Posted: 3/21/2002 11:12:45 AM EDT
Since you fellows are pretty smart and good at math, I want to pose
the following question? Who is right?
Here is the scenario:
You are forced into playing a game of Russian Roulette. You are presented
with two options.
Option #1 allows you to load 1 round into the wheel of a sixshooter. You
must spin the wheel in regular RR fashion, and pull the trigger against your
own head. You must repeat this operation six times in order to win.
Option #2 allows you to load 5 rounds into the wheel, but you only have to
spin the wheel and pull the trigger once to win.
Which option would provide you the greater chance of Winning?
Our Marketing teacher told us that most people would choose Option #1
because it "seems" safer. He says that people are more likely to choose the
option with seemingly less risk. This is true, but he said however, that
choosing Option #2 would give you the best chance of survival because of the
actual probabilities.
Here is where I disagreed. I maintain that you have a greater chance of
survival by choosing Option #1.
His reasoning is that on Option #1 you have a 1 in 6 chance of being killed.
This seems great, but if you take this chance 6 times, you have a 1/6 + 1/6
+ 1/6 + 1/6 + 1/6 + 1/6 = 6/6 chance, or a virtual certainty of being
killed. You are better off by taking a 1 time 5/6 chance of being killed
than a 6 times 1/6 chance. His chance of living to see another day is 16.7%
My argument is that you have a decent chance of living through all six
trigger pulls. Therfore the odds cannot be anywhere close to 6/6 or 100%
certain. This means that the professor has incorrectly figured his odds on
Option #1.
My arguement is that you are dependent upon a string of outcomes in order to
survive. Each event has an equal probability of occuring each time, but the
chances of stringing together desirable outcomes shrinks with each trigger
pull.
For illustration purposes I will use a coin. Heads, you lose, Tails, you
win. Game: You have to flip 3 tails in a row to win. Question: What are
your odds of winning? Well, the first flip yields you a 1/2 chance of
remaining in the game. Remember that if you ever flip a heads, you will
immediately lose. The second flip, while still giving you a 1/2 chance of
staying in the game, gives you a 50% chance on a 50% chance. The third flip
adds another 50% chance to the equation. We can now calculate our odds of
winning three tails in a row to be 1/2 * 1/2 * 1/2 = 1/8. We have a 12.5%
chance of winning this game.
This is the same formula that can be applied to Option #1 in Russian
Roulette. Each time you pull the trigger you have a 5/6 chance of advancing
to the next trigger pull. If we must perform this operation 6 times, we
have 5/6 * 5/6 * 5/6 * 5/6 * 5/6 * 5/6 = 15625/46656, or about 33.5% chance
of surviving the game. Each time you pull the trigger in this scenario, you
decrease your chances of moving on to the next round. After many many
trigger pulls, say 50, your survivability rate is .011%.
What I am asking you to do is give me your input on who is correct:
The (Marketing) Professor: Option #1 = 6/6 chance vs. Option #2 = 5/6 chance
of being killed.
The (Mediocre) Student: Option #1 = 33.5% chance vs. Option #2 = 16.7%
chance of survival.
Thanks for your input.


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The (mediocre) student is correct. This must be a public school teacher. I am no mathematician, but it is obvious the effect of six 1/6 chances following one another is NOT cumulative. You have a 1/6 chance of death EACH TIME. Subsequent trigger pulls stand alone each time. Please tell him I said he is a dumbass.



I will tell him thanks!
He is a Professor at Bradley University. You are probably familiar with it (being from IL).
I am taking PostGraduate classes there because my employer requires continuing education. They pay, so I don't complain.


Please consider the paper industry before not printing this message.

I just picked up on the whole key to the problem: He's a [b][i]marketing[/i][/b] professor. I've never yet met anyone in marketing with the slightest link to reality.
BTW, you're precisely correct in your calculations. He hasn't a clue.



Being a nonpro mathematician, you always have a 1/6 chance with the one bullet.
Your proffesor is an idiot.



Originally Posted By Torf:
Since you fellows are pretty smart and good at math, I want to pose
the following question? Who is right?
Here is the scenario:
You are forced into playing a game of Russian Roulette. View Quote 


Option 1 poses less risk because of the physics and properly done the math does reflect this. The type of simplified probability analysis that your teacher is applying is not correct (not withstanding the fact that his math is wrong) .
I would go with option 1.
Fis_Prod
edited to say: You math is correct by the way. however remember that the physics makes it such that the probability on any given chamber has to be weighted.



