Probability Puzzler....

[JohnnyAardvark]

Of course, casinos have the advantage of the "long haul", over which random fluctuations (i.e., "luck") even out mathematically. In this puzzle you get just one shot, so you can still lose even when you adopt the winning strategy. Nevertheless, I'd take any advantage I could get!

I agree about taking every advantage you can get!

If you were to play out this scenario a number of times it should prove this case to be true. i.e. the advantage in changing.

But does it fail in in the short term? Is the second phase REALLY part of the origonal game, where your odds were initially 1 in 3. Or is this now a totally new game where there are two possibilites and you have to chose one of the two? Since you are given the choice, to change, then if you do, you are taking a chance with "the new game?" Where as if you stick are you still playing the old game with the lesser odds?

Food for thought Hope I've explained that as well as I had hoped

I'll check back tomorrow

Regards

Steve

[bobkart]

It's still the same game, just now you know the opened box does not have the keys in it. The odds are still 1:3 that the box you picked is the one with the keys in it. But now it's 2:3 that the unopened box you didn't pick has the keys.

Only if after opening the third box did the game show host randomly redistribute the keys between the two remaining boxes would it be the "new game" you're thinking of. THEN it would be even odds.

[Fingers]

Well put sir.

And, as someone pointed out, if there were 1000000 boxes then you would be 999999/1000000 more likely to win if you switched.

Personally - I'd ask the host to consider the tree falling in an empty forest - and whilst he's pondering I'd leg it with both boxes.

[JohnnyAardvark]

Well put sir.

And, as someone pointed out, if there were 1000000 boxes then you would be 999999/1000000 more likely to win if you switched.

Personally - I'd ask the host to consider the tree falling in an empty forest - and whilst he's pondering I'd leg it with both boxes.

Yes, Nice explaination BobKart.....

I thought the starting with 1000000 boxes helped clear it up for me. In that scenario you would really have to change your mind. You would feel very hard done to if you lost that one!

Since the improvement/change in odds is relatively small (I would say relatively negligable in comparison to starting with 100000:1) I would almost be inclined to stick with original choice. Only because I have a sence of how my luck works! Anyhow thats all from me on this as I fear the odds are against me

Regards

Steve

[Downtown_Charlie]

does anyone hear rember Michael Miles and Take Your Pick?

no,

BONGGG!

sorry i'm late but but i just wanted someome to say yes or no )for those who are old enough to remember the yes/no interlude(

Michael Miles - black and white TV - Take your Pick - peak time viewing. Goodness I feel old !!!! Who can forget the Yes No Interlude and Hughie Green on Double Your Money. Now I feel REALLY old !!

Don't tell me you remember it too D.C. ?? You're not going to reminisce about the Flower Pot men and Muffin the Mule as well are you

http://www.whirligig-tv.co.uk/tv/adults/quiz/quiz.htm for a trip down memory lane.

Best wishes
Phillip

i don't actually remember Muffin the Mule.

and i defy anyone to prove otherwise.

slán

D C

[ronbo27]

.....and are you unamimous in saying that?....Lol
Cheerio!
Ron

[JohnnyAardvark]

does anyone hear rember Michael Miles and Take Your Pick?

no,

BONGGG!

sorry i'm late but but i just wanted someome to say yes or no )for those who are old enough to remember the yes/no interlude(

Dohhh!

[bobkart]

Slight non-sequitur, but: Einstein Puzzle - in case anyone hasn't seen that one yet.

[Marc]

Some psychologists would say your first choice is often your best choice as our minds are capable of resolving things extremely quickly and that changing one's mind is an emotional response. From the game show host perspective they are a) trying to create suspense for the audience but b) one could suspect they are incented to get you to switch to the losing box using subtle hints.

Marc

[bobkart]

I'm sure there's some truth to that, in situations where the choice was made using some basis for making the decision. But since in this situation they are assuming you have no basis for making the original decision (each box is equally likely to have the keys), it's hard to imagine how the first choice could have better than 1:3 odds.

[ronbo27]

Had to try the Einstein Puzzle...like these sorts of things. Sent you an e-mail. How`d I do?
Ron.

[bobkart]

Had to try the Einstein Puzzle...like these sorts of things. Sent you an e-mail. How`d I do?
Ron.

Yep, you got it.

I see typical solution times of "about an hour" for that one, by the way. It usually takes up a sheet of paper too.