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Topic: New Article on Fitch Cheney's 5 Card Trick
Message: Posted by: Thomas Henry (Apr 23, 2009 09:08PM)
Hi Gang,

I just got the new issue of the _College Mathematics Journal_ today (from the MAA), and it's got a superior article on Fitch Cheney's 5 Card Trick. Besides card magic, I think the method employed in the exposition will have all sorts of possibilities in card mentalism and probably stacked-deck work as well. The mathematics is very accessible. As a plus for students of logic, there's a nice use of reductio ad absurdum to prove one of the results. Here are the bibliographic details:

Hang Chen and Curtis Cooper, "n-Card Tricks," _CMJ_, Volume 40, Number 3, May 2009, pp. 196-201.

Now does anyone have the reference for Fitch Cheney's original write-up of the effect?

Thomas Henry
Message: Posted by: Scott Cram (Apr 23, 2009 10:52PM)
I always thought it would be funny to see this performed by Bob Fitch at a magic convention, with secret help from Earl Cheney.

In the MAA's February 2003 issue of Math Horizons, Colm Mulcahy wrote up a detailed look at the original version. [url=http://www.maa.org/horizons/Fitch-Cheney-Mulcahy.PDF]It's available as a PDF here.[/url] (While this is the original version, it's not the original write-up. The original write-up was in [i]Math Miracles[/i] by W. Wallace Lee.)
Message: Posted by: Philemon Vanderbeck (Apr 23, 2009 11:33PM)
Thank you for posting this, Scott.

I never knew about the variations before.
Message: Posted by: WilburrUK (Apr 24, 2009 09:12AM)
This (for some bizarre reason) gives me an idea for a poker variant where you only get 4 cards. The 5th (imaginary) card of your hand depends on how you arrange these 4 real cards as you lay them down.

Pro's: The deal is quicker by 20%
Con's: The show-down will probably take significantly longer and contain more arguments.
Message: Posted by: Scott Cram (Apr 24, 2009 12:50PM)
4-card versions have been around for some time. Colm Mulcahy, the author of the PDF to which I linked above, covers 4-card variations pretty well in his column [url=http://www.maa.org/columns/colm/cardcolm200502.html][i]Fitch Four Glory[/i][/url].
Message: Posted by: lboudreau (Aug 25, 2009 02:15PM)
While Fitch Cheneyís 5 Card Trick is interesting mathematically (I love playing with it and learning from it), I still prefer using another code. The code isnít as elegant as Fitch Cheneyís, but Iíve used it since the 1980ís with good results. With it, I can identify any other card in the deck with as few as 2 cards. But let me begin with the easier 4 card version.

While my assistant is out of the room, a subject removes any 4 cards from his own deck. The subject selects one and remembers it. He then turns the 4 cards face-down and moves them around to mix them thoroughly. Neither of us knows where the selected card is among the 4 face-down cards on the table. I line them up to form a row and step away. My assistant enters the room, turns the cards face-up and immediately picks out the subjectís card. In fact, she can announce the selected card, both its suit and value, without ever turning them over.

I communicate the name of the selected card to my assistant with two binary codes. The first code communicates the value and the second communicates the suit. Red/ black codes are too confining, so I resort to one-way backs if available. If not, I merely tilt the individual cards in the row slightly to the left or to the right to communicate the value. I arrange the 4 cards to communicate a 4-bit code, more than enough for the 13 card values.

The second code, which communicates the suit, consists simply of the first two spaces between the cards in the row. Are these initial spaces wide/wide, wide/narrow, narrow/wide, or narrow/narrow?

Using a similar multi-layered coding technique, Iíve communicated the identity of a third card with as few as two cards. Two one-way backs supply 2 bits. The tilt of the cards, left or right, supplies another 2 bits. Arranging the cards vertically or horizontally supplies another bit. Finally the wide or narrow spacing between the cards supplies still another bit. Thatís a total of 6 bits, more than enough to code any card in the deck. (Yes, this version takes considerable practice.)
Message: Posted by: vasili (Aug 27, 2009 11:04PM)
I do a version of the five-card trick but my confederate places the three cards face down rather than face up. I've only performed it a few times for friends, but it amazed them each time.
Message: Posted by: glowball (Jan 5, 2010 07:02PM)
FYI - I wrote a computer program using "Just Basic" that does the Fitch Cheney 5 card trick. This way you don't need an assistant to do the trick.

