Ugg--these Probability Teasers are rotting my Mind!

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Ugg--these Probability Teasers are rotting my Mind!

Postby bobbo_the_Pragmatist » Thu Nov 12, 2015 11:41 pm

I'm watching a laughably poor police drama with subtitles from Mexico called Epitaflios--really just a soap opera regarding a grisly serial killer. Does have a few good set ups and one liners enough to keep me interested and I enjoy seeing background shots of Mexico City. Shoot on the right day and it looks green and pretty.

So...Episode 8 and a new detective is assigned. She has insight to the criminal mind like Sherlock Holmes and needs to come up with 4000 Pesos to pay for computer work to enhance a video. So, of course, she does this by engaging in a game of underground Russian Roulette with only two people in attendance. The comment is made that she is greatly exceeding the odds by how many times she plays. First round is to put one bullet in the six bullet cylinder, spin it, and shoot. Then the other person can then shoot and the gun goes back to our hero, OR, the second fellow can quit and our Hero earns her $$ to fight crime. Instead after some insult game chatter is exchanged, our Hero says: "Put 4 bullets in the Chamber." blah, blah, blah but the interesting part is the "Moderator" puts 4 bullets in the chamber and shows it to guy No 2. Our hero spins the cylinder and pulls the trigger. Guy No 2 quits the game. High drama for Mexican Tv. Ha, ha.

............but what I'm thinking is that the placement of the bullets in the cylinder is known by Guy No 2. Its either 2 bullets, blank, 2 bullets, blank.....or its 4 bullets and 2 blanks. The odds of blowing you brains out on the first pull are 2 to 1. But on the second shot it depends on which of the two patterns are in the cylinder and Guy No 2 knows what that pattern was. So he knows the odds for him on the second shot are either a certainty or .....darn....its Monty Hall all over again? I know if guy 2 took the challenge that he would either survive or not but if he survived then our Hero would definitely have a bullet set up for herself.

So.....what are the odds for Guy No 2? My gut says not 50/50....so....is it 4 to 1 against? Or what?
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Re: Ugg--these Probability Teasers are rotting my Mind!

Postby OutOfBreath » Fri Nov 13, 2015 12:40 am

4/5 he dies, if bullet placements are truly random. Unlike the monty hall, there is no choice in between here. So from the outset he has 4/6 to die. But, knowing the first person got a blank, and no re-rolling of the barrel, he now know he has 4/5 to die. (That does only increase the chance from 67 to 80 percent though, so motivational logic may be lacking. Or he was hoping as she would take the first shot that she would die and he was gonna fold regardless )

Anywho, by my reckoning and the sequencing of events he has an 80% chance to die after the first is a miss. If the barrell hets rolled again, he'd have 67% chance to die.

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Re: Ugg--these Probability Teasers are rotting my Mind!

Postby bobbo_the_Pragmatist » Fri Nov 13, 2015 1:00 am

Thanks OOB. I don't know....but I think you are right. Just to quibble, there is no randomness in the placement of the bullets. The moderator placed them consciously and anyway there are only two possibilities and Guy No2 knows which one it is. He knows when it is his turn that either there is a bullet in the chamber or there is a likelihood of one. I agree likelihood if that is the situation would be 4 out of 5. I would quit the game....................if I wasn't drugged to begin with to even start playing.
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Re: Ugg--these Probability Teasers are rotting my Mind!

Postby Gord » Fri Nov 13, 2015 8:25 am

How do they play Russian Roulette? Do they spin the chamber each time before pulling the trigger, or only the first time?

If the chamber is only spun once, at the beginning, then Guy #2 knows whether or not there's a possibility of there being a bullet next. He saw the way the bullets were put into the chambers, right?

On the one hand, if the bullets were placed so that there are four bullets in a row, followed by two empty chambers, then when the woman pulls the trigger on an empty chamber (let's assume it isn't a misfired on a bullet!), we know she hit one of the two empty chambers. That means there are only two possible things that have happened: She hit the first empty chamber in the sequence, or she hit the second empty chamber in the sequence. It's 50/50 that Guy #2 will hit the second empty chamber, not 4/5.

