RE: Shooting room paradox

Richard Brodie (
Thu, 5 Dec 1996 22:05:46 -0800

Hal Finney wrote:

>Since 90% of the people who go into the room see double sixes, it
>that if you are a person in the room, the chances that you will see
>sixes is 90%, far greater than the 1/36 chance we calculated before.

I love this kind of puzzle because it shows what clear thinking is up
against. It's possible to bamboozle even the most brilliant people, at
least temporarily, by framing these probability puzzles so that our
evolved instincts give us the wrong gut feeling about the answer. This
is similar to the dreaded "Monty Hall" puzzle that created such a fuss
in Marilyn Vos Savant's column some years ago.

Before any roll of the dice, the probability that the next roll will
yield boxcars is 1/36. Very simple. If you go into a casino and played
roulette and bet 10 times as much every time you lost, that would not
change the odds of red or black coming up on the next turn.
>This represents a sort of reverse causality where events in the future
>can in effect influence the probability of events in the past. It
>to the issue of whether our existence here and now is influenced by the
>size of the human race in the far future.

Wonderful! Do you see the error in your reasoning? Half the people who
ever lived are still alive. What are the chances that George Washington
is still alive? And how infinitesimal the probability that, out of all
the eons of the existence of the universe, you and I lived now! But it's
not unlikely, don't you see? The probability of anything having happened
after it has already happened is 100%. There are an infinity of equally
likely scenarios that didn't happen.
>My personal opinion is that a random person in the room actually would
>see the dice roll as sixes, and that if I found myself in the room I
>would bet on the double sixes if someone offered me this option. What
>do you think?

I'll take that bet!

Richard Brodie +1.206.688.8600
CEO, Brodie Technology Group, Inc., Bellevue, WA USA
Do you know what a "meme" is?