Hmmm... Could a lack of analytical skills be why your professor wound up marketing? [:D]
The probability of shooting yourself in option #1 is 6/6 [b]only[/b] if the cylinder isn't spun after each pull of the trigger. Otherwise, as you calculated, the pulls are independent events and the probability of survival is indeed (5/6)^6.
If Professor Badmath is too stubborn to admit his mistake, ask him to put his money where his mouth is and play a little game of dice with you:
He gets one (cubic) die and you get six. In each round of the game, each player antes $5 and then both players roll their dice simultaneously.
If he rolls a six (analogous to dropping the hammer on the one unloaded chamber in Russian Roulette), he "survives".
If you roll anything but a one on all six of your dice (analogous to [b]not[/b] dropping the hammer on the one loaded chamber in six rounds of Russian Roulette), you "survive".
If both players "survive", the money stays in the pot and you play another round.
If neither player "survives", the money stays in the pot and you play another round.
If one player "survives" and the other doesn't, the "survivor" gets all the money in the pot.
Tell him that you want to play for ten rounds, with any money left in the pot after the tenth round to be split evenly between the players. Of course, if he insists at that point that you're only winning because you're on a lucky streak, by all means, indulge the poor man and play another ten rounds. [;)]



Originally Posted By Torf:
He is a Professor at Bradley University. You are probably familiar with it (being from IL).
View Quote 


Originally Posted By garandman:
Well, a sixshooter has a 1 in 6 chance of ruining your day, so I'd ask for one of them semiauto Tec9 junk guns, which has a 1 in 3 chance of jamming or misfiring.
[;D] [BD]
View Quote
snip
I like one chance in 6, no matter HOW many times I gotta do it.
View Quote
The "one in 6" for six times can't be added the way you did it becasue theres the possibility if the round is in chamber 1, you could land on chamber 2 all six times, or chamber 3 all six times. (Or chamber 4 or 5 or 6 all six times.)
View Quote
Or if you can add up probabilities that way, Look at it another way, each time you do option 1 you have a 5 in 6 chance of NOT being killed. Do that six times, and you end up with 30 chances out of 36 that your blue suade shoes will walk away with no grey matter on them.
I like 30 chances in 36 of being okay better than I like 5 chances outta six of seeing Kurt Kobain.
(But then, I didn;t care for him when he was alive, either)
[}:D]
View Quote 

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Your teacher is an idiot. You are absolutely right. Tell that idiot to take a ststistics course before he says something stupid like that.



Originally Posted By thebeekeeper1:
Fis_Prod, you are damned eloquent and diplomatic in the way you called the idiot an idiot. LOL [:D] View Quote 


One small point that I may have missed...
In the one hot game, is the cylinder spun BETWEEN each pull of the trigger, or are the six clicks one after another directly? Click, Click, BOOM!
If you spin after each trial, I will take option #1. If you have to pull six times in a row, I will take #2. 16.666...% chance is better than 0%...
FFZ



Originally Posted By Renamed:
Hmmm... Could a lack of analytical skills be why your professor wound up marketing? [:D]
The probability of shooting yourself in option #1 is 6/6 [b]only[/b] if the cylinder isn't spun after each pull of the trigger. Otherwise, as you calculated, the pulls are independent events and the probability of survival is indeed (5/6)^6.
If Professor Badmath is too stubborn to admit his mistake, ask him to put his money where his mouth is and play a little game of dice with you:
He gets one (cubic) die and you get six. In each round of the game, each player antes $5 and then both players roll their dice simultaneously.
If he rolls a six (analogous to dropping the hammer on the one unloaded chamber in Russian Roulette), he "survives".
If you roll anything but a one on all six of your dice (analogous to [b]not[/b] dropping the hammer on the one loaded chamber in six rounds of Russian Roulette), you "survive".
If both players "survive", the money stays in the pot and you play another round.
If neither player "survives", the money stays in the pot and you play another round.
If one player "survives" and the other doesn't, the "survivor" gets all the money in the pot.
Tell him that you want to play for ten rounds, with any money left in the pot after the tenth round to be split evenly between the players. Of course, if he insists at that point that you're only winning because you're on a lucky streak, by all means, indulge the poor man and play another ten rounds. [;)]
View Quote 


Hey, here's a math problem for you:
Rosie O'Donuts weighs 475 pounds and her lesbian lover weighs 355 pounds.
Since their mattress can only support 700 pounds of blubbery, cellulite fat at any one time, they do their strapon slogging of each other's fat lesbo asses out on the living room floor every night.
When Rosie is on top she generates between 12001600psi of pressure while ramming her squealing pigfriend below.
Now, given the above information, what is the best caliber bullet to use to ensure an 99% probability of hitting both of those pigs with a single lethal shot?


