A logis puzzle, based on a true story

by stevenyc 26 Replies latest jw friends

  • stevenyc
    stevenyc

    Oldsoul

    Think of it this way,

    suppose the host didnt throw away the empty box but said, ' do you what to keep the one you have or exchange it for these two'

    steve

  • Es
    Es

    always stick with your first choice es

  • one_ugly_time
    one_ugly_time

    Break it down... it is easy with this few of choices... In order to show it, we have to assume that Monty Hall knows the answer or he wouldn't be able to discard a box... that is why the odds increase greater than 50% to change... Here we go... Monty knows Box C wins...

    Pick A - Discard B - Swap to C, WIN
    Pick B - Discard A - Swap to C, WIN
    Pick C - Discard A or B - Swap, Lose...

    2 out of 3 times, you WIN if you swap...

    The odds increase to 2/3 BECAUSE of the knowledge required to remove a 'losing' box. If Monty didn't know the answer and randomly removed a box... well, let's see.

    Pick A - Discard B - Swap to C, Win
    Pick A - Discard C - Swap to B, Lose
    Pick B - Discard A - Swap to C, Win
    Pick B - Discard C - Swap to A, Lose
    Pick C - Discard A - Swap to B, Lose
    Pick C - Discard B - Swap to A, Lose

    The odds become 1/3 to WIN - this is the way street hustlers play the game... inverting the odds of a well known game that if played like Monty gives the contestant the advantage.

    ugly

  • Marvin Shilmer
    Marvin Shilmer

    I can?t watch this thread any more without commenting. It is absurd for anyone to think that changing one?s selection from C to B increases the odds of winning!

    When three options were available the person had a 33 percent chance of winning. Period.

    When the options were reduced to two, and the person?s choice was among the two, the chance of winning just became 50 percent regardless of whether B was selected over C. Period. The mere fact that options had been reduced is what changed the odds of winning, and not what choice the individual made!

    Marvin Shilmer, who is annoyed by bad statistical math

  • OldSoul
    OldSoul

    I think I have figured out why it works that way. The folks who said the odds are better are right. I fully expected to find roughly fifty/fifty chance. Here is some VB code I wrote to prove it:

    Function intRnd(intLB As Integer, intUB As Integer) As Integer
    intRnd = Int((intUB * Rnd) + intLB)
    End Function

    Sub trythis()
    Dim winner As Integer
    Dim remove As Integer
    Dim guess As Integer
    Dim score(2) As Integer
    Dim intLoop As Integer
    Dim intCounter As Integer
    Do
    winner = intRnd(1, 3)
    guess = intRnd(1, 3)
    ' Loop insures that remove is never equal to winner or guess, but is still random among available
    Do
    remove = intRnd(1, 3)
    Loop While remove = winner Or remove = guess
    If guess = winner Then
    score(1) = score(1) + 1
    Else
    score(2) = score(2) + 1
    End If
    If remove = winner Or remove = guess Then score(0) = score(0) + 1
    intCounter = intCounter + 1
    Loop While intCounter < 10000
    MsgBox Str(score(1)) & vbCrLf & Str(score(2)) & vbCrLf & Str(score(0))
    End Sub

    Running through 10000 iterations the process consistently returns score(1) as just about 1/2 of score(2). score(0) is a control that always returns 0 and proves that the "remove" was not equal to "winner" or "guess". score(1) represents staying with first choice, score(2) represents changing your mind.

    Here are some results:

    score(1): 3344
    score(2): 6656

    score(1): 3303
    score(2): 6697

    score(1): 3330
    score(2): 6670

    You can test the code yourself. The odds of winning are consistently nearly double if you change your choice.

  • rick1199
    rick1199


















    You are asked to pick a door

    you pick the prize door

    you pick wrong door a

    you pick wrong door b

    Wrong door b is removed

    Wrong door b is removed

    Wrong door a is removed

    you swap

    you stick

    you swap

    you stick

    you swap

    you stick

    you lose

    you win

    you win

    you lose

    you win

    you lose



    out of the 3 options from swapping 2 of them will win, so the probability is 2/3 chance of winning. Out of the 3 options for sticking 1 will win so the probability is 1/3. So you are twice as likely to win if you swap.

  • bebu
    bebu

    Actually, those other two boxes had goats, garbage cans, granny's swimsuits, etc.--remember?

    So your odds of winning something odd were very great.

    bebu

  • rick1199
    rick1199

    Let the doors be called q, r and s.


    Let Cq be the event that the car is behind door q and so on.


    Let Hq be the event that the host opens door q and so on.


    supposing that you choose door q, the possibility that you wil the car if you then switch you choice is given by the following formula:


    P(Hr^Cs)+P(Hs^Cr)

    =P(Cs).P(Hr|Cs)+P(Cr).P(Hs|Cr)

    =(1/3 . 1)+(1/3 . 1)

    =2/3


    Taken from the curious incedent of the dog in the night time by mark haddon.

  • Simon
    Simon

    If you do a simulation with random numbers then it shows you are better off swapping. I think its to do with the fact that the showman can not open just any box ... he has to open one that he knows is empty.

  • tijkmo
    tijkmo

    aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

    aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

    aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

    aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

    aaaaaaaaaaaaaaaaaaaaaaaa

    aaaargh

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