From the spectator's point of view it looks very similar to the Stangr/Mendoz Pokr Machine/TI Calculator trick. Here are the "PROS" and "CONS" between my "Fitch" program and the Pokr Machine (deliberate misspelling here so searches won't find).

The Pokr Machine lets the spectator pick the target card from their random 5 cards whereas my/any Fitch program the magician must pick the target card from their random 5. This is a "PRO" for the Pokr Machine.

Also my Fitch program does not have the special final effect that the Pokr Machine has (another "PRO" for the Pokr Machine, although that would be quite easy for me to program into the Fitch routine).

A "PRO" for the Pokr Machine is that a TI Calculator does not look as suspicious as a laptop/netbook because computers are known to have wireless mice etc (Bluetooth) so some may think there is confederate sneaking the signal into the laptop whereas the TI is more innocent.

My Fitch program does not require any sneaky entries for high 6 vs low 6 nor any sneaky entry for Kings (this has been referenced in other threads). This is a "PRO" for my/any Fitch program.

Other "PROS" for my Fitch program:

It can be run on any MS Windows computer.
It can be backed up and restored from a thumb drive so battery power loss will not hamper your recovery on your laptop/netbook.
It has several different ways of displaying the target card (determined by your radio button selection prior to doing the trick).

Types of "reveals" that you can choose:
Card from a top hat.
Card from a top hat with a hand coming out of hat.
Card from Houdini's coffin (or Nostradamus coffin or any name you pre enter on the coffin).
Card from a black hole.
Card from a time tunnel.
Card from a sun burst.
Card from a crystal ball.
Card from the Wizard of Oz.
Card from Hair E. Pot R (from wand he is holding).

You can pre choose (via radio button) which CHaSeD to use for "tie breakers" ie: CHaSed or SHaCeD or CDHS (Bridge order). I really like SHaCeD because you can visually relate gold balls on the principle part of the suit pip ie: Pretend that Spades has 1 gold ball on its point, Hearts has 2 gold balls (one on the top of each lobe), Cubs has 3 gold balls (one on each lobe), and Diamonds has 4 gold balls (one on each point). This way you can visually determine heirarchy (tie break) instantly in your mind if two or more cards are the same value. For CHaSeD and CDHS you have to think a little more.

My wife and I have performed the Annemann card mind reading for many years so am familiar with the Pokr Machine technique (they are somewhat similar I think).

I later experimented and created a non fancy Fitch routine on my cell phone using MS Excel (MS Win Mobile 6) and even programmed a routine similar to the Pokr Machine using MS Excel on my cell phone (did all development on a desktop computer and then put on a micro SD card from USB port and then inserted into my cell phone) so I can perform either program any time because I always have my cell phone with me.

Posted: Jan 5, 2010 9:07pm
I forgot about another "PRO" for the Pokr Machine - the first one or two effects the 4 entry cards can be face down as the magician picks them up and gives to the spectator to enter (the magician never sees the faces of the 4 entry cards during the first one or two effects). The first 3 effects the magician must know the target card either openly turned face up or by some other method. I have seen the Pokr Machine performed twice (once by Mendoz) and am not totally sure of all the methods but it is excellent. Both the Pokr Machine and Fitch use an ordinary deck of 52 cards. Overall the Pokr Machine is more stunning than the Fitch method, but Fitch is sweet too.

Another thing I forgot to mention is that in my Fitch laptop program you can make the "suit" position rotate so that the first effect the duplicate "suit" card is in position 1, the second effect the "suit" card is in position 2, the third effect the "suit" card is in position 3, etc. thus disguising where the "suit" card falls for those spectators who might notice that the original Fitch routine the duplicate "suit" card was always first.
Message: Posted by: stanalger (Jan 6, 2010 10:02AM)
What is the Stanger Mendoza Poker Machine?
Message: Posted by: glowball (Jan 6, 2010 12:59PM)
It is a TI Calculator that has a special program inside that can be purchased from many magic dealers for $300 to $400 range I think. Al Stanger (mathmatician/magician) wrote the program and John Mendoza markets the device.

See thread below on this formum about the "Poker Machine" for a more complete description:
Message: Posted by: TomasB (Jan 6, 2010 01:11PM)

/Ma Tos
Message: Posted by: glowball (Jan 8, 2010 01:13PM)
I'm a new user and I couldn't figure out why the "giggles" post and then took a close look at the prior user name "stanalger" and that it was from St. Louis and then said to myself "Duh". If you take the "al" out of the above name and place it in front you get "al stanger" and the fact the Al Stanger is a professor at the University of St. Louis I realized that I had been had. LOL!