I am not the means to any end others may wish to accomplish. I am not a tool for their use. I do not surrender my treasures to be flung to the winds as alms for the poor.
~ From "Anthem" 
Originally Posted By Torf:
Ha ha!
Wasn't there a Darwin award about someone who tried to play Russian Roulette with a Semiauto?
View Quote 


Originally Posted By The_Macallan:
Hey, here's a math problem for you:
Rosie O'Donuts weighs 475 pounds and her lesbian lover weighs 355 pounds.
Since their mattress can only support 700 pounds of blubbery, cellulite fat at any one time, they do their strapon slogging of each other's fat lesbo asses out on the living room floor every night.
When Rosie is on top she generates between 12001600psi of pressure while ramming her squealing pigfriend below.
Now, given the above information, what is the best caliber bullet to use to ensure an 99% probability of hitting both of those pigs with a single lethal shot?
View Quote 

Please consider the paper industry before not printing this message.

Ask the professor to prove it to you by using the gun with the 5 full cylinders. No big loss if he looses.
BTW, being a marketing guy AND a professor is two strikes. Marketing guys have only the slightest idea of reality & professors have none.


I am the last conservative.

Play the Deerslayer game with Rosie and her Big Piggie.



To calculate the correct chance of losing you must add the probability of losing each round together. The probability of each round is calculated by multiplying the chance of losing this round by the chance of making it this far.
The correct formula for chance of losing:
1*1/6 + 5/6*1/6 + (5/6)^1*1/6 + (5/6)^2*1/6 + (5/6)^3*1/6 + (5/6)^4*1/6 + (5/6)^5*1/6 = 0.665
Adding my result to your previous result equals 1, confirming the formula is correct:
0.665 + 0.335 = 1
Try asking one of the math professors there to have a "talk" with your marketing professor.



Originally Posted By The_Macallan:
Hey, here's a math problem for you:
Rosie O'Donuts weighs 475 pounds and her lesbian lover weighs 355 pounds.
Since their mattress can only support 700 pounds of blubbery, cellulite fat at any one time, they do their strapon slogging of each other's fat lesbo asses out on the living room floor every night.
When Rosie is on top she generates between 12001600psi of pressure while ramming her squealing pigfriend below.
Now, given the above information, what is the best caliber bullet to use to ensure an 99% probability of hitting both of those pigs with a single lethal shot?
View Quote 


Originally Posted By Torf:
Originally Posted By The_Macallan:
Hey, here's a math problem for you:
Rosie O'Donuts weighs 475 pounds and her lesbian lover weighs 355 pounds.
Since their mattress can only support 700 pounds of blubbery, cellulite fat at any one time, they do their strapon slogging of each other's fat lesbo asses out on the living room floor every night.
When Rosie is on top she generates between 12001600psi of pressure while ramming her squealing pigfriend below.
Now, given the above information, what is the best caliber bullet to use to ensure an 99% probability of hitting both of those pigs with a single lethal shot?
View Quote View Quote 


Originally Posted By NOVA5:
do you really think thats enough? for a clean sure kill i would use a 30mm twin cannon from a us fighter plane. strafeing run. saw them in half. View Quote 

I am not the means to any end others may wish to accomplish. I am not a tool for their use. I do not surrender my treasures to be flung to the winds as alms for the poor.
~ From "Anthem" 
Sorry sir! That was all that was available at the time! It wouldn't stop..... Ahhhhhhh!
[scarred for life]


Please consider the paper industry before not printing this message.

" There are lies, damn lies, and statistics."
Proving yet again that any idiot can make a point with bad math.[:D]
You sir are correct in your assumptions  I hope that professor isn't tenured!



First of all How old is this Professor?
Second I guess he doesn't shoot guns, or he would not use that has an example.
Third if he wants to try make sure he ties a bandana around his head. It helps a little from what I remember.
Things I try to forget always popup no matter how many years have passed.



Option #1 allows you to load 1 round into the wheel of a sixshooter. You
must spin the wheel in regular RR fashion, and pull the trigger against your
own head. [red]You must repeat this operation six times in order to win. [/red] View Quote 


Originally Posted By edpmedic:
First of all How old is this Professor?
View Quote
Second I guess he doesn't shoot guns, or he would not use that has an example.
View Quote
Third if he wants to try make sure he ties a bandana around his head. It helps a little from what I remember.
View Quote 

Please consider the paper industry before not printing this message.

Originally Posted By riddler:
Option #1 allows you to load 1 round into the wheel of a sixshooter. You
must spin the wheel in regular RR fashion, and pull the trigger against your
own head. [red]You must repeat this operation six times in order to win. [/red] View Quote View Quote 

Please consider the paper industry before not printing this message.

