# Thread: Should you switch doors?

1. Sam,

I was very wrong. Switching doors does give you a 66% chance of winning.

It is explained very clearly here: http://www.youtube.com/watch?v=mhlc7peGlGg

BTW - Mythbusters does a poor job of explaining it, probably because thy are more interesting in making a TV show than understanding what they are testing.

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thanks brian, that explaination makes a lot more sense. it is based on the probability of your first choice , not so much the swap.

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I'm still not seeing their logic in this. Yes you have a 33% chance when you pick the first time around. But when they open a door, then instead of staying with your pick at 33%, what your actually doing is just re-picking your original door at a 50% chance. So either way your falling with 50/50 odds.

4. Originally Posted by ArthurHagar
I'm still not seeing their logic in this. Yes you have a 33% chance when you pick the first time around. But when they open a door, then instead of staying with your pick at 33%, what your actually doing is just re-picking your original door at a 50% chance. So either way your falling with 50/50 odds.
That is what I thought too. I thought two doors means 50/50. But not so.

I’ll try putting it a different way. You have a 33% chance of picking the car. So let’s say you pick the car 33% of the time. They will always open and eliminate the other door with a goat behind it. Therefore, if you stick with your original pick and not switch doors you will win a car 33% of the time.

Done the other way: You have a 66% chance of picking the door with a goat behind it. Again they will open and eliminate the other door with a goat behind it. This will leave you with your pick of a goat and the other door with a car behind it 66% of the time. In that case would you rather stick with your goat or switch doors?

5. incorrect logic applied. Here's why:
Once the first door is revealed, the percentages change. The original odds were 33% car/ 66% goat. However, once the first goat is revealed, you have reduced your choices from 3 to to. This brings it down to a 50/50 chance.

Now, you won't know whether your first pick was a car or goat until the end of the show. So, if you choose door 1, he reveals a goat behind door 2, that means there are only 2 doors left and one has the the car and one has the goat. Its the best you can get. This scenario is not accepting the fact the odds change once the first door is revealed.

6. Originally Posted by hearthman
incorrect logic applied. Here's why:
Once the first door is revealed, the percentages change. The original odds were 33% car/ 66% goat. However, once the first goat is revealed, you have reduced your choices from 3 to to. This brings it down to a 50/50 chance.

Now, you won't know whether your first pick was a car or goat until the end of the show. So, if you choose door 1, he reveals a goat behind door 2, that means there are only 2 doors left and one has the the car and one has the goat. Its the best you can get. This scenario is not accepting the fact the odds change once the first door is revealed.
+1

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here's the way i think the logic works. when you make your first choice, there are two goats and one car, you have no idea which is which so you are picking a door at random. one door is as car, one door is a goat, one door is also a goat. so, choosing at random, you have a 66%chance of being wrong. The odd are 2 in 3 that you are choosing WRONG. after your choice, one door is revealed as a goat. your original choice is a 66% chance, still, that probably wrong. Since if you change, the only possible choice is the correct choice (since the other door was revealed as a goat, and you can't choose that door) you can turn your most likely wrong choice into the right choice 66% of the time.

8. Hearthman,
You will have to do a couple things before you get it:
Be open minded that you could be wrong.
Listen to as many explanations as possible because eventually one will resonate with you.
Watch the Mythbusters perform their test on Youtube. If it was a 50/50 chance they would not get the results they did.
Know that it is not about the remaining two doors. It is what is eliminated from the equation (opening a goat door every time) and the probability that a goat door is selected 66% of the time.
It’s not 50/50 at the end. It is a 66% chance that you selected a goat and that a switch will give you a car 66% of the time.

When you get it, it’s like a light bulb going off.

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