biminiblue

inconceivable.

Mirage74

You're right awul. In the mean time, you've managed to make my head explode . It has helped me, nothing like some good, mind bending debate.

brynn

Thanks awuh!

Turtle82

The man in cell A should stay where he is and I based it on the direction of the only completed tunnel as well as B being the central communicator between A and C cells. But, was quite confused by "random" when there was already a decision on the destiny of C.. didn't make sense to me... so assuming deduction wasn't possible, I had to induce thus the above.

Edit: Ugh... After posting, IC its already done... late to the party as ever.

jaynie04

I can see why no "12 step" discussion is allowed here….look what we did with 3 mythical prisoners…...

Turtle82

^

JeffreyAK

Since we aren't drinking anymore and can think straight, we can even write code to show that the results are 50/50, live or die, stay or switch.

program prisoner
call random_seed
open(unit=10,file='results.txt')
isaved = 0
idied = 0
do 100 i=1,100000 !100000 trials
c king chooses who will be pardoned. It is not the person in box 3,
c and both the warden and prisoner A know this, so there
c are two options with even probability, box 1 or box 2
call random_number(result)
if(result.gt.0.5)isave = 1 !box 1 is saved
if(result.le.0.5)isave = 2 !box 2 is saved
c prisoner A does not know which box is saved, and does not know the
c value of isave. Flip a coin, heads person A stays in box 1, tails he
c switches to box 2
call random_number(result)
if(result.gt.0.5)ipick = 1 !stays in box 1
if(result.le.0.5)ipick = 2 !moves to box 2
c now the outcome, if isave = ipick, I live, and I increment isaved by 1
c if isave not equal to ipick, I die and increment idied by 1
if(ipick.eq.isave)then
isaved = isaved + 1
else
idied = idied + 1
endif
100 continue
c print out the results
write(10,*)isaved,' out of 100000 times prisoner A lives ',
> isaved/1000.0,' % of the time'
write(10,*)idied,' out of 100000 times prisoner A dies ',
> idied/1000.0,' % of the time'
close(unit=10)
stop
end

50097 out of 100000 times prisoner A lives 50.0970 % of the time
49903 out of 100000 times prisoner A dies 49.9030 % of the time

50/50, with very tiny deviations due to random number statistics. If I pick a different random number seed, the numbers fluctuate a bit.

Carlotta

That's some good stuff but I was thinking that maybe some of us (myself included) have way too much time on our hands since we quit drinking

silentrun

I spent the last few years building up an immunity to iocane powder.



I think the thread is more interesting than the math problem itself.

The answer is 42 anyway.

PurpleKnight

Just think of all the world's problems we could crack with all this time and newfound energy on our hands!!

Watch out world!!

samseb5351

The interesting thing with this is if using the 100 boxes example and 98 boxes were randomly eliminated as we get closer to our box without it being picked our odds continuously improve exponentially, the key here is RANDOMLY removed, as we get to the last 2 boxes the chances are truly 50/50. However this does not happen in the 3 prisoners problem or the Monty Hall problem Why? Because Monty is an agent in the calculation that Knows where the prize is as is the guard in the 3 prisoners example. So each time a box is eliminated it is done so with the fore knowledge that the person selecting what is to be eliminated Knows and can choose to always leave two boxes (of which one is ours) at the end. We are being tricked into a false idea that random forces are at work, we can be amazed that in the 100 boxes example that it is us and one other that is left forgetting that there is non random intention behind the plan.
It is curious but humans tend to be conservative with making these kind of choices and naturally stick to Old ideas (imagined non risk) I have seen this over and over in my own pattern of compulsive gambling and even in my own Dogmatic approaches in recovery. It was a strong almost over the top obsession for me in gambling to imagine a Luck force involved in my gambling, almost always against rational thought, you know the Odds were always stacked against you, you know your decisions were crazy but ultimately the biggest dopamine high came from pushing the envelope and evoking the occasional hit, a weird fantasy land of Luck forces.
If I was compulsively gambling and came across the 100 boxes problem where someone knew whether or not I had the prize and selected non winning boxes to get down to me and one other, I still would be reluctant (non rational compulsion) to swap, the thought of talking the obvious and likely winning approach by swapping and the 100 to 1 chance of
Losing still has me considering an option that would be crazy to others. That just goes to show when we are in a non critical thinking platform just how easy we can make illogical decisions based upon pure emotion, superstition and habit.

dwtbd

If it weren't fun storming the castle , no one would

samseb5351

"odds continuously improve exponentially" just before people pick on this as a flaw. When I say our odds continuously improve I am only referencing the new sets of data points when boxes are eliminated (try imaging that you can bet on the results at every point as one box after the other is randomly removed)I am not saying the 50/50 chance was pre -ordained in the process from the beginning. If I was a bookie taking bets at when random selections have left you and one other, you ain't getting 99 to 1 out of me, you have every right to feel slightly more confident as each box is randomly taken away but what is the overwhelming likely that the real box with the prize will be revealed way before it gets down to two and you are one of those two.

Mirage74

Yea, I was assuming, samse, that the person removing the boxes knows where the winning box is and is purposely removing the incorrect boxes. Therefore it's not random. Even still, you're right, no bookie would pay out 99 to 1. That's how casinos make money.

If there's a chance the winning box was removed among the 98, the both remaining boxes still have only a 1/100 chance. So it's not 50/50, but both would have an equal chance, so it wouldn't matter if you switched.

samseb5351

Yes you are right however there also is the revealed component to the scenario, when it is non random and revealed as in the monty hall or revealed as in the person in cell 'C' not having the pardon, then the perception changes. I am talking about opening a box at each selection to see if contains the prize, if it was not opened under the random scenario it would be pointless because at the end the two remaining boxes are highly unlikely to contain the prize.

Mirage74

Wait, if u opened each box one at a time, and none of the (randomly selected) 98 boxes contained the prize (highly improbable), both remaining boxes would at that point have a 50/50 chance of containing the prize. Anyway, cheers!