Hi, Valence,
While the probabilities associated with the first guess remain 1/3, the
probabilities do change once one of the doors is eliminated. In the 'second
round', there are only two doors available, and you have no new information
about either one of them, and so nothing to discern that one door may be a
better choice than the other. So the probabilities now stand at 1/2, and
either door makes as good a guess as the other.
This makes the MOQ's levels look easy.
Lawry
> -----Original Message-----
> From: owner-moq_discuss@venus.co.uk
> [mailto:owner-moq_discuss@venus.co.uk]On Behalf Of Valence
> Sent: Thursday, July 11, 2002 11:08 PM
> To: moq_discuss@moq.org
> Subject: Re: MD Let's Make a Deal
>
>
> Hey all,
> I'd like to thank everyone who took a crack at the Let's Make a Deal
> puzzle. I wish I could ceremoniously reveal the correct "solution" but I
> don't know what is. Your guesses are as good mine (and in many cases,
> better). Your various responses have kept me thinking and I'm still not
> quite sure where I come down on it. Although everyone's input has been
> helpful, I think the disagreement between Glenn and Lawry expresses the
> problem well.
>
> Let's kick it off with Glenn...
>
> GLENN (as slightly edited by rick to reflect a 3 door game, just for
> consistency's sake)
> In the 3 door version of the puzzle, your initial guess has a
> probability of 1/3 to have the good prize. All 3 doors have this
> probability, and the sum of their probabilities add to 1 (as they must).
> When Monty opens a door that shows a booby prize, the probability
> that that
> door has the good prize drops to 0 (obviously).
>
> RICK
> Obviously. But this is where your account and Lawry's seem to part
> ways. The question is now what happens to the probability that the
> remaining doors have the prize.
>
> LAWRY says
> With the new information you now know that the good door is one of the
> remaining two. While the odds HAVE changed, from 1-in-3 to 1-in-2,
> switching your choice will neither increase nor decrease the odds
> of picking
> the right one.
>
> but
>
> GLENN says (as slightly edited by rick to reflect a 3 door game, just for
> consistency's sake)
> ...the sum of the probabilities doesn't equal 1 anymore (it
> would equal
> 2/3), and that is a no-no. Since the probability of your original pick is
> fixed at 1/3, the other 2/3 of the probability has to be assigned to the
> remaining door. Since there is only one other unopened door, the
> probability of it containing the prize is 2/3.
>
> RICK
> The schism between Lawry and Glenn seems to revolve around the effect
> that acquisition of new information has on the way the odds are
> calculated.
> Or more precisely, whether the probability that your original pick is the
> good door remains fixed, or whether it shares in the surplus created by
> dropping the probability of the eliminated door to 0.... I'm not
> sure who to
> believe here... I wish I had paid more attention in Stats 101.
> Why should what happened in the first pick matter at all? Once Monty
> moves on to the second pick, he is, in effect, asking you to choose again,
> from scratch. But now with the benefit of the information that one of the
> doors was wrong. You still have no reason to suspect that one door is
> anymore likely to be the good door. What possible significance could the
> fact that one of the doors is now being called "your original choice"
> instead of "door #1" have? You still don't know where the prize is. How
> are the odds any different than if Monty had just started with
> two doors and
> asked you to choose between them?
> Yet, Glenn's 100 door example seems pretty inescapable....
>
> GLENN
> Suppose there are 100 doors instead of 3. 99 have booby prizes
> and you pick
> door 57 (because Heinz has 57 flavours :)). Monty then opens 98 of the
> doors, each with a booby prize. (He can do this because he knows what's
> behind every door.) Only door 66, and your original choice, door
> 57, remain
> closed. He then offers you the opportunity to switch. By your reasoning,
> door number 57 has switched from having a 1% chance to a 50% chance for
> being the good prize because all those other doors are no longer
> an option.
> That's not sensible. Obviously you would switch. There's a 99% chance the
> good prize is behind door 66.
>
> RICK
> I would be interested in hearing Lawry respond to this.
>
> And finally....
>
> ERIN
> Wierd you emerged from lurkdome. I just searched and emailed friends that
> smurf quote you once posted because it was related to what we were
> discussing.
>
> RICK
> If I've said it once, I've said it a million times... Never
> underestimate
> the intellectual appeal of blue gnomes wearing phallic hats.
>
> take care,
> rick
>
>
>
>
>
>
> MOQ.ORG - http://www.moq.org
> Mail Archive - http://alt.venus.co.uk/hypermail/moq_discuss/
> MD Queries - horse@darkstar.uk.net
>
> To unsubscribe from moq_discuss follow the instructions at:
> http://www.moq.org/md/subscribe.html
>
MOQ.ORG - http://www.moq.org
Mail Archive - http://alt.venus.co.uk/hypermail/moq_discuss/
MD Queries - horse@darkstar.uk.net
To unsubscribe from moq_discuss follow the instructions at:
http://www.moq.org/md/subscribe.html
This archive was generated by hypermail 2b30 : Sat Aug 17 2002 - 16:02:25 BST