss
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O.K I have experimented a little. It seems to me that we might be able to use the 'Two doors to freedom' methodology to get directly from six variables to just the one. In other words we do not need to use the 'Taquila Hustle Principle' at all!

Let us say that whether the spectator follows the role of truth teller or liar is decided by placing a coin upon the respective variable.We then merely point towards any other unknown variable. Once we have made our mental elimination we simply transfer the coin onto another unknown and not yet mentally eliminated variable which then determines the spectator's new stance as either a truth teller or liar.

Once mentally eliminated we ignore the variables and do not place the coin upon them nor point at them. They are out of the game as far as we are concerned.The only exception to this rule relates to when there are just two unknown variables left as will be seen in a minute.

We leave all the cards in the row. Thus we give nothing away to the spectator.

When there are two unknown variables left that they could be thinking of we simply place our coin on any already mentally eliminated card. Remember all the spectator will be seeing is six variables in a row. They will not be aware of our inner mental workings.

Since we already know that the truth/lie stance connected to this eliminated card (the one our coin is now on) will certainly be a truth sayer we now just need to point towards any one of our two remaining unknown cards.The answer will tell us which of these two cards is the card the spectator is thinking of and which is not!

However the spectator will not be aware of this. They will not be aware that any discriminations have been made by you.

Then (and this important) as a red herring we continue on to place the coin on to any other eliminated variable in the lineout and continue for a final time pretending to be reading their body language and listening to their voice even though we aready know what we need to know!

It has not been easy to outline my thoughts in writing. Hope you can make head or tail of it.
a brown 1968
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Hi Andy ,

Your maths brain better than mine . I think I follow what you are saying

With my version - 3 cards are eliminated in round 1 and not reliant on TH or 2 Door

2 Door principle gets us from 3 to 2

TH principle from 2 to 1

I do not want to be asking too many questions

Andy
Andy Moss
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Yes, this is an open thread so we must be careful.

Your own avenue of thought sounds intriguing!

One last thought with respect to my own 'Two doors approach' is that using FOUR variables seems to be the optimum for perfecting disguising the methodology and gives us a streamlined presentation.Four variables is just about adequate for most mentalist presentations.

The principle will certainly work with six variables but then it becomes inherently too long winded and repetitive for my liking.
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