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Ok, so I have to ask for a clarification here. There is one prize and 2 goats behind 3 doors, correct? 33% chance by just picking a door that you'll win your washer/dryer combo and a year's supply of tide. Monte opens a door and there is a goat behind it. Whether Monte picked his door intentionally or not, there are 2 doors left and one of them has a goat and one has a prize.

What makes your choice of door not 50-50 to win? Why would switching doors change those odds? how would this change if you would rather win the goat because your mom washes your clothes anyway?

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Mutlipart answer:
1. This is not pocketfives, so assume you do your own laundry and would rather have the washer/dryer combo than the goat.
2. If you want more explanations than a goat could eat in an hour, google "monty hall problem". It was originally unleashed on the world by Marilyn Vos Savant in her "Ask Marilyn" column and the academic world's reaction to it was LOL.
3. I will give you my personal take on the answer which I did not find in any other explanation.

Think of the problem in terms of "equity" rather than "probability". Like if you have a small flush draw and are drawing against someone you read for Jacks over Tens (in stud). Your "probability" of winning the hand is 20% if your read is correct, but say he also has a third pair or a 4 flush to go with it? So your "equity" in the pot has to take into account the odds that your read is right, and the odds you make your hand and it holds up.

So in the Monty Hall problem, with all three doors closed you have a 33% probability that the prize is behind the door you chose, and also a 33% "equity" in the prize. If we conduct 100 trials, then when Monty opens one door, your average "equity" will go up to 67% (since if he opened two doors it would be 100%).

If he opened the goat door KNOWING it was a goat, then every trial will be the same... you see a goat. Your original "equity" was 33%, thus the "equity" in the other two doors was 67%. Only one of these other doors is still closed, so it's 67% certain the prize is behind it.

If Monty opens a door at RANDOM, you will be shown a goat 2/3 of the time, but the prize 1/3 of the time! If you're shown the prize, you have 100% "equity" if you're allowed to switch to that door. So your "equity" when you're shown a goat must be 50% to balance the equation:
(Shown prize)*100% + (Shown goat)*X = Avg "equity"

Where X is your "equity" for the "Shown goat" case.

(1/3)*100% + (2/3)* X = 67%
X = 50%

So the if the opened door has a goat behind it in this case, the "equity" of each remaining door must be 50%.