ThomasB "giggles" may have picked up on that fact before I just now did!

Al, congratulations on the wonderful program you wrote "The Incredible Poker Machine"! I have been wondering that since you are a mathematics professor and magician and so was Fitch Cheney, did you have knowledge of Fitch's trick prior to writing your program? Was it an inspiration for you?

P.S.: To others - check this link below about Fitch Cheney:

Posted: Jan 13, 2010 12:42am
Click on link below to see Fitch trick performed using my Fitch laptop computer program (note: you may have put your computer on full brightness to see it well):
Message: Posted by: memdoctor1952 (Mar 28, 2010 11:29AM)
How does one add the "reveals" that Glowball writes about? I would love for the target card to come out of a top hat.
Message: Posted by: captainsmiffy (Mar 28, 2010 11:47PM)
You can buy the aforementioned machine direct from Mr Mendoza at a considerably reduced price than that mentioned above....I did and am extremely happy with the machine. Wonderful bit of kit.
Message: Posted by: glowball (Mar 29, 2010 07:23PM)
In reply to memdoctor:
I have written two programs to do the Fitch Cheney trick:

1) A program written in "Just Basic" that has a myriad of ways to reveal the target card including a card rising from a top hat.

2) A spreadsheet program written in MS Excel that will run on just about any device that supports spreadsheet entries. I have made this program free to the public and can be easily copied and used (see the thread here on "Fitch on a Spreadsheet"). This spreadsheet program just reveals the target card as a giant "QS" (for example). It is very impressive to the audience.

The first program (the basic program) has many hours of programming and is not yet available to public, but I'll tell you how the top hat presentation was done should you want to try to do it yourself:

Use MS Paint to create an image of a top hat (bit map file) and name it say "tophatbase.bmp" then copy it creating another image of the top hat with just a little bit of a playing card poking up from the top hat and name it "tophatout01.bmp".

Then copy that file creating "tophatout02.bmp" and show about a tenth more of the card coming out. Create about 10 images each showing about a tenth more of the card until you have "tophatout10.bmp" showing a full card. The card image shows the back of a playing card (otherwise you would need to have 10 times 52 images = 520 images just to show each playing card come out!). No thanks, just show the back rising.

Now you need the final display for 52 images (one for each playing card) to show the proper card replacing "tophatout10.bmp" with say "tophatQS.bmp".

How do you present these cards, well you have to write a "Just Basic" program (the program language is free, check the internet) and write a routine to quickly show the "tophatbase.bmp" then "tophatout01.bmp" then "tophatout02.bmp" ... then "tophatout10.bmp" then "tophatQS.bmp".

Another note: when you create these images you have to tediously "paint" each suit pip but once you create it you can copy and paste a pip multiple times on your paint screen so you don't have to reinvent the wheel for the various cards. I recommend you create a "10" card first, then you can erase one pip and change the indicies to create a "9". An "8" card can be used as the base for a "6". A "5" card can be used as the base for a "4". Use this techniqe and the image creation goes faster than you might think. Remember that all these card images must also have the top hat immediately below the card picture.

What about the logic for the 4 entry cards? Well that is another story and would require a much bigger post.
Message: Posted by: memdoctor1952 (Mar 30, 2010 06:54AM)
Thanks to Glowball for the quick response. I will use the Excel program for now.
Message: Posted by: glowball (Mar 30, 2010 06:50PM)
To memdoctor:
When entering the 2nd, 3rd, 4th cards, what do you prefer for your tie-breaker suit sequence (in case 2 or 3 of those cards are the same value)?

Do you prefer CHaSeD, or SHaCeD, or Bridge order (CDHS)?
Message: Posted by: memdoctor1952 (Mar 31, 2010 11:16AM)
I use bridge from 2C to AC, then diamonds, hearts and spades. I also use Aronson.
Message: Posted by: glowball (Mar 31, 2010 01:35PM)
To memdoctor:
For bridge order and (Aces high) you will need to put in:
cell C101: 2C
cell C102: 3C
cell C103: 4C
cell C112: KC
cell C113: AC
cell C114: 2D
cell C115: 3D
cell C152: AS

I do not recommend using Aronson (or any stack) for the 3 cards because its just not necessary and more mental gyrations.

This is the beauty of using a spreadsheet because you can easily customize the way you want to do it!

