Solution to the Gecko problem

[new_trader]

I came to find out if I was right and now I find out the question was bloody wrong...two firing pins...randomly placed bullets...

I know what you're thinking. "Did he fire six shots or only five?" Well, to tell you the truth, in all this excitement I kind of lost track myself. But being as this is a .44 Magnum, the most powerful handgun in the world, and would blow your head clean off, you've got to ask yourself one question: Do I feel lucky? Well, do ya, punk?

 

[Skill Leverage]

revolver, 2 chambers randomly distributed bullets.

you have a 2 in 6 chance of dying.
first pull of the trigger -click. empty chamber.

you have removed an empty chamber from the scenario.

if you pull the trigger again, the chances are 2 out of the remaining 5 chambers contains a bullet.

if you re-spin, you reset the chances, and have a 2 out of 6 again.

in the above scenario:
pulling the trigger again means a 3/5 = 60% survival rate.
re-spinning gives you a 4/6 = 66.67% survival rate.

There are two firing pins in this scenario mate. Why don't people read the bloody initial conditions before answering... do you think I would have given such a long answer if it could have been this simple?

 

[Skill Leverage]

This is the way I figure it:

After the first spin you have a 2/6 chance of dying, also, you don’t know you have to pull the trigger twice, but I assume you are told there are two bullets?
I put the gun to my head and pull trigger- “click” - I don’t die.

Now I’m told I must pull the trigger again!

I would think to myself, - “If I spin the cylinder again then my chances of dying are going to be 2/6. But, because I now know that I’ve just fired an empty chamber, the chances of it being the empty one just before one with a live bullet is only 1/6. I’d be better of just pulling the trigger again.”

Am I dead?

Yes, because you didn't understand that there are TWO firing pins.

 

[Skill Leverage]

I came to find out if I was right and now I find out the question was bloody wrong...two firing pins...randomly placed bullets... [/I]

If you answered a question incorrectly in an exam because you hadn't read it properly, would you just tell the examiner their question was wrong? Interesting tactic.

 

[MrGecko]

In a multiple Firing Pin or un-adjacent bullet scenario, the odds of survival by firing again and re-spinning are equal. The only way one can create a probability advantage is if the Bullets are adjacent and there is 1 firing pin.

Why?

Because, after a "click" in the adjacent bullet, One firing pin scenario, you know for certain that there is only one bullet that can kill you... and this is where the advantage comes from. In all other circumstances, this is not the case.

 

[Skill Leverage]

Finally, someone who gives an answer, gives it the smug 'Why?', and actually gets something right

 

[MrGecko]

Ha! You should meet my Parents... for many many years they struggled to find the solution to the Gecko problem!

 

[Skill Leverage]

If you're asking, I'm dancing.

 

[MrGecko]

revolver, 2 chambers randomly distributed bullets.

you have a 2 in 6 chance of dying.
first pull of the trigger -click. empty chamber.

you have removed an empty chamber from the scenario.

if you pull the trigger again, the chances are 2 out of the remaining 5 chambers contains a bullet.

if you re-spin, you reset the chances, and have a 2 out of 6 again.

in the above scenario:
pulling the trigger again means a 3/5 = 60% survival rate.
re-spinning gives you a 4/6 = 66.67% survival rate.

No.

After the 1st "click", the bullets are not re-distributed in the chambers over the remaining 5 spaces - the arrangement of the bullets is defined before the 1st firing.

So, after one "click", what are the chances of you firing again and being dead? Its the probability that the empty chamber you just fired was immediately before one with a Bullet. There are two of these chambers, so you are dead if the original spin landed on one of these two, probability = 1/3.

If you choose to spin again, you are dead if you land on a bullet, probability = 1/3.

The confusion arises because the bullets are not re-distributed after the first "click".

 

[Skill Leverage]

After the 1st "click", the bullets are not re-distributed in the chambers over the remaining 5 spaces - the arrangement of the bullets is defined before the 1st firing

Someone else is having this very problem on the other thread... plus there are TWO FIRING F(!*#ING PINS HERE!

 

[new_trader]

Yes, because you didn't understand that there are TWO firing pins.

UP YOURS

http://www.trade2win.com/boards/660678-post1.html

You are handed a revolver, with two bullets placed in adjacent chambers in the 6-chamber cylinder. The cylinder is spun to a random position and the loaded gun is handed to you. You put the barrel to your head and pull the trigger - an empty click.