Your professor is obviously wrong. In reality with a 1/6 chance of dieing  six times  you have a 6/36 chance of dieing which equals 1/6.



OOoooooooppps! I missed that. [:D][:D][:D]



Hey, Torf
I have an idea. When this thread plays out, how about printing it and presenting it to him? You may get "extra credit!" LOL I'll bet he would stroke out over the Rosie post. [}:D]
Edited: I forgot to mention, explain to him that as long as it's Thursday, the probability ratio is 6/6 to the tenth power that he MUST give you extra credit. He'll understand what that means, or at least pretend to. LMAO



option 2 cause it doesnt say you gotto point it at yourself.


"I come in peace. I didn’t bring artillery. But I’m pleading with you, with tears in my eyes: If you fuck with me, I’ll kill you all." General James N. Mattis

I hate math I would have said that the probabilities were equal.
frickin math...gotta hate it



Originally Posted By thebeekeeper1:
Hey, Torf
I have an idea. When this thread plays out, how about printing it and presenting it to him? You may get "extra credit!" LOL I'll bet he would stroke out over the Rosie post. [}:D] View Quote 

Please consider the paper industry before not printing this message.

The way to figure the first case is to determine the probability of your not dying on all of the trials. For independent trials, that's (5/6)^6 or 0.33489. The probability of your being killed is the complement of that, 1  0.33489, or 0.6651.
The probability of your being killed with five rounds in a sixshooter is 5/6 or 0.8333.
You're better off playing six times.
"Seven years of college down the drain"
Bluto Blutarsky, Faber College '63.



Originally Posted By Shadowblade:
Your professor is obviously wrong. In reality with a 1/6 chance of dieing  six times  you have a 6/36 chance of dieing which equals 1/6.
View Quote 


hmmm...how about choice "C" NONE of the above.



Here is your answer. Are you mad, know your invincible in death and life? Then you win. For when these games were played in my day and age it meant something. It had nothing to do with Statistics. We couldn't even count half the time. SHIT this was a way out from misery for some Gooks and Americans macho BS.
Anyone remember the game along with the Cox fight and the little suckle while the ref picked the bullet up said, @ men sit 1 man lives 1 man dies and neither reaches his GOD. They are both cowards. You remember that line. Who cared. You get pulled out dead stripped thrown to the dog. The winner big heroes until he bit the next round.
It was nothing like the Dear Hunter, or what ever BS Movie depicts our attitude has fighting men there. GOD FOR GIVE ME FOR THE EVIL I PERFORMED AND THE LIVES I LEFT WASTED. GOD FOR GIVE ME FOR DOING NONTHING THEN AND NOT SAVING ANYONE ALIVE ON 9/11/ WHY DID this stupid game have to be played with airplanes and towers. IT WAS A HIT AND MIS SITUATION...FORGIVES ME MY BROTHERS AND SISTERS I WILL FIND YOU ALL. WHERE EVER YOU LAY. Please find peace at this time. You are in my mind 24/7 along with the insanity we live with now GOD BLESS ALL OUR FALLEN & INJURED WORKERS



Originally Posted By Torf:
Actually I was thinking of showing this to my boss (who was also there), until The_Macallen showed up. Now? Forget it! View Quote 

I am not the means to any end others may wish to accomplish. I am not a tool for their use. I do not surrender my treasures to be flung to the winds as alms for the poor.
~ From "Anthem" 
Torf,
You are right, your professor is wrong. Your problem is a binomial distribution, and you are calculating the probability of getting 6 successful outcomes in a row. The formula is:
P(X)= n!/[X!(nX)!] * p^X * (1p)^(nX)
where
P(X) is the probability of X successes
n is the sample size (six in this case)
p is probability of success (5/6 in this case)
1p is the probability of failure (1/6)
X is the number of successes
The stuff with ! after are factorials  ex. 3!=3*2*1.
If you plug in all the numbers, your final equation is just (5/6)^6, which is what you calculated intuitively  I'm just backing you up with the equations.
In closing, your MARKETING professor is a dumbass. Tell him to stick with building systems to sell crap to stupid people.



After getting through my last psychotic episode about the past and now. The answer is depends how lucky you are that day. I think play either way it's a 1*6 chance.
I have seen and I mean seen people play that game. This is how it was played. 1 bullet, spin the chamber. Depending on whom was loading he would cock it then give it to you.
If I figure it out there were guys who could play for hours and survive. Some first shot out of the game. Some played for weeks. Sooner or later they lost.
Your Professor should be sat down given a gun. You ask him 5 or 1 bullets. If he wins you get a (D). If he loses you get a (A). See if he will take the odds he only has to play once.
Forgive me for my ranting last post. It is a 1*6 chances either way you play.



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