Mathematicians - Remote Viewing experiment odds needed.

[randwill]

Dopers might find this little challenge interesting. A skeptic, Ben Harris, is challenging anyone who claims to be able to ‘remote view’ to identify a target placed in a closed box. The target is a card with a number (0-9) and a letter (A-Z) written on it in one of three colors (red, blue or yellow). A ‘hit’ would consist of the viewer getting all three pieces of information correct. You can read about it here:

REMOTE VIEWING EXPERIMENT

My question for the mathematically inclined here is about the odds. What are the odds of someone getting all three correct with one guess? No need to show your work, but I’m a math dunce, so I’d be impressed.

[Darth_Sensitive]

10 numbers x 3 colors x 26 letters = 780 combos

So a person will be right randomly 1/780 times, or .128% of the time.

EDIT: Order of number and letter counts too. a1 is different from 1a. So multiply combos by 2. 1560 possible choices. Or a .064 % chance of random perfection.
I would divine: vertically stacked, letter on top, color = green, letter = omega, number = pi.

[Kimmy_Gibbler]

@randwill

Dopers might find this little challenge interesting. A skeptic, Ben Harris, is challenging anyone who claims to be able to ‘remote view’ to identify a target placed in a closed box. The target is a card with a number (0-9) and a letter (A-Z) written on it in one of three colors (red, blue or yellow). A ‘hit’ would consist of the viewer getting all three pieces of information correct. You can read about it here:

http://remoteviewingchallengenge.blogspot.com/

My question for the mathematically inclined here is about the odds. What are the odds of someone getting all three correct with one guess? No need to show your work, but I’m a math dunce, so I’d be impressed.

1/780.

There are 780 possible outcomes. Each outcome can be enumerated by [digit][letter][color], which give 10263 outcomes.

[pulykamell]

@Darth_Sensitive

10 numbers x 3 colors x 26 letters = 780 combos

So a person will be right randomly 1/780 times, or .128% of the time.

EDIT: Order of number and letter counts too. a1 is different from 1a. So multiply combos by 2. 1560 possible choices. Or a .064 % chance of random perfection.
I would divine: vertically stacked, letter on top, color = green, letter = omega, number = pi.

The website seems to also say case distinction on the letters is important. So multiply that by 2 again.

[Darth_Sensitive]

I couldn’t decide if it was saying case was important to guess/view, or that uppercase letters on the card would be denoted with an underscore to prevent confusion between an uppercase I and a lowercase l.

[OldGuy]

@Darth_Sensitive

I couldn’t decide if it was saying case was important to guess/view, or that uppercase letters on the card would be denoted with an underscore to prevent confusion between an uppercase I and a lowercase l.

That would imply case was important. Otherwise you could simply say there is an upper case (or lowercase as the case may be) letter.

[pulykamell]

@Darth_Sensitive

I couldn’t decide if it was saying case was important to guess/view, or that uppercase letters on the card would be denoted with an underscore to prevent confusion between an uppercase I and a lowercase l.

Ah. Actually, I think your reading is correct. Although it seems like it could be worded better.

[Darth_Sensitive]

@OldGuy

That would imply case was important. Otherwise you could simply say there is an upper case (or lowercase as the case may be) letter.

It seems to imply it, but isn’t specific that it’s important, like it is with other stuff. I would want it worded better.

[Ponderoid]

The OP said the challenge was open to anyone, and my first thought was that this was going to be way too easy to game, given that it’s all too easy to crowdsource the problem and cover all possible combinations. But the challenge is only to a specific person, and they’re only going to get one shot before a new combination is picked.

The case does indeed matter:

Note: in all cases, the LETTER can be EITHER upper or lower case. The distinction, which is REQUIRED is expressed by UNDERSCORING the LETTER in the instance of UPPER CASE ONLY.

As does the orientation, i.e. whether the number or the letter comes first.

The subject (Silvio) needs to reveal the number and the letter, the orientation (is the letter to the left of the number or the right of the number (ie: 6a or a6) AND THE COLOR of the marking pen used to write both (RED, BLUE or YELLOW).

So I make the probability to be:
1 / ( digits * (lowercases + capitals) * colors * orientations)

or

1 / ( 10 * (26 + 26) * 3 * 2)

=

~ 0.00032
There is some wiggle room in that the underline is only required to be present on a capital letter. If I was taking this challenge, I’d improve my odds a bit by picking a lower case letter and number that can be interpreted either right side up or upside down as a different pair: 1q, or 0n or the like.

[friedo]

@Ponderoid

There is some wiggle room in that the underline is only required to be present on a capital letter. If I was taking this challenge, I’d improve my odds a bit by picking a lower case letter and number that can be interpreted either right side up or upside down as a different pair: 1q, or 0n or the like.

Yeah, the requirements seem needlessly complicated and open to nitpicking. You could design an experiment with similar odds by ignoring case and order, and just adding more symbols (say two letters and a number) and more colors.

Let’s say we have two letters and a number, order unimportant, and five colors (red, green, blue, yellow, black.)

That gives us 26 * 26 * 10 * 5 = 33,800 combinations, with no worrying about case or orientation.

[RedSwinglineOne]

@friedo

Yeah, the requirements seem needlessly complicated and open to nitpicking.

I agree. The cap/non cap and letter/number order choices each only increase the number of possible outcomes by 2, but makes the game more complicated and increases the odds of a ‘partial hit’. The test taker could argue that he can ‘see’ a 6 and a T in the box, but can’t tell the order, or claim that spirits don’t understand capitalization.

[Elendil_s_Heir]

Dr. Venkman, is that you…?