Now, you are told that you must pull the trigger one more time. Do you re-spin the cylinder, or just pull the trigger again?

The word TWO only appears before bullets...OK?

 

[Skill Leverage]

Why are you linking to a COMPLETELY different thread, for a COMPLETELY DIFFERENT problem? Why not put your thoughts on THAT THREAD in THAT THREAD like everyone else, you f***ing anagram of TRADER.

 

[Skill Leverage]

I have serious doubts about the human gene pool after this weekend.

 

[trendie]

There are two firing pins in this scenario mate. Why don't people read the bloody initial conditions before answering... do you think I would have given such a long answer if it could have been this simple?

I read it. I just couldnt visualise 2 firing pins. My bad.
I guess I am a retard after all.

So, 6 chambers, 2 consec bullets, 2 randomly distributed firing pins.

I will have another go. (even though you have put forwrard an answer)

 

[new_trader]

Why are you linking to a COMPLETELY different thread, for a COMPLETELY DIFFERENT problem? Why not put your thoughts on THAT THREAD in THAT THREAD like everyone else, you f***ing anagram of TRADER.

Yes, good point!

 

[Skill Leverage]

Apologies to both of you for being overly abrasive, I realise it's much easier to understand a question when you're the one of the people asking it.

Trendie I'd be interested to see your thoughts, I'm pretty sure my answer is solid, but the nature of these things is that you make one small oversight and the whole house of cards comes down.

SL

 

[trendie]

You have a 6-chamber revolver with multiple firing pins, containing 2 bullets in adjacent chambers. You put the gun to your head, pull the trigger once and get a click. If you are forced to pull the trigger again, should you re-spin the cylinder, or just fire again?


OK. assume chambers 1 and 2 contain the consec bullets.

Possible distribution of firing pins.
Consecutive pins. (x,x+1)
First pull of trigger - click. (firing pins were NOT 6 and 1, 1 and 2, or 2 and 3)
Firing pins were:
3 and 4
4 and 5
5 and 6.
On next pull,
3 and 4 becomes 4 and 5. (click)
4 and 5 becomes 5 and 6 (click)
5 and 6 becomes 6 and 1 (Bang)
Survival rate = 66.67% (when firing pins consecutive)=
EDIT: given that the opening options were a 50/50 chance of killing yourself, you are better off taking the next pull rather than a re-spin.

Pins with one space between them: ie, (x, x + 2)
Possible options: ( 1 and 2 have bullets)
1 and 3, = bang
2 and 4, = bang
3 and 5, = click
4 and 6, = click
5 and 1, = bang
6 and 2. = bang
Only (2 and 4) and (4 and 6) are viable first pull options. Since you survived, these are only valid options.

(2 and 4), leads to (3 and 5) and click.
(4 and 6), leads to (5 and 1) and bang,
Survival rate = 50%. (when firing pins 1 gap apart)
EDIT: default possibility is 2/6 of surviving with a re-spin, so taking the pull again is the best option.

Final option: with 2 spaces between them (x, x+3).
Firing pins were:
1 and 4 (bang)
2 and 5 (bang)
3 and 6 (click)
4 and 1 (bang)
5 and 2 (bang)
6 and 3. (click)
Since the first pull resulted in a click:
3 and 6 goes to (4 and 1) bang
6 and 3 goes to (1 and 4) bang
Unless I am very much mistaken, you get killed 100% of the time if the firing pins are 2 gaps apart!!
EDIT: the default chances are 2/6 of survival, so you would be better off taking the re-spin.

Unfortunately, I cant find an algebraic format for these, Since the numbers are manageable, its possible to go thru them manually.

 

[Skill Leverage]

Just glanced at this but it looks good to me; I went a little further using combination theory to determine your best course of action should you not know any of initial conditions, you're just handed the gun. Mine was a lot more long-winded too, because I fancy myself a bit.

Nice work

 

[Skill Leverage]

Think you may have pulled up a small flaw in my solution as well, which as I said means the whole lot goes to ****... I've got my numbers slightly wrong in the 'adjacent pins' section havent I... time to make an adjustment!

 

[Skill Leverage]

My analysis has been updated (thanks Trendie); there is now a distinct edge for pulling the trigger again.

Thank God people are actually checking this stuff, otherwise some poor soul could have read this and then blown his brains out based on poor advice.