Astor Mental by Astor from AstorMagic is a great effect - 5 ESP cards are displayed, numbered 1 to 5 - 5 more ESP cards are used - the cards are mixed and the 5 cards are, with backs to audience, and as determined by audience member(s), inserted into the numbered (1 to 5) slots - once the board is turned around they match the order in which the first 5 cards have been displayed.

Now my question: what are the odds of this happening in real life ? ( You could then mention this number to your audience as you put the cards back in)

In other words would I be correct in assuming that the chances (odds) of placing one of the five cards in it's correct corresponding position would be one in five or expressed as a percentage as 20%?

What are the chances and percentages for cards 2,3,4, and 5 all subsequently being placed in the correct order?

Thank you!

1/5 for the first one, 1/4 for the second, 1/3 for the third and then 1/2 for the remaining two, so the total chance for all to be right is 1/120. (these probabilities assume the previous ones were right)
I think that what you asked was that ASSUMING the first is right, what are the chances the remaining four will be right, that's easy enough, 1/36

(Can someone check my working? Haven't been to school for a long time)
Phill

You're exactly righ, Phillsmiff.

Phew! Mr Cooper would be proud.

Phill

It's a bit more complicated.

p of exactly 5 correct = 1/120
p of exactly 4 correct = 0 (if 4 are correct, the fifth must also be correct)
p of exactly 3 correct = 10/120
p of exactly 2 correct = 20/120
p of exactly 1 correct = 45/120
p of exactly 0 correct = 44/120

Certain other outcomes can be calculated from these. E.g., probability of at least three correct = (10+0+1)/120 = 11/120

Mike

Thank you Gentlemen!

One could not assume that the first one is right, which would make the probabilities surely much much higher to get all 5 correct.

5 ESP cards, lets call them a,b,c,d,e which are mixed and not seen - what are the chances of these arbitrarily matching 5 ESP cards (visible and laid in a row 1 to 5? (a being 1, and e being 5)

The probability for this situation is 1/120 as previously indicated. The probabilities for 0,1,2,3, and 4 correct are also as given in my post above.

Mike

The probability of at least one correct match is 1 - 1/2! + 1/3! - 1/4! + 1/5! = 76/120 which is almost 2 out of 3. So usually you will have the opportunity to (inadvertently?!) expose the face of one or two of the cards in the process of placing them in the slots the spectator chooses.

Wow, I just say man you got all five. I'm not good at math but That's amazing. It's astronomically almost impossible.

You should have yourself checked out by a physicist.

Really that's awesome.

I'm totally with John! Actually, I would just say, "the odds of getting each of them matched, on top of the odds of them matching in perfect order, is like, thousands to one... it'll never happen!!" No one gets math, none will question it...

And as a math teacher sitting in the audience, I would stand up and loudly correct the misinformed performer.

Math illiteracy should never be condoned or propagated.

To each his own... but I have to say it pains me to know that you would openly heckle a fellow performer just because math is your field...

So much of what we do is based on untruths or half-truths used to enhance performance. Perhaps scientists in the audience should loudly decry any mentalist who uses the term "test conditions." Physicists should stand up and heckle the metal benders or any performer who uses "quantum physics" in their pseudo explanation.



(clarification--I only disagree with your last statement, Philemon... I still love and respect you!!)

Seth

I completely agree.

It's possible to weave a story of fiction, and yet keep the essential facts correct.

Considering that most mental effects have probabilities of success of 1 out of 5 or 6, then an effect in which the odds of matching all five is 1 out of 120 is substantially more impressive (perhaps too much so). The fact that most people misunderstand probabilities is already enough to impress with the proper presentation of even a 1 out of 2 effect (e.g., which hand contains the coin).

As Ambrose Bierce once said, "Lottery: A tax on people who are bad at math."

I find it fascinating that there are those who will go out of their way to expose a "fraudulent psychic" who is just using cold reading with Tarot cards at a coffee shop for $20, and yet will knowingly propagate false scientific, mathematical, or psychological properties in pursuit of entertainment.

We can deceive while still educating and making things better.