[dba-Tech] Three Doors Problem

Gustav,

Doesn't matter which door you pick initially. It remains correct in terms
of probability always to choose to switch. No matter what your initial
choice, you have a 1/3 chance of correctness. That leaves two doors. I open
one of them to reveal a bad choice. At that point, if you stick with your
original choice, your chances remain 1 in 3 (33%). However, if you switch,
your chances increase to 1 in 2 (50%). I know it's difficult to see why,
but if you prefer a little empirical evidence, try this:

Take 3 playing cards and 3 coins. I don't know Danish currency, so I'll say
2 pennies and 1 nickel, the latter being the "good" choice and the former
the "bad" choices. Place the coins beneath the cards and then try out the
alternatives.

Remember that I (or in this case you) know what's beneath each card, so
that no matter which card you choose initially, the host is always able to
turn a "bad" card.

Don't feel bad if it doesn't sink in immediately. When first published in
Scientific American magazine, this caused a furor unlike anything in the
magazine's history. Statisticians with strings of credentials as long as
your arm fought against its answer, but eventually had to admit the
correctness, no matter how counter-intuitive. Always switch.

Although not immediately relevant, I should add that for about three years
I made my living playing backgammon, and played in dozens of tournaments
including several world championships. I also played against some of the
finest in the world at that time. I read every book published about the
game and learned almost everything I know about probability from studying
those books and the game itself. For centuries, it was almost entirely a
game of luck. No one knows for sure, but sometime around 1920 the doubling
cube was introduced into the game. That changed everything. The game became
a study of probabilities, not a game of pure chance.

A.

On Tue, Sep 11, 2012 at 8:31 AM, Gustav Brock <gustav at cactus.dk> wrote:

> Hi Arthur
>
> That's a strange experience. I had to think about this, but when I
> realised that initially you most likely had picked a bad door, then Stuart
> is of course right - when a bad door is revealed, the door you didn't
> select is most likely the good door.
>
> /gustav
>
>
>