Yea. It’s a loser that tells you exactly where the car is 66% of the time…..
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Yea. It’s a loser that tells you exactly where the car is 66% of the time…..
It doesn't matter that he knows. When he reveals #3 to be a goat, we both know that #1 and #2 conceal a goat and a car. His knowledge is immaterial since we get to choose.
For those having a hard time grasping why you should switch doors, imagine that instead of 3 doors there are 1,000 doors, with 999 goats and one car. The host knows where the car is, and asks you to pick a door. After you pick a door he opens up all but one of the remaining doors, revealing 998 goats. There are two doors left, the one you initially chose, and the one he didn't open.
Should you stay with your original choice or switch to the door he didn't open?
Should you stay with your original choice or switch to the door he didn't open?
Ok, since it’s 50/50…..
Let’s run it 1,000 times.
My $55 to your $50 per hand
I’ll fly to you and we’ll take three cards.
2, 2, A.
We mix them up face down. You pull one to the side. I get to look at the other two cards and turn one over.
You have to keep your chosen card. You win when you have the A. I win when you don’t.
The odds are derived from your likelihood of making the winning choice with your first pick.
The key is that Monty knows where the car is. He knew what door to open to show a goat. Therefore the original odds do not change. If he had not known which door to open, if there had been a chance of him inadvertently showing the car by opening one of the other doors, then the odds would become 50/50.
The only way you win without changing your choice is to have picked the winning door correctly the first time.
Maybe this guy can explain it better…
It's not a game with repeated hands and infinite money. When Monty introduces the final condition, it becomes a game of wits at 50/50.
If we ran it 1,000 times at $50/$55 odds….
You’d be saving almost $1k to cut me a check for $14,000
You’d be saving almost $1k to cut me a check for $14,000
This logic is why there are people who won’t fly but will drive a car.
Odds are odds. One time or a million.
Let’s say if you jump off a cliff. You’ll die 9 times out of 10. But you only jump once.
Do you think your odds are 50% or 90% that you’ll die.
Really? It seems to me that if both the doors you didn't choose are goats you win every time. You lose when you pick a goat door.
And if, after you take your card, I show you one of the two cards, one that I know is not an ace, it doesn’t change the chances of you having picked the ace at all…
Using the always swap strategy, you can only lose when he turns over a goat if the other card he didn’t turn over is also a goat..
Correct. And you have a 2 in 3 chance of having picked a goat door initially. Which is why you should change.
And we already know that 66% of the time the car will be one of the two cards you didn’t pick.
So, when you swap (since you already got rid of a goat) you now take his 66% chance and give him 33%
You literally reverse the odds.
Everything before the elimination of door 3 is patter. What you really have is two doors, a goat and a car, and a choice of one or the other everything else is a distraction. 50/50
Think about it this way……
When you pick 1 of 3, it’s 33%. I think everyone is in full agreement.
So, he gets rid of a goat. And then let’s you literally take his 66% chance.
That 66% chance of the other two cards being the car doesn’t magically disappear. It’s 66%.
Now you literally get to swap hands.
When you pick 1 of 3, it’s 33%. I think everyone is in full agreement.
So, he gets rid of a goat. And then let’s you literally take his 66% chance.
That 66% chance of the other two cards being the car doesn’t magically disappear. It’s 66%.
Now you literally get to swap hands.
Wrong. Ignore the 66% nonsense one of the doors and one goat are non-players. Start at the point that a door and a goat are eliminated. Your actual choice is between the two remaining doors, one goat and one car, regardless of your initial choice you still get to choose one of the two doors. 50/50
How about this.
You pick one card and you don’t get to turn it over.
He has two cards and also doesn’t turn them over.
Would you trade your 1 card for the other 2 cards?
Of course you would.
That’s exactly what’s happening here. You are swapping hands. Your one card, for his two.
You pick one card and you don’t get to turn it over.
He has two cards and also doesn’t turn them over.
Would you trade your 1 card for the other 2 cards?
Of course you would.
That’s exactly what’s happening here. You are swapping hands. Your one card, for his two.