It's amazing how many people refuse to believe that switching improves your odds.
I remember a day at work about 3-4 years ago where a co-worker (a very solid network engineer, not a dude flipping burgers) and I got into a heated discussion about it. He just wouldn't believe it so I made it easy on him and I'll do it for the retards here.
Play out each scenario with the prize being in bag #2. Keep in mind that when Tunare in this case reveals a second bag, it CANNOT be the winning bag. So if you've picked bag 1, bag 3 will be revealed 100% of the time. If you pick bag 3 it will be bag one revealed 100% of the time. If you pick bag 2, it could be either.
You pick bag one and keep it = lose.
You pick bag two and keep it = win.
You pick bag three and keep it = lose.
You pick bag one and switch to bag two = win.
You pick bag one and switch to bag three = cannot be done, revealed as a loser.
You pick bag two and switch to bag one = lose.
You pick bag two and switch to bag three = lose.
You pick bag three and switch to bag one = cannot be done, revealed as a loser.
You pick bag three and switch to bag two = win.
So you can very simply look at this and say, if I stay I have a 1 in 3 chance (33%), if I switch I have a 2 in 4 chance (50%).
Switch every time. Like was stated above, you improve your odds 17%.
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