For the two duplicate suit cards I highly recommend using Aces low in cells A101 thru A152 because the mental math is easier. For example if the two duplicate suit cards are JS and 3S then the JS will be the first card entered and the 3S will be the revealed card and their difference is 5.

Its easier to determine the difference with Aces low because you can say to yourself "how many to get from a Jack to a King, h'mm, that's 2" and then say to yourself "how many more to arrive from zero to 3, duh, 3" so you can say to yourself "2 + 3 is 5" therefore "I need to sequence the three cards as H L M". The point of all this about Aces low in the duplicate suit list is that you can use the revealed card value itself (in this case 3) to add to the 2 (in this example).

Your thoughts?
Message: Posted by: WilburrUK (Mar 31, 2010 05:00PM)

I can't really see (I don't have your spreadsheet, so this is just from the description) how it makes any difference whether you consider Aces low or high, there is still the same distance between a jack and a 3 regardless, and you can count to a king and then add regardless.

If changing these cells in the spreadsheet slightly alters the internal workings, it shouldn't make any difference to what the user needs to think about. Or am I missing something?
Message: Posted by: glowball (Mar 31, 2010 06:54PM)
WilburrUK, you are absolutely correct on all counts. Good catch. I had put my mind in a box so to speak.

The A101 column is for the duplicate suit cards so that means you could start your list with any card of the suit say 5C in A101 then in A102 have 6C and so on wrapping around and ending with 4C in A113. Then A114 starts the next suit etc.

A nice neat starting point does give a good visual reference when first creating your spreadsheet and will help you spot typo errors so it would not make sense to start with the 5C, but if Memdoctor wants to start with the deuce of Clubs in the duplicate suit column (the A101 column) that will work fine, but has no bearing on his tie-breaker scheme. The tie-breaker scheme is determined by the C101 column.

Go to the link below to see the actual program:
You can copy and paste the cells to a fresh spread sheet and try it.

Note to others joining this thread: the C101 column is for the three cards' L M H determination (not for the duplicate suit cards).

Apologies to Memdoctor,
I also got off track (too busy at work is my excuse) about the C101 column.
For Memdoctor's Aces high bridge order I should have said the C101 column has:
C101: 2C
C102: 2D
C103: 2H
C104: 2S
C105: 3C
C106: 3D
C107: 3H
C108: 3S
C109: 4C
and so on until C152: AS (Ace of Spades last in the list).

This way the C101 column functions as a tie-breaker for situation of two or three cards having the same value (for the 2nd, 3rd, 4th cards entered by the spectator).

You could do it by using my erroneous C101 list in my previous post (using deuce thru Ace of Clubs then deuce thru Ace of Diamonds and so on), however that would be quite a departure from the Fitch Cheney mental process of determining L M H of the three cards and using a tie breaker of Bridge order (my erroneous C101 list method there would be no tie-breakers because all Clubs would be lower than all Diamonds, etc.).

Posted: Apr 1, 2010 1:56pm
After sleeping on the subject I'm thinking that the erroneous C101 Bridge order may actually work pretty well mentally for someone who plays Bridge a lot because they are so in tuned to the suit order CDHS and the Aces high within each suit.

Let's try it with 5 cards being: 8D, 7H, 3S, 8C, JS
The 3S will be the revealed card and the JS will be the first card entered (a difference of 5). These duplicate suit cards rely on the A101 list.

The other (three) cards entry order will be: 7H, 8C, 8D (this is H L M using the erroneous Bridge C101 list that I posted).

If using the corrected Bridge tie-breaker C101 list then the sequence would be: 8D, 7H, 8C (this is the H L M using the corrected C101 list).

I played a lot of Bridge 50 years ago as a teenager, but would struggle to use the erroneous C101 list, I'll stick with the corrected C101 list technique.
Message: Posted by: DaddyDoodle (Jul 23, 2010 03:44PM)
On 2010-01-08 14:13, glowball wrote:
P.S.: To others - check this link below about Fitch Cheney:

Your link requires a username and password.
Message: Posted by: John Rogers (Apr 19, 2011 07:00AM)
Reading this thread has inspired me seek somebody to write a javascript for me to do a version of the fitch cheney 5 card trick. I like the 4 card version using a face down face up 6 bit code to signify the 6 possibles. I want the javascript to get its info from a form using radio buttons. Anybody here up to the task? I would gladly pay for the javascript to use on my website woodencigars.com as a fun page for my subscribers.
John Rogers
Message: Posted by: Scott Cram (Apr 19, 2011 03:56PM)
PM'd you.