A logis puzzle, based on a true story

by stevenyc 26 Replies latest jw friends

• 

  OldSoul

  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.

  That is why in my simulation there is a routine that selects one the showman KNOWS is empty.

  ' 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

  I thought the same thing you did, that since he is randomly removing one he knows to be empty, the odds would be reduced to 50/50 because the empty one could never have been the correct choice. The numbers don't lie, and they consistently work out to roughly 100% greater chance (from 1/3 up to 2/3) of winning if you swap.

  Respectfully,
  OldSoul
• 

  Elsewhere

  So, did the guy with the car or not?

  If so, was there an explanation for him logically choosing the correct box or was it just a play on probabilities?
• 

  OldSoul

  Elsewhere,

  The question was whether he should swap, not what he should do to win. So, yes, the answer was a play on probabilities. And it wouldn't have been improbable enough to get the Heart of Gold halfway 'round a Cheerio, not a very economical improbability at all considering the need for some sort of Brownian motion fluid.
• 

  toreador

  I think this question was in a Parade Magazine a while back and was asked of Marylyn Vos Savant.

  I cant remember what she said though.

  Tor
• 

  toreador

  http://www.j-bradford-delong.net/movable_type/2003_archives/001271.html

  Here you go. Here is some discussion on it.
• 

  one_ugly_time

  Nice job OldSoul --

  Very nice little program !!! It takes alot to convince you... and it's good to see you convinced yourself !

  It is a very interesting puzzle and twists are "natural" logical thinking.

  Nice stats rick1199... a few years ago I think I could have actually written that out - but only if it were a homework assignment :)

  ugly
• 

  funkyderek

  Marvin Shilmer, who is annoyed by bad statistical math:

  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!

  And yet it does. It's certainly counter-intuitive but the actual, demonstrable reality is that changing your mind increases the odds of winning. But don't worry, you're certainly not the first person to have been so dogmatic and so completely wrong on this subject. When Marilyn vos Savant presented it as a problem in her column, she got the same sort of angry replies from people who thought they understood mathematics.

  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.

  Not at all. The reason is that the option that was removed definitely was a losing option.

  It's really quite easy. Whatever you pick at the start has a one in three chance of being correct and a two in three chance of being incorrect. If you stick with that option, you will win - on average - one third of the time. That must mean that if you change your mind, you will win two-thirds of the time.

  The mere fact that options had been reduced is what changed the odds of winning, and not what choice the individual made!

  You're right. The options being reduced does change the chance of winning from a simple one in three lottery to a weighted probability. There is still a two-thirds probability that your initial choice was wrong. The option removed is definitely a losing option, but the odds of the prize being in the group of two options you rejected is still two out of three. Monty gives you more information about that group (essentially which option in the group, if any, is a winner) which gives you a two in three chance of winning if you switch.

  This is actually quite a simple piece of mathematics, even though it fools almost everybody initially (it even got me!). It's fine not to know. It's fine to be pretty sure you're right until shown otherwise. But to state that the contrary position is "absurd" when you haven't even looked at the argument is stupid. Marvin, the post immediately above yours contains all you needed to see that you were wrong.

  one_ugly_time wrote:

  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...

  Now, you ignored that because you were so sure you were right that you didn't need to check. Sorry to make an example of you like this, Marvin, but it's something we all have a tendency to do to varying degrees, and it's something that needs to be highlighted. You always need to check.