A while back, I posted that the choice is 50-50 to either keep the original prize door, or swap with the unopened door, and *nobody* bothered to jump in.
The correct choice is to always switch. The real problem is that when people try to explain their solution, they make it overly complex (or they used it as an intro to push their particular brand of "enlighenment"). A simple "truth table" suffices.
You vs The Other Doors
0 -- 0 -- 1
0 -- 1 -- 0
1 -- 0 -- 0
The same setup after removing one of the other doors that doesn't have the prize:
You vs The Remaining Door
0 -- 1
0 -- 1
1 -- 0
So, what does this have to do with Deal or No Deal?
Here's the scenario - you're down to 2 suitcases - the one you picked in the beginning, and one left on-stage. One of them has $1,000,000.00, and one has $0.01.
Do you swap?
Your friends and family are giving you the following advice:
- The Monty Hall scenario applies - swap.
- The Monty Hall scenario doesn't apply - It's 50-50. Do whatever you want.
- The odds of you picking the $1,000,000.00 were 1/26. Swap.
- The odds of you avoiding picking the $1,000,000.00 up until now were 1/25 - so its 95% sure you're holdng the million - don't swap.
- The odds of you picking the $1,000,000.00 at any point were 1/26+1/25+1/24+
- The ods that you'll make the right decision are 50-50. Do whatever you want.
- The odds that you've made the right pick 25 times in a row are astronomical. Swap.
Do you swap, and why or why not?
Follow-up: Just prior, you've been offered a "deal" of $300,000.00 for your suitcase. This is well below the average expected payout of a half-million. Do you take the "deal?"