California Trilogy: City of Angels - On Camera (Game Over)

[Talilan]

ok well I guess I'm fairly deficient at most complex maths, I do think mith wouldn't include an easily breakable puzzle in the game with his maths knowledge. If there's no way to necessarily isolate a very good result reliably, perhaps we could aim for very good

or

good, if that someone assists the searching process (I'm not sure if it does).

- ortolan

[Talilan]

I agree with ort, we don't have to shoot for the moon. A good would be acceptable if we can't guarantee a very good.

So, the problem with Thok's idea is that it depends on all 7 questions AND a no at the first step.

By using the halves strategy, in 4 questions we can get a group of 5 numbers where at least 3 (and possibly more) are good or very good. We could choose the 4 most trusted to ask the questions. Then Q5 could try and get a set with no very goods, if we succeed Q6 and Q7 could give us more info (assuming no liars).

But is this the best we can do?

~Tal

[Talilan]

What about the obvious simple strategy: We each choose 5 numbers and ask whether bad+very bad=0. Even if only one of us gets a yes, we'd be guaranteed at least a neutral. I do not know what the odds are but I think this strategy is worth considering because it doesn't absolutely depend on everyone playing their part honestly.

~Tal

[Talilan]

the scum might have countered that based on the plan we put out earlier and just made all the choices alternate

[Talilan]

When I refer to numbers I'm always talking about random numbers. We can generate our own 5 random numbers between 1 and 75, or get one of the most trusted to generate a randomized order, if we're going the working-together route.

~Tal

[Talilan]

Link removed. See the rules for allowed tags. - Mod

[VP Baltar]

Carrie puts her hand to her ear.

WHAT! I CAN'T HEAR YOU THROUGH THESE DAMN BUNS!

ANYHOW, I DON'T THINK OUR PLAN SHOULD RELY ON PEOPLE NOT LYING BECAUSE THERE IS SURELY SOMEONE HERE WHO FOLLOWS THE DARK SIDE OF THE FORCE.

WHAT ABOUT THIS PLAN?

Carrie picks up a cocktail napkin from a passing waiter, unfolds it and begins to rapidly scribble with a black marker she had craftily concealed in her weird space robe. When she is finished she holds it up for the group to read.

Q1: Have the most trustworthy person select a group of numbers (not sure if they should be random or sequential) so we have decent odds of getting at least one Very Good in there. If the answer is no, repeat with a new set of numbers (though I think that is unlikely).

Q2 (hopefully): Have another trustworthy person ask if five of those numbers contains a Very Good.

Q3-7: If above is yes follow Thok's plan of cycling them out with a single selection from the other five numbers. If answer is no, ask about the other five numbers having a Very Good.

If we manage to get a very good in the first question (I don't know what the odds are, maybe someone could crunch those numbers) I think we should just keep working down from most to least trustworthy with the questions. Odds would be in our favor to find the Very Good before it came to the least trust worthy person getting their question.

I think this is a nice combination of the plans and doesn't necessarily depend on noone being a liar.

[ShadowLurker]

I'm heading out soon so I'm only on here for a short while but Mr. Godwin, could you actually calculate the probability of 6 not being Very Good and there being >1 very goods in the set {1,2,3,4,5}? I can do it later when I come back but I'd like to make progress ASAP as I don't trust the off stage people at all.

Also keep in mind that method only takes up 6 questions, so would we be able to salvage some of the chance with a 7th question?


Also, WHERE IS OUR STUNTMAN?

[VP Baltar]

Happy Birthday, SL!

[Thok]

The obvious 7th question would be "Does {1,2,3,4,5} contain exactly 1 very good?". If it does, then we can choose 6 safely, if not we bite the bullet and pick one of {1,2,3,4,5} randomly, with at least a 2/5 chance of succeeding.

The odds of {1,2,3,4,5} having exactly 1 very good is (I believe) 5(70c14)/(75c15)=5*60*59*58*57*15/75*74*73*72*71=42%. So 100%-42%-32%=26% chance the set contains at least 2 very goods. Roughly 8/10 of that 26% (actually less, but I'm lazy) 6 is less than very good, although we're probably happy with the extra 2/10 when it's good also.

(You can compute the probability of {1,2,3,4,5} having exactly k very goods as (5 C k)(70 C 15-k)/(75 C k). For a given k the probability of 6 not being very good is the obvious (70-[15-k])/70=(55+k)/70. Now sum over all k, if you want. I'm lazy, especially because most of the probabilities will be small.)

[GoofballsAndBaloons]

The probability of a given set of 5 numbers containing at least one "VERY GOOD" is 68.3%.

[GoofballsAndBaloons]

Now suppose that the first player is out of luck, and doesn't have a "VERY GOOD" in his or her set.

The next player has a 71.3% chance of having a "VERY GOOD" in his or her set.

In the extremely unlikely event of 6 consecutive failures to find a "VERY GOOD" then the last player has a 91.9% chance of a "VERY GOOD."

[GoofballsAndBaloons]

I talked to my husband, and there's a way to calculate the likelihood that someone lied.

Any objection to my going last, or to have the last player follow my instructions?

[Talilan]

Sorry if I'm missing something G&B, but once we find a set containing a 'very good', do you have a plan how we narrow down which particular number IN the set to vote for? It's not enough to find a set that has one 'very good' in it, if we have no idea which item is the 'very good'.

