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That only works if you randomly eliminate one card. The card that is turned over is not random at all. It’s always a goat. And it’s always *after* you picked a card randomly.

That’s why you would lose 66% of the time if you didn’t swap. Because you are apparently not able to grasp how this works. Again, if you are correct, it’s a no brainer that you bring $50,000 and I bring $55,000 and we play for $50 and $55 per hand. You can’t lose if it’s 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.

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...

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.

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..

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.

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

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...

Yea. It’s a loser that tells you exactly where the car is 66% of the time…..

Guys, there’s literally a Wikipedia page for this. It’s not a new question. This is ages old. The only reason it’s not a casino game is that it’s too much of a sucker’s bet for enough people to fall for.

Lol….no. That only works if he does *NOT* know what’s behind the doors. The “conditional” part of the conditional probability is that he *knows* what’s behind the doors.

Let’s say you have a Texas Holdem hand where you see the flop. You get all your money in and you’re 33% to win. Would you ever say it’s 50/50 because it’s a one time thing and you win or lose? Of course not. It’s 33%

That’s the wrong answer and why it’s a brain teaser. It’s conditional probability.

Let’s say there are 3 doors. You pick door 1. But you can’t see behind it. I *know* what is behind door 2 and 3. And I’m going to open one and show you. It will *always* be a goat. Because I can’t open the car. That’s the catch and what makes this different. So, 66% of the time, the car...

There is no “but”. Your odds are 66% if you switch. One time or 1,000 times. If you don’t switch, your odds are 33%. One time or 1,000 times.

You’ll see the only time you “lose” when swapping doors is when both of the doors you didn’t choose are goats.

You can even do an at home simulation with cards. Take two deuces and an ace. Mix them up face down. Then set one to the side. Flip the two others over and anytime there is a 2 and an Ace as those two cards, mark a win in the “switch” column. This would be the same as assuming you always...

You go broke. They have run simulations to death on this. It’s not even debated anymore. The only way you win is bet with enough odds to overcome the 66%. It’s no random or 50% once someone who knows what’s behind the doors gets rid of one after you’ve picked a door first.

The easiest explanation: You pick wrong 66% of the time. Which means Monty has the car in one of those doors 66% of the time. But, it says he knows where it is. Which means he never opens the car door and he has the car 66% of the time. So, you use this knowledge to your advantage and flip...