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[Neonivek]

The one doesn't go back and forth evenly, it's random. He may answer truthfully to all three questions, or lie on all three.

So... he could end up answering all the questions truthfully or with lies.

And all you know is he is one of the two individuals.

[Darvi]

Because testing through repeated trial is so much more valid than mathematical proof

I still remember the math I needed to disprove the 1 = 2

Which technically isn't math because it breaks the important  rule of not dividing my ze-OH SHIT.

The one doesn't go back and forth evenly, it's random. He may answer truthfully to all three questions, or lie on all three.

So... he could end up answering all the questions truthfully or with lies.

And all you know is he is one of the two individuals.

Three.

[Lectorog]

The one doesn't go back and forth evenly, it's random. He may answer truthfully to all three questions, or lie on all three.

So... he could end up answering all the questions truthfully or with lies.

And all you know is he is one of the two individuals.

Yes. If I interpreted the puzzle correctly. Are you pointing out that I said something incorrect or obvious, or are you making another point?

[GlyphGryph]

Sweet, I think I'm on the verge of solving this.

[Soadreqm]

I think I'm trying to apply probability to decision making rather than actual chances of winning. Either way, it seems to only be making sense in my head.
Trying something else:
If a given individual has a 1/2 probability of staying with a 1/3 chance of winning, and a 1/2 of going to 2/3, what does that make their overall probability? Does this represent the uneducated decision?

I think I see what you're saying. Most people can't handle probability, so they'll be making the choice effectively blind? Heh, maybe. People don't really behave with mathematical randomness, though. I think people generally tend to value things they have higher than things they could have. Like, whatever is behind the door you picked is yours, and if you take the other door, you'd have to let go of it. You're likely to have more of an emotional bond to the door you already chose. And speaking of choosing, people also tend to value their decisions higher than they have any right to. To switch doors, you'd have to admit that you made a wrong choice on round one. And the host is probably trying to trick you into switching. It's HARD to make a decision at random. >:]

As for the second question, the chance of winning is [cases where you win] / [all cases] = ( 1/2 * 1/3 + 1/2 * 2/3 ) / ( ( 1/2 * 1/3 + 1/2 * 2/3 ) + ( 1/2 * 2/3 + 1/2 * 1/3) ) = (1/6) / (1/6 + 1/6) = 1/2. Intuitively enough, if you successfully pick a door completely at random, disregarding previous choices, your chance of getting the "right" one is the same as if you had not made any previous choices.

Because testing through repeated trial is so much more valid than mathematical proof.

It kind of is, you know. Assuming you're actually trying to predict the behaviour of a real system, an empirical test is the only thing that can ultimately show that your model doesn't have any stupid mistakes, with the added bonus of showing any calculation errors. And if you're NOT trying to predict the behaviour of a real system, and the thought experiment is just a pointless logic exercise showing off the completely abstract and meaningless rules of probability with no connection to the real world, using words like "game show", "goat" and "door" is irresponsibly misleading. >:]

[Darvi]

My temporary solution still relies on the random guy being (un)cooperative, but at least it only needs two questions :V

[Neonivek]

My temporary solution still relies on the random guy being (un)cooperative, but at least it only needs two questions :V

Just find a question that is true or false no matter if you lie or tell the truth and make that the individual question.

[GlyphGryph]

First, let's keep 1,2,3 as whatever for this next step, and use TLR to refer to Truthteller, Liar, and Ranom)

Okay, thought about it for a minute. Our first question failed to resolve the "yes/no" situation, as I'd hoped, so let's try a different tact - Now that we know part of the benefit of the initial question, we might be able to squeeze a bit more out of it by making it less trivial. If we ask if person 1 is the random guy (a verifiable piece of information we can use to verify other bits later on), we have 12 possible results:

(We'll call

Code: [Select]

1 is a liar (2 is truthful, 3 is random)
1 2 3 |
a b a | A is tue
a b b |
b a a | B is true
b a b |

1 is a liar (2 is random, 3 is truthful)
1 2 3 |
a a b | A is tue
a b b |
b a a | B is true
b b a |

1 is random (2 is liar, 3 is truthful)
1 2 3 |
a b a | A is tue
b b a |
a a b | B is true
b a b |

1 is random (2 is liar, 3 is truthful)
1 2 3 |
a a b | A is tue
b a b |
a b a | B is true
b b a |

No
Now, we still know that the odd person out is NEVER going to be random - the random guy will always share his answers with one of the other two.

So for out five distinct "results" and potential outcomes for 1,2,3
aab - RTL, RLT, TRL, LRT
abb - TRL, TLR, LTR, LRT
aba - TLR, RLT, LTR, RTL
bab - TLR, RLT, LTR, RTL
bba - RTL, RLT, TRL, LRT

And now, for each of these, we need to figure out which of the possible four configurations is correct... which is the next step. And we have an important additional bit of knowledge linking a or b to true/false no matter which situation we get - if we find the truthteller/liar/random dude, we'll instantly have another identified thanks to this first question (and then we'll be done). But we still need to identify at least one...

But I'm taking a break now.

[Darvi]

Uh, what is the initial question?

E:Oh right okay.

You also forgot about the 1 = trueteller scenarios, but I guess that's okay because I dunno.

[Neonivek]

By the by "If you were the opposite, would you say the sky is blue?"

The one who tells the truth will say no

The one who lies would say no

The one who randomises... wouldn't say anything because he has no opposite and thus the question doesn't apply.

There you go... answer

You now know "No" and you know who is random. You just establish who tells the truth...

Mind you... if someone jumps in and says they all would say no... then it begs another question. Until then I will just say I answered the question in two moves.

[Darvi]

I guess the random guy would just say yes or no, because the opposite would be saying the opposite of what he'd say, which is, well, either no or yes.

[Leafsnail]

The random guy would have to alternate, otherwise he could act in exactly the same way as one of the others by chance (say, telling the truth in response to all three questions) and it would be impossible.  It's just that he starts off on a random truth/non-truth.

[Reelya]

This is actually looking like an easier version of an existing puzzle. In the full version all 3 questions must be to one god exactly. And the random guy is listed as "completely random", not alternating.

[Neonivek]

I guess the random guy would just say yes or no, because the opposite would be saying the opposite of what he'd say, which is, well, either no or yes.

It wouldn't be the opposite of what he would say. He has to be the opposite. There is no opposite of the random guy

The closest would be that instead of random he would be consistant... but in consistancy he would be random and thus there is no answer because he cannot know his answer and thus would remain silent.

The random guy would have to alternate, otherwise he could act in exactly the same way as one of the others by chance (say, telling the truth in response to all three questions) and it would be impossible.  It's just that he starts off on a random truth/non-truth.

That assumes he will alternate within your set. For all you know he will answer the next million questions with truth... but the million + 1 question will be false.

[Leafsnail]

This is actually looking like an easier version of an existing puzzle. In the full version all 3 questions must be to one god exactly. And the random guy is listed as "completely random", not alternating.

Isn't that literally impossible, though?  There's no way to distinguish "A guy who tells the truth" from "A guy who happened to tell the truth 3 times in a row".