Here’s the mental exercise to demonstrate that:

I’m going to illustrate the situation where there’s a car (that you want) behind one door and nothing behind the other doors (to avoid the wise guy answer–http://xkcd.com/1282/)

1. Hall offers you a choice of opening one door or opening two doors. You have a 2/3 chance of getting the car if you open two doors, so you pick that.

2. Different scenario: You pick one door, then Hall offers you the choice of sticking to your door, or opening the other two doors. You have a 2/3 chance of winning if you switch.

3. Same scenario as 2, but Hall adds: “I can look behind the doors, and I can see that only one of the two doors that you didn’t pick has a car”. You already knew that (there’s only one car), so that doesn’t change your decision. You should still switch.

4. Same scenario as 3, but Hall then opens the door to the empty room (remember, he knows what door has what). Still doesn’t change your knowledge, or the probabilities. You still should switch.

Scenario 4 is the Monty Hall paradox. The paradox arises from the apparent inconsistency between your choice initially and Hall’s perfect knowledge and reaction to your choice (if you initially picked the goat, then he wouldn’t show you that door).

Any parallel to this paradox and Rabbi Akiva’s paradox of הכול צפוי, והרשות נתונה is left to you as the Rabbinic Authority.

Danny Wachsstock

]]>Just read your essay on “the dance” in Jewish World Review. Fabulous and thank you.

“Where did he learn to do the “Dance of David?” was the question asked by our Israeli tour guide, Yizza Goren. It was March 16, 1973. We sat in the Egged tour bus overlooking Jericho as Yizza told us the explanation about why the walls fell down. When he finished his story, the song leader of our Charismatic Christian group began to play his guitar and sing a song and we joined in. It was a joyful, upbeat song of faith in the Word of the G-d of Abraham, Isaac, and Jacob.

As we were singing, Gordon Kess, our 70 yr old facility manager in the church stood in the aisle of the bus and began to dance, much like we do in our worship and praise services. That’s when Yizza asked his question. It was a confirmation to us that we were doing the right thing – dancing before the Almighty to show our trust and hope in is “lovingkindness which endures forever”.

Your essay reminded us of the beauty of the gift of the dance. Thank you. May HaShem “increase you more and more, you and your children” Psalm 115

E.Leonard