Quote:netzerunJon:

I've been working on the Wizard's coin toss problem. I sense a screw-up there as the answer is not independent of p. Apparently he thinks well of you, as he expected you to show up there and put a timer on your response. I'll study your bet proposition and get back to you. In the meantime perhaps Crystalmath would like to jump in. He has been following the thread. Don't forget that your first solution agreed with mine: 1/3 and 1/3 for switch and no switch if Monty chose at random.

I agree with unJon. It depends on whether or not the host’s choice is random. If the choice is random, and he reveals a goat, the initial door has a 50% chance of winning. Bayes agrees too.

As for the coin problem, the answer is independent of p, except when p=0 or p=1; in those cases the answer is 2. For all other cases, the answer is

Quote:billryanJames wins the showcase and picks Door #1. He has one third chance to win. That days filming ends so they pick it up tomorrow. James is busy so his identical twin Jeff takes his place, but James forgets to tell him which box he picked. Monty opens Door B and asks Jeff if he wants to switch. As Jeff doesn't know which box James chose, it's 50-50 ,correct? Just as he is going to take Door 1, a power outage occurs forcing the taping to be canceled. When it resumes, neither Brother can attend. They pick you to attend and make the choice. When James chose, it was one in three. When Jeff chose it was one in two. Both picked Door 1. What is your best choice?

In the original game, before any power outage or absence, we had a 3 door probability issue. The two doors that were rejected are identified and identifiable. If there was a powere outage and the two unopened doors got shuffled, then the probability of selecting the good door would be 50/50 because knowledge has been removed. Anyone keeping an eye on the outage (shuffle tracking) would have the 66.7 / 33.33 probabilities.

Quote:unJon

You then pick and reveal the contents of one of the remaining two cups I didn’t pick. If you reveal the prize, we start again and no money changes hands.

That didn't take long. What you are describing is the second game the Wizard analyzes in his article. I have no problem with his answer but I don't think it is a game worth analyzing because it would not be good show business.

I urge you to get back to the thread about the unbalanced coin. It is turning into a real doozy and I think the Wizard has underestimated the complications.

Quote:netzerI have to go do some yard work now.

Is it common to do yard work at 9:30pm in South Africa?

Hilarious. I’d say this whole netzer detour was a waste of time, but it was fun to pull out Bayes theorem.Quote:CrystalMathIs it common to do yard work at 9:30pm in South Africa?

Quote:unJonHilarious. I’d say this whole netzer detour was a waste of time, but it was fun to pull out Bayes theorem.

It is better to adopt a respectful tone until you know who you are dealing with. Get back to the Wizard's biased coin problem and see what joy awaits you.

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