I would stick with my original pick because either choice still leaves me with 50/50 odds. It seems logical enough, but i'm not that good with numbers. Maybe i should higher a financial analyst and pay them to help me decide. I should have majored in finance.

What would you do if you went out to your car and one of you tires had the lugnuts removed? Calling AAA is not an option.

Haha, as a grad student about 15-20 years ago we argued about this one for a whole afternoon until one of us wrote a quick C program to prove that door #2 has a 2/3 probability of winning. It's counter-intuitive, but nevertheless…

As long as I had four or five lug wheels I would take one lug nut off of each of the other three wheels and put them on the wheel missing the lugs.

Ah – the Monty Hall paradox. It's older than the hills, but still fun. The odds of winning are better when you switch your door, so you should always switch. This can be easily proved by writing down the probability tree for the problem. Intuitively, Monty gives you additional information when he opens the door. This is information you didn't have when you first made your choice, which is why it makes a difference.

I would stick with my original guess because it seems like many times your gut instinct is correct and by second guessing yourself you will make the wrong choice many times. I would also feel worse if I did change my guess and then found out that I was correct before I second guessed. The big question is that if you had won the car would you risk it to go for the big deal at the end of the show?

I don't know, really. I never saw the show, believe it or not, so I don't know what kind of odds to expect.

This is a case where gut instinct is wrong. Behaviorists say we have an 'agent' which does basic probability inside us, but it is limited and doesn't handle this sort of situation well. It is mathematically provable that your chances are twice as good if you switch.