## Thursday, March 16, 2006

### Why is Deal or No Deal right?

One of the first posts I did here was on the Monty Hall problem. In short: you are presented with three doors (1,2,3) and are told there is a prize behind one of them. You select door one (at random). The host reveals that behind door number 2 (2 being one of the doors you didn't select) there is no prize. At this point, your best strategy is to switch to the third door since there is a 2 in 3 chance of the prize being behind door number three.

So, my question today is, why doesn't Deal or No Deal fall into this trap? When there are only two suitcases left to be opened, plus the one the contestant chose: why can the execs at NBC say there is a 1 in 3 chance of the highest prize being in the suitcase the contestant chose at the beginning?

Or am I wrong and they are lying to the viewers?

In case you aren't familiar with the game, you can play it online at addicting games.

1. Because none of the 3 cases have been opened yet out of the ones left. That is why there is still a 33% chance.

2. No, I'm afraid that's not the answer.

Let me rephrase the question: Why is the chance of the highest prize being in your case 1/3, not 1/26 (as it was when you made your original selection).

In Monty Hall, even though they've revealed what's behind one of the doors, you're chances of selecting the prize is still 1/3. In Deal or No Deal, the chances of you having the 'big prize' is 1/3 (when you are down to 3 suitcases) even though you have opened up 23 cases at this point.

3. I think I'll leave this one up for a few days and see if anyone can come up with the same reasoning I had.

I also ran a simulation to test it out.

4. Becaue the other cases have alredy been eliminated. and the last 3 are still unopend. You still have 3 amounts left that could be possible. You only get to keep 1 of the 3 amounts possible. 33%

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