Think about it. If she hit an empty chamber, and there are four bullets in a row, then Guy #2 can't hit the second bullet in the row, or the third, or the fourth -- because the woman would have hit the bullet right before any of those three. That eliminates three of the possibilities out of the original six. And Guy #2 can't hit the first empty chamber out of the sequence of two, because that would mean the woman had hit the last bullet in the sequence of four; that eliminates a total of four out of the original six possibilities. There are only two possibilities remaining, and (assuming a purely random spin of the chamber) the two remaining possibilities are equally likely.

On the other hand, if Guy #2 knows the two empty chambers are not in a row, then he knows a bullet is next and he will automatically lose if he keeps playing.
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Re: Ugg--these Probability Teasers are rotting my Mind!

Postby djembeweaver » Fri Nov 13, 2015 9:27 am

Gord is bang on.

I only have one minor quibble with bobbo's assessment of the number of possible configurations. There are 3 possible configurations not 2:

111100

111010

110110

But that doesn't change Gord's analysis since only one has two adjacent blanks.

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Re: Ugg--these Probability Teasers are rotting my Mind!

Postby TJrandom » Fri Nov 13, 2015 9:55 am

I don`t think I would agree to play even if I knew the pattern was 000000.... just creepy, really.

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Re: Ugg--these Probability Teasers are rotting my Mind!

Postby bobbo_the_Pragmatist » Fri Nov 13, 2015 7:21 pm

Gord--they did not spin the cylinder between shots. 50/50 strikes me as correct as well. I think I'm overly spooked by Monty Hall where two choices is NOT 50/50. Evidently, math is not intuitive to me. RATS.

Speaking of not intuitive===dj==HOLLY CRAP. Thank you for the quibble. Cracks me up I can't even visualize the possibilities.

Tj==I agree. My policy is not to play, or even stay, in a room where there is a gun. That just starts the clock ticking.............
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Re: Ugg--these Probability Teasers are rotting my Mind!

Postby Gord » Fri Nov 13, 2015 10:29 pm

I play Dungeons & Dragons; I do probabilities in my head all the time.

For example: In the game this week, I had to "train my dog to do five tricks". I could either train each trick individually, taking one week per trick and having a 75% chance of success each time, or I could train all five tricks at once, taking five weeks and having a 75% chance of success overall. If speed is an issue, it would be best to train all five at once. However, I decided I would give myself ten weeks to accomplish the task. What then would be the chances of success if I tried either option?

Summary: Option #1, two chances to succeed at least once at a 75% chance each try vs. Option #2, ten chances to succeed at least five times as a 75% chance each try.

This one had me messed up for a while; I could tell that Option #2 had a better chance of success, but I couldn't do the maths in my head! :mrgreen: It took me until after I got home and could write it out on paper and look up a few things online before I worked out the actual chance.
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Re: Ugg--these Probability Teasers are rotting my Mind!

Postby bobbo_the_Pragmatist » Fri Nov 13, 2015 11:09 pm

Gord: I see an "inconsistency" in saying "the game this week" when your move could take up to 10 weeks to accomplish? Or do you overlap games in such cases?
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Re: Ugg--these Probability Teasers are rotting my Mind!

Postby Gord » Sat Nov 14, 2015 1:44 am

That's because I'm talking about Dungeons & Dragons, a fantasy role-playing game. There are real weeks, like the ones we measure in real life, and "game weeks" like the ones the characters "live" in the game. My move, for me, only takes a moment to achieve (I simply say, "My character takes ten weeks off to train his dog"), but for my imaginary character it is an expenditure of "game time" and occurs only in the imaginations of the people thinking about what's happening "in the game".

If that still doesn't make sense, think of it as watching a movie. "In the movie I watched this week, James Bond took ten weeks to train his dog." It didn't take me ten weeks, and my watching of the movie didn't affect James Bond training his dog. James Bond and I experienced entirely different measurements of time.
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