~Tal

[VP Baltar]

I know I'm no math whiz, but is there something wrong with the plan I proposed?

[Talilan]

It's a bit over my head, but I'll try and think it through when I get home from work today.
Tal

[GoofballsAndBaloons]

Death, you wrote: "...

but once we find a set containing a 'very good', do you have a plan how we narrow down which particular number IN the set to vote for?

"

Indeed, it's a bit like the game "Mastermind." Have you ever played "Mastermind?" Of course not. You all have video games now. But when I was a wee Tabris, that's all we had. I had a pocket Mastermind and every time I was finished with my school work during class, I'd pull it out and challenge a neighboring student.

However, there is scum here and the scum iza gonna lie. I have one little trick in my pocket to try to catch one scum. It's not guaranteed, but the threat is real, I am not bluffing, and I hope that fear of getting caught will keep them honest.

[hewitt]

Okay sorry I've been away but the plan sounds good to me, whatever, sounds pretty straight-forward to me.

[Talilan]

Carrie said

"Q1: Have the most trustworthy person select a group of numbers (not sure if they should be random or sequential) so we have decent odds of getting at least one Very Good in there. If the answer is no, repeat with a new set of numbers (though I think that is unlikely).

Q2 (hopefully): Have another trustworthy person ask if five of those numbers contains a Very Good.

Q3-7: If above is yes follow Thok's plan of cycling them out with a single selection from the other five numbers. If answer is no, ask about the other five numbers having a Very Good.

If we manage to get a very good in the first question (I don't know what the odds are, maybe someone could crunch those numbers) I think we should just keep working down from most to least trustworthy with the questions. Odds would be in our favor to find the Very Good before it came to the least trust worthy person getting their question.

I think the plan might fall down if you start with a set of (e.g.) 10 that has more than one 'very good' in it and they are distributed so there is at least 1 'very good' in each grouping of 5. I think it means you have to rely on a truthful answer to all 7 questions, and can't easily see who lied if someone does the dirty on us.

~Tal

[Talilan]

Death points a long, bony finger suspiciously at Count De Morcef...

STRAIGHTFORWARD? WHAT ABOUT ALL THIS IS STRAIGHTFORWARD?

[hewitt]

Meaning I don't really see any flaws with the plan and I really don't care. I'm just going to do what everybody wants me to do, report back my answers then wait for the scene to be over.

[ShadowLurker]

Revised plan:

Someone ask the question "Does the set 1,2,3,4,5 contain a Very Good?"

32% chance of no (60C5/75C5) => Thok's plan?
I also realized that if we ask {1,2,3,4,5,6,7,8,9,10}, it'll be more efficient. If we get a No, we can search another 4, then 3, then 2, etc.
If we get a yes, we can use the remaining questions to ask {1,2,3,4,5,6}, {1,2,3,4,5,7}, {1,2,3,4,5,8} etc.

47% chance of yes and there being 1 => If yes, does the set {2,3,4,5,6}, {1,3,4,5,6}, {1,2,4,5,6}, etc. contain a very good?

21% chance of yes and 2 => After two questions further questions, if we receive two Yes, we'll try and find another sent without a Very Good maybe and then use it as a baseline to ask about this set? Worst comes to worst, we have a 40%+ likely-hood of getting one in this scenario, which is the least common one.

---

I'm not understanding your plan Tabris, could you formulate it all into one speech?

[VP Baltar]

Well, Death, I don't think you're quite right. If there were a very good in each set of five, it wouldn't matter. Once the second question clarifies that we have a very good within our set of five (which is why a trustworthy person should ask it), we should be able to quickly single it out with our remaining questions.

As an example, say our second question indicates that the set {1,2,3,4,5} contains at least one very good.

Q3: Does the set {6,2,3,4,5} contain at least one very good?
If the answer here is no, then we already would have a strong indication that 1 is the correct answer. If not we move on to:

Q4: Does the set {1,6,3,4,5} contain at least one very good? etc.

Now, if we get our first to questions correct, we should be able to single out the very good very quickly.

The problem you propose is if there is multiple very goods in our five number set. Yes, that would make us less certain in our final guess, but I suppose we could throw in one question that asks if there are at least two very goods just in case.

I think we might need to use all seven questions to be sure, but I don't think this method is as dependent upon no one lying to be at least somewhat accurate and give us good odds.

[VP Baltar]

SL's plan may work as well, though it does seem dependent upon truth telling all the way around.

I think we should figure out our mode of attack soon though so no one has the chance to lurk near deadline and mess up the plan.

[GoofballsAndBaloons]

A beautiful lady lurking in the shadows said: "

I'm not understanding your plan Tabris, could you formulate it all into one speech

?"

Naturally, as far as elimination of numbers go, what you describe is a no-brainer. But once we have a positive result, we can narrow it down by asking again with a set of partially OVERLAPPING numbers.

That's the easy part. The more complex part is the detection of liars. What my

husband

gay lover patiently explained to me is that

you can actually calculate how many players may have lied

. A-ha. My lover is not just a mathematician, he's a statistician, of the Bayesian persuasion. So he can actually adjust the results with a predicted value of how many players may be lying, for murderously accurate results. There is more, and more deadly, but I don't want to show the scum all my weapons.

Conclusion, if anybody dares lie, I will catch them. There are ways. And the ways are many.