But the odds have changed.  Remember the phrase: "discard 50 of them,
face up so we can both see them",  we've changed to sample size from 52
to 2. Since both parties know the value of the other 50... they are no
longer relevant.  Do you believe the game would have continued if the
Ace of spaces was in one of those fifty cards? No! The rules changed
once the 50 cards were examined.

Perhaps we should change the items we are talking about to something
more at home like... 52 application procedures.  One with a bug.  We
both inspect the code on 50 and agree that they are bug free.  What are
the odds that yours or mine is the problem.  100%  (trick... remember
the OR). And 100% yours because I know I write guud coad.  :-)

Tim Ericson wrote:
>
> Craig Fairchild wrote:
>
> >Let's play a game.
>
> Okay!
>
> >Let's call it "Find the Ace of Spades".
>
> Sounds fun!
>
> >We'll use a 52 card deck.
>
> Fine...
>
> > After the deck is randomly shuffled, you get to pick a card
> > face down, and put it in front of you, remaining face down.
>
> Okay, it's in front of me - so I have a 1 in 52 chance of
> having the Ace of Spades, you have a 51 in 52 chance.
>
> > I'll take the remaining 51 cards examine them, discard 50
> > of them, face up so we can both see them, and then place the
> > remaining card face down.
>
> So at this point _you_ *know* who has the Ace of Spades, just
> as Mr. Hall knows which door the prize is behind.
>
> > Now we're left with two cards, yours and mine. Since we've
> > seen the other 50 cards, we know that one of our two is the
> > Ace of Spades. So we both have a 50-50 chance of having the
> > Ace of Spades - right? :-)
>
> Wrong.  The odds have not changed!
>
> With my original card I had a 1 in 52 chance and you had a 51
> in 52 chance - those odds don't change just because you've
> turned over 50 of the cards you have!
>
> *Because* you know who has the Ace of Spades - that's the 'All
> other things being *equal*' part - things *aren't* equal!  If
> I'm allowed to choose between odds of 1 in 52 versus 51 in 52,
> I'll switch!
>
> > Being a gentleman, I'll give you quadruple your money on any
> > wager you'd care to make that you have the Ace of Spades and
> > not I. We can play all night if you'd like! :-)
>
> Being a gentleman as well, I'll *take* that quadruple money 51
> out of 52 tries (because I'll swap cards with you *every* time!)
>
> Now if you wanted to add a third person to this little game, and
> that person were to pick a card for each of us take to put face
> down, with the guarantee that *one* of those cards was the Ace
> Spades, *then* the odds would be 50-50 (because _you_ *don't*
> know) - In which case, I'm not playing.   :-)
>
>  +-------------------------------------------------------------------+
>   My mind is my own, as are my ideas and opinions.
>   My heart, body, and soul, however, all belong to others.       Tim.
>  +-------------------------------------------------------------------+
>   Tim Ericson            tericson      DenKor Dental Management Corp.
>   Sr. Systems Analyst     at denkor    503-526-4440 (my direct number)
>     (& Systems Manager)     dot com         http://www.denkor.com
>   Programming HP3000s since 1983!      Quality dental care since 1970!
>  +-------------------------------------------------------------------+
>   UDCs and Command Files:  http://www.denkor.com/hp3000/command_files
>  +-------------------------------------------------------------------+