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.

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...

Thanks for sharing the above, was just thinking out loud.

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.

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

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.

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.

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

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.

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.

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

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.

I have been doing some further thinking.

Three variables. Let's use the numbers 2, 3 and 4 written on cards as a way of a simple example although we could use any three objects that offer us a dualistic way of distinguishing them (such as two metalic and one plastic object hidden under pots).

The number cards start out face up at the start in 2,3,4 left to right order. We then turn our backs. The spectator is then asked to swap any two variables around "so as to mix up the order of the numbers to make then random". They are then asked to make a SECOND swap "for good measure".

Although we cannot now know the exact order of the three variables we DO know the following is true. The CYCLICAL order moving towards the right from the variable 2 of the three variables will remain unaltered.(i.e 2 to 3 to 4). We will make use of this knowledge later on in this presentation.

We will always mark the speaker by way of asking the spectator to place a coin upon the relevant card. We verbally advise as to the target for the question e.g. "The question is directed to the middle variable". Thus no confusion. This methodology will also allow us to be blindfolded or to turn our backs if we so wish to do so.

The instruction for the spectator is that they must tell the truth with respect to the two even numbers but may either answer truthfully or lie with respect to the odd number.
Now we simply undertake the basic methodology for the 'two doors to freedom' (there is a website link in this thread as kindly offered to us by Doug for clarity).

At the end of this after our ONE question "Is this number odd?" we will of course be in the position where we now know which of the variables are odd and which two variables are even within the three variable line up.

But what if we also wanted to ascertain the EXACT IDENTITY of the three variables?. Well that can be achieved with a second simple question. Simply move the coin to any one of the two now known EVEN numbers (2 or 4).

We can then ask the spectator to once again answer appropriately depending upon the nature of the number.Of course we know that since this speaker number is even that their answer will always be the truth as we now direct this second question at the ODD number! The nature of our second question is...

"Is this number smaller than the number with the coin on it"

If the answer is yes than we know that the variable that has the coin under it MUST be 4.

If the answer is no then we know that the variable that has the coin under it MUST be 2.

Since we know that the cyclical order of the data runs from 2 to 3 to 4 it is then simple logic to determine the EXACT POSITIONS AND IDENTITIES of all three variables and we can do this with our back still turned away!

So in summary (and for clarification).

To gain information as to a definite 'door to freedom' just the one questioner/target required.

To gain information as to the locations of the false door and the two true doors two questioners/targets are required.

To gain information as to both the locations of the false and the true AND the complete identities of all the data then the third question/target is required.

I hope this summary helps. It is not easy to explain in words.

O.k. Let us now build upon the above a little. Here are a few more thoughts. Rather than the rather abstract numbers 2,3,4 let us use tangible objects for our examples.

Large white feather, D+D metallic figurine of a goblin, white angel shaped candle.

The goblin is naturally the liar who may either lie or speak the truth at will. The two white objects objects "The feather of truth and the angel of justice" will naturally only speak the truth.(Note that this presentation is meant to be a quirky one! Choose your own objects and line of presentation)

Now a feather obviously weighs less than the metallic figurine which in turn obviously weighs less than the candle. The feather and the candle are obviously non metallic.The figurine is obviously metallic.

The objects may be randomly placed under large coffee cups whilst our back is turned.

After our first directly question/target "Is this object metallic" we are in the position to venture a 'guess' as to the fact that one of the three objects "might be" non metalic. This is a vague but suspense building pre reveal.

After our second question/target "Is this object metallic" we ought to affect confusion if there is a seeming contradiction in the information that we are receiving.It further raises interest in what we are trying to achieve.

For our third question we may use as the questioner any now known non metalic object and direct our question to the other now known non metalic object."Is this object heavier than this one". We know for certain that the answer will be true. We will therefore be able to distinguish between feather and candle.

We are now in the position to divine the position and the identity of all three hidden objects.

Depending upon our own chosen presentation we do not have to travel all the way down the avenue of presentation with respect to the questions. So for example if we wanted a presentation based upon Treasure Island and "the dreaded curse of the black Spot" then only one or two questions at most would be required.

I have enjoyed learning the questioning technique for two doors to freedom. Thanks to ddyment for the link to the explanation.

If three cards are used instead of shells and marbles (say two black and one red), an easy extension after using the questioning technique would be to use cards from a one way deck to then be able to find the troll/ogre without asking questions in order to mislead those who are correctly seeing it as a logic puzzle. It would take a bit of audience management to keep the cards properly aligned.